EVAPORATION Droplets of Pure and Complex Fluids

International st 1 Workshop

WETTING & EVAPORATION

Droplets of Pure and Complex Fluids

BOOK of ABSTRACTS

Chaired by

David BRUTIN

David FAIRHURST

June 17-‐20, Marseilles, France

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1st International Workshop on WETTING AND EVAPORATION: DROPLETS OF PURE AND COMPLEX FLUIDS organized from June 17th-20th, 2013 in Marseilles, France

The Editorial The first International Workshop on Wetting and Evaporation of Droplets of Pure and Complex fluids was held from June 17th to June 20th, 2013 in Marseilles, France (DROPLETS 2013). It was organized in the Mechanical Engineering Department (Polytech’Marseille – ME) of the Aix-Marseille University (AMU) in close cooperation with the Nottingham Trent University (NTU). From Young’s early work on contact angles, through to Deegan’s more recent study of the coffee ring formation, there is still much interest in the behaviour of droplets. Motivation comes from both fundamental scientific intrigue to varied industrial applications. The objective of this workshop was to explore beyond the coffee ring effect, by bringing together researchers with a common interest in droplets but with different backgrounds and expertise: modelling to experimental; wetting and evaporation; simple and complex liquids, including biological fluids, nanofluids, polymers and colloidal suspensions... The workshop consisted of six keynote lectures: Vladimir Ajaev (Southern Methodist University, USA), Mathematical modelling of evaporating sessile droplets on heated surfaces Terence Blake (University of Mons, Belgium), Understanding dynamic wetting - the contribution of the molecular-kinetic theory Daniel Bonn (University of Amsterdam, The Netherlands and ENSCP Chimie Paritech, France), Droplets of complex fluids Masao Doi (Toyota Physical and Chemical Research Institute, Japan), Effects of skins formed in the drying of polymer solutions David Quéré (Department of Physics, ESPCI & Ecole Polytechnique, Paris, France), Leidenfrost phenomena: at the frontier between evaporation and wetting Martin Shanahan (Universite de Bordeaux, France), Wetting & evaporation of sessile drops: some fundamental parameters In addition to these keynote lectures were 22 plenary and 29 parallel oral presentations. 83 posters were also presented. The workshop concluded by an open discussion forum / brainstorming. The program was shaped to encourage questions, interactions, group discussions and exchanges. The main topics covered by the workshop were: Static and dynamic wetting, spreading Pure fluids, nanofluids, colloids, biological fluids Polymers, surfactants, super-spreaders Evaporation, condensation Sessile, pendant, levitated drops Phobic and philic surfaces, substrate chemistry Cracks, delamination, pattern formation Terrestrial and microgravity experiments 5

Due to interest in the topics and the appeal of the six well-known keynote speakers, 151 abstracts were submitted worldwide from 32 different countries with 56% coming from Europe (20% from France, 13% from Germany, 9% from Belgium, 5% from United Kingdom and The Netherlands...). In addition, the USA, China, Japan and India were also well represented. Based on the 134 abstracts accepted and confirmed for a presentation at DROPLETS 2013, this book of abstracts has been prepared and divided into five topics: Topic 1 – Droplet wetting and dynamics Topic 2 – Thermal properties and heat transfer Topic 3 – Evaporation dynamics Topic 4 – Spatial distribution within drying Topic 5 – Use of external forces The European Space Agency (ESA) and the French Space Agency (CNES), among other partners, supported this event due to an interest in developing space experiments on wetting and evaporation of droplets of pure and complex fluids. ESA and CNES provided ten travel and accommodation grants to enable European Masters and Ph.D students to participate in the workshop. Besides this book of abstracts, a special issue in the Journal of Colloids and Surfaces A contains selected papers of contributions given at the conference, and serves alongside the extended abstracts, as a kind of proceedings showing the state of the art of the various scientific fields discussed during the meeting. Due to the success of DROPLETS 2013, the organizers hope that this will be the start of a biennial workshop on droplets wetting and evaporation which will in the future gather all the community for a few days of fruitful talks and discussion around wetting and evaporation. We hope that you enjoyed the workshop and Marseilles during these four days, Dr. David BRUTIN Associate Professor at Aix-Marseille University (AMU) Dr. David FAIRHURST Senior Lecturer at Nottingham Trent University (NTU)

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Table of Contents

Editorial.…………………………………………………..………………………………………..….5 Keynotes………………………………………………………….…………….……………..……..11 Topic 1 – Droplet wetting and dynamics……………………………………….…..…….…..…..23 Topic 2 – Thermal properties and heat transfer…………………………………….……...……94 Topic 3 – Evaporation dynamics………………………………………………………….….…..117 Topic 4 – Spatial distribution within drying……………………………………………...………155 Topic 5 – Use of external forces…………………………………………………………..……..233

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Table by abstract number ABSTR. K1 K2 K3 K4 K5 K6 1 2 3 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 24 25 26 27 28 29 30 31 32 33 34 35 36 37 39 40 41 42 43

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FIRST AUTHOR AJAEV BLAKE BONN DOI QUERE SHANAHAN STAROV DUTTA CHOUDHURY BUTT PILAT DOGANCI BORMASHENKO BORMASHENKO PETIT KIM TARASEVICH BORMASHENKO TALBOT CAMARGO CARLE CARLE MCHALE MCHALE SPERLING BOUZEID VENZMER GELDERBLOM LOHSE MERTANIEMI KUCHMA PITTONI BOUZEID CRIVOI SADEK JANSEN TOTLAND ZHANG SHIN CHUANG LEBEDEV HERBERT CHINI CHINI

PAGE 13 15 17 18 19 20 119 157 159 25 235 161 163 26 165 96 167 28 169 98 171 236 238 30 173 175 32 177 99 240 120 33 179 181 183 122 35 242 244 124 185 101 126 128

ABSTR. 44 45 46 47 48 49 51 53 56 59 61 62 63 65 66 67 68 69 70 71 72 73 74 75 76 77 79 80 81 82 83 84 85 86 87 88 89 91 92 94 95 96 97 98

FIRST AUTHOR PAGE KOVACH 246 LOPES 130 MAKI 187 ASARE-ASHER 37 HOUBRAKEN 131 BASAROVA 39 KARPITSCHKA 247 PRAKASH 189 LABORIE 133 KETELAAR 249 VANCAUWENB… 251 GOEHRING 191 SEMPELS 193 VANDEWALLE 253 DUPAS 41 DELL'ARCIPRETE 195 KITSUNEZAKI 197 MUSTERD 43 GILET 45 JEHANNIN 47 DEHAECK 135 LIU 137 CHEN 139 GOPAN 103 KIRSTETTER 255 MAQUET 105 KAHL 199 TSAI 49 BONI 141 SINGH 143 DE RUITER 50 MOREAU 107 DOUMENC 145 KHATUN 201 JANECEK 109 DAVITT 52 DELON 54 SOULIE 203 EALES 205 KARPITSCHKA 56 NAKAHARA 206 YU 147 DUPRÉ-BAUBIG… 58 LOPES 111

ABSTR. 99 100 101 103 104 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 125 126 127 128 130 132 133 134 136 138 140 141 143 144 145 146 147 148 149 150

FIRST AUTHOR PAGE HURAUX 208 ONDARÇUHU 60 ONDARÇUHU 62 DUPAS 64 MSAMBWA 210 ROJEWSKA 66 KAJIYA 212 BALDWIN 256 YANG 214 FELL 68 ALLY 70 SELLIER 72 PIRAMUTHU 258 MAYSER 260 TIMONEN 262 MEDICI 113 DIEHL 74 MARIN 216 MORAILA-MART… 218 DOPIERALA 76 GROSSIER 220 PAPADOPOULOS 78 DO-QUANG 80 LU 222 MACHRAFI 149 AHMED 82 PROCHASKA 84 TSOUMPAS 86 TERPIŁOWSKI 88 RYMUSZKA 264 NOGUERA 224 GATAPOVA 115 BOHR 226 DAUBERSIES 228 HERNANDEZ-C… 229 IRVOAS 151 ZOGRAFOV 266 LEGENDRE 90 MOKARIAN 231 ZAITSEV 92 LAUX 268 BALAZS 153

Table by first author name ABSTR. 128 K1 111 47 150 108 49 K2 140 81 K3 8 9 14 24 31 5 16 17 18 74 42 43 3 39 32 141 88 83 72 67 89 117 125 7 K4 120 85 66 103 97 2 92 110

FIRST AUTHOR AHMED AJAEV ALLY ASARE-ASHER BALAZS BALDWIN BASAROVA BLAKE BOHR BONI BONN BORMASHENKO BORMASHENKO BORMASHENKO BOUZEID BOUZEID BUTT CAMARGO CARLE CARLE CHEN CHINI CHINI CHOUDHURY CHUANG CRIVOI DAUBERSIES DAVITT DE RUITER DEHAECK DELL'ARCIPRETE DELON DIEHL DO-QUANG DOGANCI DOI DOPIERALA DOUMENC DUPAS DUPAS DUPRÉ DE BAU… DUTTA EALES FELL

PAGE 82 13 70 37 153 256 39 15 226 141 17 163 26 28 175 179 25 98 171 236 139 126 128 159 124 181 228 52 50 135 195 54 74 80 161 18 76 145 41 64 58 157 205 68

ABSTR. 138 26 70 62 75 121 41 143 48 99 144 87 34 71 79 107 51 94 59 86 11 76 68 44 29 56 149 40 146 73 27 45 98 126 127 46 77 118 114 19 20 116 28 147

FIRST AUTHOR GATAPOVA GELDERBLOM GILET GOEHRING GOPAN GROSSIER HERBERT HERNANDEZ-C… HOUBRAKEN HURAUX IRVOAS JANECEK JANSEN JEHANNIN KAHL KAJIYA KARPITSCHKA KARPITSCHKA KETELAAR KHATUN KIM KIRSTETTER KITSUNEZAKI KOVACH KUCHMA LABORIE LAUX LEBEDEV LEGENDRE LIU LOHSE LOPES LOPES LU MACHRAFI MAKI MAQUET MARIN MAYSER MCHALE MCHALE MEDICI MERTANIEMI MOKARIAN

PAGE 115 177 45 191 103 220 101 229 131 208 151 109 122 47 199 212 247 56 249 201 96 255 197 246 120 133 268 185 90 137 99 130 111 222 149 187 105 216 260 238 30 113 240 231

ABSTR. 119 84 104 69 95 136 100 101 122 10 6 113 30 53 130 K5 106 134 33 K6 112 63 37 82 91 21 1 15 12 133 115 35 80 132 61 65 25 109 96 148 36 145

FIRST AUTHOR PAGE MORAILA-MARTI... 218 MOREAU 107 MSAMBWA 210 MUSTERD 43 NAKAHARA 206 NOGUERA 224 ONDARÇUHU 60 ONDARÇUHU 62 PAPADOPOULOS 78 PETIT 165 PILAT 235 PIRAMUTHU 258 PITTONI 33 PRAKASH 189 PROCHASKA 84 QUERE 19 ROJEWSKA 66 RYMUSZKA 264 SADEK 183 SAHNAHAN 20 SELLIER 72 SEMPELS 193 SHIN 244 SINGH 143 SOULIE 203 SPERLING 173 STAROV 119 TALBOT 169 TARASEVICH 167 TERPIŁOWSKI 88 TIMONEN 262 TOTLAND 35 TSAI 49 TSOUMPAS 86 VANCAUWENBE.. 251 VANDEWALLE 253 VENZMER 32 YANG 214 YU 147 ZAITSEV 92 ZHANG 242 ZOGRAFOV 266

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Keynotes

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1 Int. Workshop on Wetting and evaporation: droplets of pure and complex fluids th th Marseilles, France, June 17 to 20 , 2013

MATHEMATICAL MODELING OF EVAPORATING SESSILE DROPLETS ON HEATED SURFACES Vladimir AJAEV, Mahnprit JUTLEY Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA E-mail: [email protected]

Studies of evaporating droplets on heated substrates are often based on simplified assumptions of either constant temperature or constant flux at the substrate-droplet boundary. However, in experiments the substrates are often characterized by two or more layers of different materials with unsteady temperature distributions in each of them. A numerical model of this situation was developed in Sodtke et al. [1] but it is limited to the case of evaporation into pure vapor while in experiments the most important case is that of evaporation into moist air so that diffusion of vapor through air is the key limiting mechanism for evaporation. Apart from the simulations from [1] and a simplified model proposed in Sobac & Brutin [2], little attention is paid to the detailed modeling of the effect of unsteady heat conduction in the substrate on droplet dynamics. The objective of the present work is to extend the approach developed in Sodtke et al. [1] to the case of evaporation into air. The geometric configuration is that of a thin droplet on a heated multilayer substrate, as sketched in Fig. 1. Each layer has cylindrical side boundary of radius R with the adiabatic conditions satisfied there. We assume the problem to be axisymmetric and use the cylindrical coordinates shown in the sketch, all scaled by the characteristic radius R. Unsteady heat conduction in each layer is described by the heat equation written in cylindrical coordinates. Conditions of continuity of flux and temperature at layer interfaces are applied, together with fixed temperature condition at the bottom. The latter is motivated by experimental set-ups with Peltier elements maintaining essentially constant temperature.

and define the characteristic length scales in the radial 1/3 and vertical directions to be R and R Ca , respectively. The viscosity µ and the surface tension at the air-liquid interface σ are assumed to be constant; the characteristic flow velocity is based on the evaporation rate. If the capillary number is small, the Navier-Stokes equations simplify to the standard system of lubrication-type equations [3,4]. Thus, the dynamics of droplet shape evolution is determined by a single equation for droplet height h which is the function of radial coordinate and time,

ht + EJ = −

1 ⎡ 3 1 ⎤ rh (hrr + hr + Π ) r ⎥ ⎢ 3r ⎣ r ⎦ r

The local evaporation rate J is determined in terms of local vapor concentration which in turn is assumed to be a linear function of temperature; E is the evaporation number.

Fig. 2 Typical results for interface shape snapshots at equal time intervals

Fig.1: Sketch of the geometric configuration considered, with thin droplet on a two-layer substrate

In the description of the viscous flow in the liquid droplet we employ the capillary number Ca = µU / σ

The system is discretized using the finite-difference approach, resulting in a system of equations for values of temperature, concentration, and the interfacial height at points on the surface. The time stepping is then performed using the SUNDIALS package. Typical results for evolution of the interface shapes are shown in Fig. 2. The disjoining pressure is important near the apparent contact line and is incorporated in to the model using the classical non-retarded London-van der Waals models. We also explore the possibility of different substrate wetting properties modeled through different forms of disjoining pressure as discussed in [5].

Keynote AJAEV

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References [1] Sodtke C, Ajaev V.S., Stephan P., Dynamics of volatile liquid droplet on heated surfaces: theory versus experiment, J. Fluid Mech. 610, pp. 343-362, 2008 [2] Sobac B, Brutin D, Thermal effects of the substrate on water droplet evaporation, Phys. Rev. E 86, 021602, 2012 [3] Oron A., Davis S., Bankoff S., Long-scale evolution of thin liquid films., Rev. Mod. Phys, 69 (3), pp. 931-938, 1997. [4] Ajaev V.S. Interfacial fluid mechanics: a mathematical modeling approach, Springer, New York, 213 pp. 2012 [5] Ajaev V.S., Klentzman J., Gambaryan-Roisman T., Stephan P., Fingering instability of partially wetting evaporating liquids, J Eng Math, 73 (1), pp. 1–8, 2011.

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UNDERSTANDING DYNAMIC WETTING: THE CONTRIBUTION OF THE MOLECULAR-KINETIC THEORY Terence D. BLAKE Laboratory of Surface and Interfacial Physics, University of Mons Ave. Victor Maistriau 19, 7000 – Mons, Belgium. E-mail: [email protected]

The phenomenology and equilibrium thermodynamics of wetting have been studied for more than 200 years. The topic is now fairly well understood, though still a fertile field of research. By contrast, the systematic study of dynamic wetting, i.e. the process by which a liquid spreads or is forced to spread across a solid surface is much more recent. The first reasonably complete molecular model, the molecular-kinetic theory (MKT) was not published until 1969 [1] and the first quantitative hydrodynamic model in 1976 [2]. Since then, the subject has grown steadily [3,4]. However, despite this attention, there remain major unanswered questions relating to the detailed physics of a moving contact line. We now have at least five distinct types of semi-predictive models (the MKT, the evaporation/condensation model, classical lubrication models, the interface transformation model of Shikhmurzaev [5] and the diffuse-interface model) plus three simulation methods (computational fluid mechanics, molecular dynamics and lattice-Boltzmann techniques). As the literature reveals, there is little consensus between these approaches and not a little controversy [4]. In addition, there are several aspects that have received scant attention from theoreticians, pose challenges to current models, and yet are successfully exploited by Industry. Examples include the influence of solid-liquid interactions, dynamic wetting of complex surfaces, reactive wetting, dynamic wetting transitions, and hydrodynamic and electrostatic “assist”. This presentation will introduce some of these issues and review the contribution made by the MKT. Experiment has shown that the contact angle θ between a liquid and a solid is dependent on the speed and direction in which the liquid meniscus moves across the solid surface, i.e. it is velocity-dependent. The underlying assumption of the MKT is that this dependence is due the local disturbance of the three interfacial tensions acting at the contact line. The disturbance creates a surface tension stress

(

γ L cos θ 0 − cos θ

)

of the contact line are governed by two parameters, the frequency κ 0 of random molecular displacements between interaction sites across the energy landscape of the solid and λ the average distance of each displacement. If a stress is applied to the zone, it will € reduce the energy barriers to displacement in the direction of the stress, while enhancing those in the reverse direction. Thus, the contact line will tend to move in the favoured direction. Combining these ideas and exploiting the theory of stress-modified reaction rates leads to the following relationship between the velocity of the contact line U and the dynamic contact angle θ : ' γ * U = 2κ 0 λ sinh) L cos θ 0 − cos θ , (2) ( 2nk BT +

(

)

(

κ 0 = ( k BT h) exp −ΔgW* nk BT

)

(3)

In these equations, kB and h are, respectively, the € Boltzmann and Plank constants, T is the absolute n ≈ 1/ λ2 is the number of solid-liquid temperature, € interaction sites per unit area and ΔgW* is the specific activation free energy of wetting. If the argument of the sinh €function in eq. (2) is small, then the relationship reduces to the linear form: € U = γ L cos θ 0 − cos θ /ζ (4)

(

)

The quantity ζ = k BT κ λ is termed the contact-line friction and gives a measure of the local dissipation at the moving € contact line. In the MKT, it is this dissipation that gives rise to the velocity-dependence of the € angle rather than other sources such as simple contact viscous flow. Since its initial statement [1], the MKT has been successively refined to take specific account of the viscosity of the liquid ηL [6] and solid-liquid interactions as characterized by the work of adhesion Wa 0 = γ L (1 + cos θ 0 ) [7]. These developments lead to 0

3

(

κ 0 ≈ ( k BT ηL v L ) exp −Wa 0 nk BT

)

(5)

(1) € that seeks to restore equilibrium. Here, γL is the surface tension of the liquid and θ 0 is the equilibrium contact angle. €

where v L is volume of the molecular unit of flow. Recently, the link between the MKT and the more general Kramers theory of rate processes has been € established formally [8]. €

At the molecular level, the contact ‘line’ is really a ‘zone’ of small but finite€ size, comparable in thickness to its component interfaces. As in the bulk, the fluid molecules within the zone are subject to intense thermal activity, but within the three-phase zone (TPZ) this activity is moderated by interactions with the solid surface. According to the MKT, equilibrium fluctuations

Comparison with experiment has shown that eq. (2) provides a good description of the behaviour of the dynamic contact angle and that the parameters κ 0 and λ obtained by fitting data are consistent with the model [4,6]; thus, for example, λ is of molecular size. Other experiments (e.g. [9]) have demonstrated that as € predicted by eq. (5), κ 0 is inversely proportional to the

Keynote BLAKE

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viscosity and exponentially dependent on −Wa 0 ; conversely the contact-line friction increases linearly with viscosity and exponentially with the work of adhesion. Large-scale molecular dynamics simulations of droplet spreading have confirmed these € findings and shown close agreement between the fitted values of κ 0 and λ and those obtained by direct interrogation of the internal dynamics of the simulations [8,10].

€ During the period of its development, the MKT has been applied to several practical problems, especially those arising from industrial applications such as liquid coating, ink-jet printing and mineral flotation. Two examples will be outlined here in order to illustrate the utility of the model; further issues will be discussed during the presentation. An important issue in liquid coating is the preparation of the substrate to ensure both successful coating at high speeds and subsequent adhesion of the coated layer, both during and after drying. Wetting is a fundamental prerequisite in each case. It might, therefore, be thought that both could be enhanced by maximising the wettability of the substrate, i.e. by treating the substrate so that θ 0 ~ 0. But, this is not generally the case. One of the main factors limiting coating speed is the onset of air entrainment. This dynamic wetting transition occurs as θ approaches 180˚. Thus, eq. (2) predicts that for € given values of κ 0 and λ the maximum wetting speed is achieved when θ = 180˚ and θ 0 = 0. However, from eq. (5) it is apparent that for a given liquid, κ 0 is at a 0 minimum € when θ = 0. We therefore have two competing effects. On one hand improved wettability € increases the driving force for wetting, while on the € other it increases the dissipation at the contact line, i.e. € the contact-line friction. This competition means that there will usually be an optimum wettability that maximises the coating speed. Indeed, it transpires that relatively hydrophobic surfaces ( θ 0 ~ 90˚) can be coated at higher speeds than more wettable ones, an effect that has been patented (see Fig. 1).

€

Fig. 1: Maximum coating speed found for various gelatin coated substrates as a function of the calculated static contact angle of water [11].

Poor wettability is usually bad for adhesion. But, serendipitously, in the case of the gelatin substrates that are described in the patent, dry gelatin is as hydrophobic as paraffin wax, but rapidly becomes fully 16

wettable on contact with water, thus adhesion is maintained. This transition has been exploited extensively in the high-speed coating of photographic products. Of more fundamental interest, the MKT can also be used to explore the kinetics of the transition. Fig. 2 shows θ versus U (log scale) for water on a gelatin-coated substrate. The data were obtained in a forced wetting experiment over a very wide speed range. As can be seen the data fall into three distinct regimes. At the lowest speeds θ increases steeply with U, it then uncharacteristically falls, before increasing less steeply once again to ~ 180˚. The data can be analysed using the MKT to show that the low-speed regime corresponds to the fully wettable surface, the high-speed regime to the hydrophobic surface and the intermediate regime to the transition between the two. From the speeds at the beginning and end of this transition one can estimate the kinetics of the surface

transformation. Fig. 2: Dynamic contact angle of water on a gelatin-coated substrate. The solid lines are fits to eq. (2). References [1] Blake T.D., Haynes J.M., Kinetics of Liquid/liquid displacement, J. Colloid Interface Sci., 30, pp. 421-423,1969. [2] Voinov, O.V., Hydrodynamics of wetting, Fluid Dyn., 11, pp. 714-721, 1976. [3] de Gennes P-G., Wetting Statics and dynamics, Rev. Mod. Phys., 57(3), pp. 827- 863, 1985. [4] Blake T.D., The physics of moving wetting lines, J. Colloid Interface Sci. 299, pp. 1-13, 2006. [5] Shikhmurzaev, Y.D., The moving contact line on a smooth surface. International J. Multiph. Flow, 19, pp. 589-610, 1993. [6] Blake T.D., Dynamic contact angles and wetting kinetics, in Wettability, Berg, J.C., editor, Marcel Dekker, New York, 1993, pp. 251-309. [7] Blake T.D., De Coninck J., The influence of solid-liquid interactions on dynamic wetting, Advan. Colloid Interface Sci., 96, pp. 21-36, 2002. [8] Blake T.D., De Coninck J., Dynamics of wetting and Kramers’ theory, Eur. Phys. J. Special Topics, 197, pp. 249-264, 2011. [9] Li H., Sedev R., Ralston J., Dynamic wetting of a fluoropolymer surface by ionic liquids, Phys. Chem. Chem. Phys., 13, pp. 3952-3959, 2011. [10] Bertrand E., Blake T.D., De Coninck, J., Influence of solid-liquid interactions on dynamic wetting: a molecular dynamics study, J. Phys. Condens. Matter, 21, 464124 (14 pp), 2009. [11] Blake T.D., Morley S.D., US Patent 5,792,515, 1998. [12] Blake T.D. Forced wetting of a reactive surface, Advan. Colloid Interface Sci. 179-182, pp. 22-28, 2012.

Keynote BLAKE

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DROPLETS OF COMPLEX FLUIDS Daniel BONN Institute of Physics, University of Amsterdam, Science Park 904, NL-1098XH Amsterdam LPS de l’ENS, 24 Rue Lhomond, F-75231 Paris Cedex 05 E-mail: [email protected]

In many processes such as for instance spray painting or the deposition of pesticides on plant leaves, one first has to form droplets and subsequently deposit them on a surface. Both processes are highly non-linear, and some aspects of them are still ill understood, even for simple fluids. I will discuss both drop formation and impact of droplets of complex fluids, in order to see what the differences are with the reference case, that of a simple fluid. In this way, I will show that the presence even of minute amounts of polymers or surfactants can greatly affect drop formation, drop impact and the subsequent spreading of drops. References [1] Wetting and spreading, D Bonn, J Eggers, J Indekeu, J Meunier, E Rolley, Reviews of modern physics 81 (2), 739 (2009) [2] Drop Formation in Non-Newtonian Fluids, Mounir Aytouna, Jose Paredes, Noushine Shahidzadeh-Bonn, Sébastien Moulinet, Christian Wagner, Yacine Amarouchene, Jens Eggers, and Daniel Bonn Phys. Rev. Lett. 110, 034501 [3] Effect of Surface Tension Variations on the Pinch-Off Behavior of Small Fluid Drops in the Presence of Surfactants M. Roché, M. Aytouna, D. Bonn, and H. Kellay Phys. Rev. Lett. 103, 264501 (2009) [4] Superspreading: aqueous surfactant drops spreading on hydrophobic surfaces S Rafaï, D Sarker, V Bergeron, J Meunier, D Bonn, Langmuir 18, 10486 (2002).

Fig. 1: Droplets on plant leaves; as the plant leaves clearly repel water and pesticides are usually sprayed in aqueous solutions, there is a major challenge in getting the droplets to stick to the leaves, in order for the active substances to be deposited. I will discuss a few strategies that have been employed to increase the efficiency of deposition by using complex fluids.

Keynote BONN

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EFFECTS OF SKINS FORMED IN THE DRYING OF POLYMER SOLUTIONS Masao DOI Center of Soft Matter Physics and Its Applications, Beihang University, Beijing, 100191 China E-mail: [email protected]

When a polymer solution with volatile solvent is dried, the polymer concentration near the surface becomes high, and polymers often form a layer which has distinctively different rheological property from that of bulk solution. The layer is called skin. The skin layer is considered to be an elastic membrane though the detailed rheological study has not been done[1]. It is known that once such skin layer is formed, it creates various problems. For example the surface of the dried polymer films is not flat; dimples and wrinkles often appear and bubbles remain trapped in the film (see Fig.1). We conducted experiments to clarify the relation between the skin formation and the bubble formation. We measured the time dependence of the pressure in the solution in the process of drying by the simple method shown in Fig.2. We found that the pressure in the solution decreases after the skin is formed, but remains constant with further evaporation of the solvent. We also measured the time dependence of the bubble size, and found that it generally obeys the diffusion limited growth law r ( t ) = A t − t 0 (see Fig.3). From our experiments, we concluded that (i) the gas in the bubble is a mixture of solvent vapor and air dissolved in the solution, (ii) the bubble nucleation is assisted by the pressure decrease in the solution covered by the skin layer(see Fig.4), and (iii) the growth of the bubbles is diffusion limited, mainly limited by the diffusion of air molecules dissolved in the solution. These results are obtained for polymer solutions placed in a cup. When polymer solutions are dried on a flat plate, there appear phenomena which indicate that the pressure in the solution may be higher than the atmospheric pressure (see Fig.5). The reason for this will be discussed.

Fig.1. Problems caused by the skin formation in the drying process of polymer solution. Left: dimples, right: bubbles.

Fig.3. Time dependence of the bubble radius in PMMA and PVAc solution. The solid lines indicate the curve of the diffusion limited growth law r ( t ) = A t − t 0.

Fig.4. Mechanism for the bubble nucleation in the solution with skins

Fig.5. Puncture of the skin formed at the surface of polymer solution by drying. The phenomena indicate that the pressure in the solution can be higher than the atmospheric pressure.

References [1] Y. Shimokawa, T. Kajiya, K. Sakai, and M. Doi, Measurement of the skin layer in the drying process of a polymer solution, Phys. Rev. E 84 051803 1-9 (2011) [2] S. Arai and M. Doi, Skin formation and bubble growth during drying process of polymer solution, Eur. Phys. J.E. 35 57 1-9 (2012) [3] S. Arai and M. Doi, Anomalous drying dynamics of a polymer solution on a substrate, submitted Fig.2. Left: the method used to measure the pressure in the solution during drying. Right: Time dependence of the pressure in the solution

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Keynote DOI

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LEIDENFROST PHENOMENA: AT THE FRONTIER BETWEEN EVAPORATION AND WETTING Dan SOTO, Guillaume DUPEUX, Christophe CLANET and David QUÉRÉ ESPCI & École Polytechnique, Paris, France. E-mail: [email protected]

A drop deposited on a very hot solid levitates, owing to the formation of a cushion of vapor between the solid and the liquid. This is the so-called Leidenfrost phenomenon, which generates purely non-wetting situations, since the liquid contacts air and vapor. We discuss the characteristics of Leidenfrost states – how the phenomenon can be extended if using textured substrates, how solids can be also placed in a Leidenfrost situation, or to what extent the friction of liquids can be reduced in such cases.

The conjunction of a low friction with the production of vapor can be exploited to generate self-propulsion. If the substrate is made asymmetric, or if the levitating body itself is asymmetric, self-motions can be observed, as first discovered by Heiner Linke in 2006. We plan to discuss in particular the origin of the force driving these motions, and also how the solid design can be chosen in order to optimize the motion (in terms of force, and velocity).

Keynote QUERE

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WETTING & EVAPORATION OF SESSILE DROPS: SOME FUNDAMENTAL PARAMETERS Martin E.R. SHANAHAN1, Khellil SEFIANE2, Ross MOFFAT2, Daniel OREJON2, Vasileios KOUTSOS2, Alex ASKOUNIS2

1

Univ. Bordeaux, I2M, UMR 5295, F-33400 Talence, France.CNRS, I2M, UMR 5295, F-33400 Talence, France. Arts et Metiers ParisTech, I2M, UMR 5295, F-33400 Talence, France. 2 Institute for Materials and Processes, School of Engineering, The University of Edinburgh, King’s Building’s, Mayfield Road, Edinburgh EH9 3JL, United Kingdom. E-mail: [email protected], [email protected], [email protected]

be quite complex, and we discuss various aspects here. For example, the tendency for a solid/liquid system to “opt” for either TL pinning or “stick-slip” motion is intrinsically related to the surface roughness of the solid; a rough solid allowing easier pinning. Less obvious, propensity for pinning is directly dependent on the initial value of contact angle. This can be related to hydrophobicity, depending on the liquid [8].

Jumps of TL Radius (mm) Radius (mm) Radius (mm) Radius (mm) Radius (mm) Radius (mm)

Sessile drops are frequently used to characterise solid surfaces, using the measured contact angles of “probe” liquid drops, assuming them to be true, equilibrium values. By applying Young’s equation and one of various equations proposed to relate interfacial (solid/liquid) tension to the surface tensions of solid and liquid and their various components [e.g.1-3], estimates of the surface properties can be obtained. Neglecting any possible doubts attached to the validity of the various interpretations, a serious problem is that of the measured contact angle itself. A simple force balance predicts an equilibrium value, but it is well-known that a range of values is usually accessible; giving rise to what is generally termed “wetting hysteresis”. This range may be very large, depending on the system. The causes are multiple, including solid surface roughness, solid deformation by capillary forces, local adsorption and chemical reactivity. However, a ubiquitous effect that has been largely overlooked till the mid 90s is that of concomitant evaporation [4]. Unless the drop is strictly at equilibrium with its vapour, which is highly unlikely, there will be liquid transfer, usually evaporation decreasing drop volume. How this occurs is far from trivial, and one of the first surprises was that due to Deegan et al. in their seminal work and others [5, 6], who convincingly showed that evaporation is exacerbated near the triple line (TL). If the TL is “pinned”, i.e. remains in its initial position during evaporation, liquid replenishment leads to an advective current, parallel to the solid surface. If it is not pinned, then a phenomenon of “stick-slip” can occur, in which contact angle decreases to a certain value, with the TL pinned, followed by a rapid TL jump to smaller contact radius and concomitant increase in contact angle [7].

1.0 0.8 0.6 0.4 0.2 1.0 0.8 0.6 0.4 0.2 1.0 0.8 0.6 0.4 0.2 1.0 0.8 0.6 0.4 0.2 1.0 0.8 0.6 0.4 0.2 1.0 0.8 0.6 0.4 0.2

0.1%

0.05%

0.025%

0.01%

0.001% Virtually continuous TL motion

water 0

500

1000

1500

2000

2500

Time (sec) Fig. 1: Schematic representation of the “stick-slip” process in which evaporation at constant contact radius leads to an energy imbalance, finally depinning the triple line [7].

Fig. 2: Evolution of contact radius with time for droplets of nanofluids of different TiO2 concentrations [9].

The play-off between evaporation and TL motion can 20

Keynote SHANAHAN

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A pure liquid in general favours continuous motion of the TL. However, if the liquid is laden with (nano-)particles, “stick-slip” behaviour becomes predominant. For a nano-suspension, the relative particle content is important for determining the type of behavior expected [9]. During the “stick” phase the above-mentioned advective, replenishment current transports particles to the TL [5], and these form a deposit which effectively anchors the dewetting front. The form of these deposits is of considerable interest and, in certain cases, they can adopt a complex crystalline structure [10].

References (a few) [1] Girifalco, L.A., Good R.J., A theory for the estimation of surface and interfacial energies. 1. Derivation and application to interfacial tension, J. Phys. Chem., 61, pp. 904-909, 1962. [2] Fowkes F.M., Attractive forces at interfaces, Ind. Eng. Chem., 56, pp. 40-52, 1964. [3] van Oss C.J., Chaudhury M.K., Good R.J. Monopolar surfaces, Adv. Coll. Interface Sci., 28, pp.35-64, 1987. [4] Bourgès-Monnier C., Shanahan M.E.R., Influence of evaporation on contact angle, Langmuir, 11, pp. 2820-2829, 1995. [5] Deegan R.D., Bakajin O., Dupont T.F., Huber G., Nagel S.R., Witten T.A., Contact line deposits in an evaporating drop, Phys. Rev. E, 62, pp. 756-765, 2000. [6] Hu H., Larson R.G., Evaporation of a sessile droplet on a substrate, J. Phys. Chem., 106, pp.1334-1344, 2002. [7] Shanahan M.E.R., Simple theory of stick-slip wetting hysteresis, Langmuir, 11, pp. 1041-1043, 1995. [8] Shanahan M.E.R. , Sefiane K., Moffat J.R., Dependence of volatile droplet lifetime on the hydrophobicity of the substrate, Langmuir, 27, pp. 4572–4577, 2011. [9] Orejon D., Sefiane K., Shanahan M.E.R., Stick-slip of evaporating droplets: Substrate hydrophobicity and nanoparticle concentration, Langmuir, 27, pp. 12834-12843, 2011. [10] Askounis A., Sefiane K., Koutsos V., Shanahan M.E.R., Structural transitions in a ring stain created at the contact line of evaporating nanosuspension sessile drops, Phys. Rev. E, 87, 012301, 2013.

Fig. 3: (a) Optical micrograph showing particle ring stain. (b) topographic image with areas of interest. (i-iii) FFT analysis of these areas showing crystalline form [10].

Keynote SHANAHAN

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22

Topic 1 Droplet wetting and dynamics

23

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WETTING OF SUPERAMPHIPHOBIC SURFACES

Hans-Jürgen BUTT,1 Periklis PAPADOPOULOS,1 Xu DENG,1 Frank SCHELLENBERG,1 Ciro SEMPREBON,2 Martin BRINKMANN,2 Matteo CICCOTTI,3 Longquan CHEN,4 Doris VOLLMER1 1

2

Max Planck Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany 3 Laboratoire PPMD/SIMM, UMR 7615, ESPCI, 10 rue Vauquelin, 75005 Paris, France 4 Center of Smart Interfaces, Technical University Darmstadt, 64287 Darmstadt, Germany. E-mail: [email protected]

Superamphiphobic surfaces exhibit fascinating physical properties, such as contact angles with water, aqueous solutions and non-polar liquids greater than 150° and low contact angle hysteresis. Tilting a superamphiphobic surface by a few degrees is already sufficient for a drop to overcome adhesion and to roll off. Characteristic and essential for the unique properties are microscopic pockets of air that are trapped beneath the liquid drops (Cassie state). Prospective applications include self-cleaning, anti-fouling, drag reduction in micro fluidics and efficient gas exchange. For applications superamphiphobic layers need to be

made in a simple, self-assembled process. This often leads to the use of aggregates of spheres. Here, I discuss the optimal design of superamphiphobic layers fabricated from highly porous aggregates of nano- or micro¬spheres. This leads to criteria of how to optimize such layers for a particular applica-tion. The considerations are based on stability criteria valid in the static case. For highly dynamic liquids additional effects are important. Therefore we carried out drop impact experiments on superamphiphobic layers. The results are presented and will be discussed.

Abstract #005

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GENERAL THERMODYNAMIC APPROACH TO YOUNG, WENZEL AND CASSIE-BAXTER EQUATIONS Edward BORMASHENKO Ariel University, Physics Faculty, 40700 Ariel, P.O.B. 3, Israel. E-mail: [email protected]

Contact angles serve a natural macroscopic characteristic of wetting of solid substrates [1]. When the surface is ideal (atomically flat, chemically homogeneous, isotropic, insoluble, non-reactive and non-deformed solid) the equilibrium contact angle is called the Young contact angle [1]. When it is rough or chemically heterogeneous it is called the apparent contact angle. The Young contact angle depends on the triad of surface tensions and is given by the famous Young equation [2]. Wetting of rough and chemically heterogeneous surfaces is generally reduced to the Wenzel and Cassie-Baxter equations [3-5]. These equations have been derived rigorously recently basing on the principle of virtual work, minimization of the free energy of the drop and concepts supplied by nonextensive thermodynamics [6-8]. The contact angles predicted by these equations depend on interface tensions and parameters of the surfaces [3-8]. The less obvious is the dependence of contact angles on external fields exerted on a droplet (gravity, electric field, etc.). We demonstrate the general thermodynamic approach clarifying this problem and allowing very general grounding of the Young, Wenzel and Cassie-Baxter equation. Consider the liquid drop deposited on an ideal solid substrate and exerted to external potential U(h, x) in the situation when the spreading parameter is negative. When a droplet is deposited on such an ideal substrate as described in Fig. 1, its free energy G could be written as [9]: a

[

G(h, h ʹ′) = ∫ 2πγx 1 + h ʹ′2 + (1) + 2πx(γ SL −0 γ SA ) + U ( x, h)]dx , dh , γ SL , γ SA , γ are the surface where h ʹ′ = dx

tensions at the solid/liquid, solid/air liquid/air interfaces correspondingly. We also suppose that the droplet does not evaporate, thus the condition of the constant volume V should be considered as: a

V = ∫ 2πxh ( x )dx = const .

(2)

0 Calculation of the shape of the droplet is reduced to minimization of the functional: a

~ G(h, hʹ′) = ∫ G(h, hʹ′, x )dx , 0

(3)

~ G (h, h ʹ′, x ) = 2πγx 1 + h ʹ′2 + (4) + 2πx(γ SL − γ SA ) + U ( x, h) + 2πλxh , where λ is the Lagrange multiplier to be deduced from 26

Eq. (2). We are not interested in the shape of a droplet but in contact angle θ. We suppose that the boundary (the triple line) of the droplet is free to slip along the axis x. Thus, we solve the variational problem with free endpoints. Thus the conditions of transversality of the variational problem should be considered. The transversality condition at the endpoint a yields [9]:

~ ~ (G − hʹ′Ghʹ′ʹ′ ) x =a = 0, ~ where Ghʹ′ʹ′ denotes

(5)

the

~ h ʹ′ derivative of G .

Substitution of Formula (4) into the transversality condition (5), and taking into account h( a ) = 0 ,

U ( x = a, h = 0) = 0

will give rise to the famous

Young equation:

cos θ Y =

γ SA − γ SL γ

.

(6)

Expression (6) presents the well-known Young equation. It asserts that the contact angle θ is unambiguously defined by the triad of surface tensions: γ , γ SL , γ SA . Equation (6) tells us that the Young angle depends only on the physicochemical nature of the three phases and that it is independent on the droplet shape and external field U under very general assumptions about U, namely U = U(x, h(x)). The external field may deform the droplet but it has no influence on the Young angle θY. The Wenzel and Cassie equations may be derived in a similar way. When a droplet is placed on a rough surface and wets it, the free energy is given by: a

[

G(h, h ʹ′) = ∫ 2πγx 1 + h ʹ′2 + 0

+ 2πx(γ SL − γ SA )~ r + U ( x, h)]dx .

(7)

Equation (7) is very similar to Eq. (1), the only r which is the roughness difference being parameter ~ ratio of the wet area; in other words, the ratio of the real surface in contact with liquid to its projection onto the horizontal plane. Use of the transversality conditions (5) and the condition of the constant volume (2) yield the Wenzel equation:

cos θ * = ~ r cos θ Y . * where θ is the apparent

(8)

contact angle (defined as an equilibrium contact angle measured macroscopically on a solid surface that may be rough or chemically heterogeneous) [2]. Consider now the Cassie-Baxter wetting of flat chemically heterogeneous surfaces. Suppose that the

Abstract #009

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surface under the drop is flat, but consists of n sorts of materials randomly distributed over the substrate. Each material is characterized by its own surface tension coefficients γ i,SL and γ i,SA , and by the fraction f i in the substrate surface,

f1 + f 2 + ... + f n = 1 . The free

energy of an axisymmetric drop of a radius a exposed to an external field U(x,h) will be given by the following expression a

[

(9)

The transversality condition (5) and the constancy of volume (2) give rise to Cassie-Baxter apparent contact angle θ * : n

∑ f (γ i

cos θ =

i ,SA

1

− γ i ,SL ) .

γ

(10)

It is demonstrated that apparent contact angles are insensitive to the external fields satisfying the demands defined above. It is noteworthy that the use of the notion "apparent contact angle" (as well as the use of the Wenzel and Cassie-Baxter approximations) is justified on the scale much larger than the characteristic scale of surface roughness or heterogeneity [10].

y

U(x,h)

h(x) θY -a

[

]

+ 2πx (γ SL − γ SA ) + πω 2 ρhx 3 + U ( x, h ) dx

n ⎤ + 2πx ∑ f i (γ i ,SL − γ i ,SA ) + U ( x, h )⎥dx . i =1 ⎦

*

a

G(h, h ʹ′) = ∫ 2πγx 1 + h ʹ′2 + 0

2

G(h, hʹ′) = ∫ 2πγx 1 + hʹ′ + o

“electrowetting”) is treated in Ref.15. Curiously the equilibrium contact angles remain the same even for rotating sessile droplets. Consider sessile droplet rotating stationary with the ideal substrate with the angular velocity ω. In this case the free energy will be given by the following expression:

a

x

Fig. 1: A cross-section of the spherically-symmetrical droplet deposited on the ideal solid substrate and exposed to an external field U(x, h).

Generalization of the presented approach for the situation when the line tension is considered is possible. It leads to the Neumann-Boruvka equation for flat surfaces [9] and to the generalized equation describing wetting of rough surfaces [11]. The same approach extended to wetting of curved surfaces leads to the generalized Young, Wenzel and Cassie-Baxter equations [12]. The use of Wenzel and Cassie-Baxter equations needs some care due to the fact, that only an area of the solid substrate adjacent to the triple line exerts an influence on equilibrium contact angles, predicted by Eqs.6, 8, 10 [13-14]. Eqs. 6, 8, 10 are true when interfacial tensions γ SL , γ SA , γ are insensitive to the external

(11)

Exploiting the constancy of volume (2) and the transversality conditions (5) yields the well-known Young equation (6). The Wenzel and Cassie-Baxter equations may be obtained in a similar way for sessile droplets rotating with rough and chemically heterogeneous surfaces. Indeed, the rotation of the substrate is reduced to the introducing of the efficient

~

2

3

potential energy U (h, x ) = πω ρhx + U ( x, h) , which does not influence equilibrium contact angles. We demonstrated that the Young, Wenzel and Cassie equilibrium contact angle are insensitive to the volume of a droplet, external fields and even to the rotation of the substrate. This insensitivity has been already demonstrated by various researchers [16-18], but the most general thermodynamic grounding of this result is obtained within a variational approach to the static problem of wetting. References [1] Young Th., Philos. Trans. R. Soc. London, 95, p. 65, 1805. [2] de Gennes P.G., Brochard-Wyart F., Quéré D., Capillarity and Wetting Phenomena, Springer, Berlin, 2003. [3] Cassie A.B.D., Baxter S., Trans. Faraday Society, 40, p. 546, 1944. [4] Cassie A.B.D., Discuss. Faraday Society, 3, p. 11, 1948. [5] R. N. Wenzel, Ind. Eng. Chem., 28 (1936) 988–994. [6] Bico J., Thiele U., Quéré D., Colloids and Surfaces A, 206, p. 41, 2002. [7] Letellier P., Mayaffre Al., Turmine M., J. Colloid Interface Sci., 314, p. 604, 2007. [8] Whyman G., Bormashenko Ed., Stein T., Chem. Phys. Letters, 450, p. 355, 2008. [9] Bormashenko E., Colloids and Surfaces A, 345, p. 163, 2009. [10] Nosonovsky M., Langmuir, 23, p. 9919, 2007. [11] Bormashenko E., Journal of Colloid and Interface Science, 360, p. 317, 2011. [12] Bormashenko E., J. Phys. Chem. C, 113, 17277, 2009. [13] Gao L., McCarthy Th., Langmuir 23, p. 3762, 2007. [14] Bormashenko E., Langmuir, 25, p. 10451, 2009. [15] Bormashenko E., Mathematical Modelling of Natural Phenomena, 7, p.1, 2012. [16] Blokhius E. M., Shilkrot Y., Widom B. 86, p. 891,1995. [17] Lubarda V. A., Soft Matter, 8, p.10288, 2012. [18] Lubarda, V. A. Acta Mech. 2013, doi:10.1007/s00707-013-0813-6

field U(x,h). More complicated case, when interfacial tensions depend on external field (this takes place in

Abstract #009

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TOWARDS UNDERSTANDING HYDROPHOBIC RECOVERY OF PLASMA TREATED POLYMERS: STORING IN HIGH POLARITY LIQUIDS SUPPRESSES HYDROPHOBIC RECOVERY Edward BORMASHENKOa,b*, Gilad CHANIELa,c

a

b

Ariel University, Physics Faculty, 40700, P.O.B. 3, Ariel, Israel., Ariel University, Chemical Engineering and Biotechnology Faculty, 40700, P.O.B. 3, Ariel, Israel, c Bar Ilan University, Physics Faculty, 52900, Ramat Gan, Israel. E-mail: [email protected]

Plasma treatment is broadly used for modification of surface properties of polymer materials [1-2]. The plasma treatment creates a complex mixture of surface functionalities which influence surface physical and chemical properties and results in a dramatic change in the wetting behaviour of the surface [3-11]. Plasma treatment usually strengthens hydrophilicity of treated polymer surfaces. However, the surface hydrophilicity created by plasma treatment is often lost over time. This effect of decreasing hydrophobicity is called “hydrophobic recovery” [12-18]. The phenomenon of hydrophobic recovery is usually attributed to a variety of physical and chemical processes, including: 1) re-arrangement of chemical groups of the surface exposed to plasma treatment, due to the conformational mobility of polymer chains; 2) oxidation and degradation reactions at the plasma treated surfaces; 3) diffusion of low molecular weight products from the outer layers into the bulk of the polymer, 4) plasma-treatment induced diffusion of additives introduced into the polymer from its bulk towards its surface [15]. Occhiello et al. classified the complicated processes occurring under hydrophobic recovery according their spatial range, i.e. short-range motions within the plasma-modified layer, burying polar groups away from the surface and long-range motions, including diffusion of non-modified macromolecules or segments from the bulk to the surface [16]. At the same time, the precise mechanism of this effect remains obscure. We demonstrate in our paper that dipole-dipole interaction of the plasma treated polymer and molecules of the surrounding medium plays an important role in the hydrophobic recovery. We exposed extruded low-density polyethylene (LDPE) films to cold air radio frequency inductive plasma under following conditions: frequency about 10 MHz, power -2 100 W, pressure 6.7·10 Pa. The time span of irradiation was 1 min. Immediately after the treatment films were immersed in organic liquids: ethanol (dehydrated), C2H5OH, acetone, (CH3)2CO, carbon tetrachloride, CCl4, benzene, C6H6 and carbon disulphide, CS2. The roughness of LDPE films was established by AFM as 50±4 nm. The roughness of the LDPE film did not change after plasma treatment. Experiments were carried out at the different temperatures of liquids: the first under the temperature of 30±3°, and the second under the temperature of 8±2°. In addition, the hydrophobic recovery of LDPE films was studied at ambient conditions (temperature 25±5°) and air humidity 30-40%, and also when the irradiated 28

films were kept under low vacuum. Contact angles (static and advancing) were measured by a Ramé-Hart Advanced Goniometer Model 500-F1. The advancing contact angle was measured by the needle-syringe method. For the study of the hydrophobic recovery the contact angles were measured every two hours during the first 12 hours after the plasma treatment; thereafter contact angles were taken every 24 hours. Before measurement of contact angles, the LDPE films were dried for 10 min at -2 the low vacuum of 6.7·10 Pa at the ambient temperature. We established that the time dependencies of the static contact angle are well approximated by the empirical formula:

~

t

t

~− (1) θ (t ) = θ (1 − e ) + θ 0 = θsat − θ e τ , where θ 0 corresponds to the initial contact angle established immediately after the plasma treatment, τ is −

τ

the characteristic time of restoring of the contact angle,

~ θ

is

the

fitting

parameter,

and

~

θsat = θ + θ 0

corresponds to the saturation contact angle. Parameters τ and θ sat established by the fitting of the experimental data according to Eq. (1) for various immersion liquids are summarized in Table 1. It is noteworthy that the same exponential fitting satisfactorily describes the process of hydrophobic recovery at both the initial and advanced stages of the films’ ageing. The characteristic time of restoring of the static contact angle τ, and the saturation angle θ sat or LDPE films kept under ambient conditions in vacuum and humid air are summarized in Table 2. Firstly we conclude from the data presented in Tables 1, 2 that the film surface does not completely lose its hydrophilicity achieved by the plasma treatment. This is true for both immersed films and films kept in humid air and vacuum. The saturation contact angle θ sat is far from its initial value (with one exception, namely films immersed in CS2). This observation was reported also by Pascual et al. [15]. Secondly, we conclude that humidity slowed down the effect of hydrophobic recovery, and this observation coincides with the same reported by other groups [13-15]. Thirdly, it is seen that the characteristic times of hydrophobic recovery established for LDPE films immersed in all kinds of liquids (see Tables 1, 2) are lower than those measured for vacuum and humid air. This observation may be related to removal of low-molecular-weight oxidized

Abstract #014

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materials from the surfaces of plasma-treated LDPE by liquids (due to the effect of surface “washing”) Table 1. Parameters of hydrophobic recovery fitted according Exp. (1), observed with various liquids. Liquid

Molecular dipole moment, D

τ, days

τ, days

t=30°C

t=8°C

θsat,°

θsat,°

t=30°C

t=8°C

Acetone

2.88

0.046

1.25

55

54.6

Water

1.854

0.854

4

56.3

80

Ethanol

1.69

1.492

1.639

70.5

70

Benzene

0

0.013

0.649

79

96

CS2

0

0.001

0.026

90.7

107

CCl4

0

0.01

0.578

82

89

Table 2. Parameters of hydrophobic recovery fitted according Exp. 1, observed in humid air and vacuum. Medium

τ, days

θsat,°

Humid air

1.785

78

Vacuum

0.476

57

Now we address the impact of polarity of the liquid on the hydrophobic recovery. Consider that in our study we used organic liquids, built of molecules possessing very different dipole moments (for dipole moments (supplied in Debye) of the molecules see Table 1). It is clearly seen, that high polarity liquids such as acetone, ethanol and water markedly slowed down hydrophobic recovery. At first glance, these observations could be easily explained by dipole-dipole interactions between molecules of plasma-treated polymer and molecules of the surrounding liquid. Such interaction may prevent rotation of hydrophilic polar groups appearing on the surface of plasma-treated polymer, and consequently slow down the process of hydrophobic recovery. However, the closer inspection of the problem of hydrophobic recovery of plasma treated polymers immersed in liquids shows that relating the phenomenon to the dipole-dipole interactions of molecules of polymer and liquid needs more profound grounding. Indeed, intermolecular interaction is comprised of contributions from Keesom, Debye and London dispersion interactions. Remarkably, all three kinds of attractive interactions constituting the van der 6

Waals intermolecular potential decrease as 1 / r [19]. It is generally accepted that the London dispersion forces dominate in the van der Waals interactions, and they are one-two orders of magnitude stronger than the Keesom and Debye ones [19]. At the same time, the London dispersion forces are independent of the permanent dipole moments of molecules; thus the permanent dipole moment plays a minor role in the intermolecular interactions. Hence, it is unclear why high polarity liquids such as water, acetone or ethanol markedly retard the hydrophobic recovery. The puzzle will be resolved if we suppose that polar groups of polymer arising from plasma treatment are spatially fixed. In this case dipole-dipole interaction will

3

decrease as 1 / r . When molecules are fixed, the dipole-dipole interactions will dominate on the London dispersion forces. Moreover, it could be demonstrated that when dipoles are even partially fixed the angle-averaged pair potential of intermolecular 3

interaction in certain cases decreases as 1 / r . Our findings are supported by the results reported by Kaminska et al. [8]. Kaminska et al. studied the change of polar and dispersive (London) components of free energy of various polymers exposed to plasma treatment [8]. They reported the significant increase of the polar component of the free energy for plasma-treated polymers, whereas the change of the dispersive part of the free energy was minor [8]. We conclude that liquids built of molecules possessing high dipole moment significantly retarded hydrophobic recovery. The reported results show a practical way of the effective suppression of the hydrophobic recovery of cold plasma treated polymers, namely immersion in high polarity liquids (including water). Decreasing the temperature renders restoring of hydrophobicity of plasma irradiated films. References [1] Yasuda H.K. (Ed.), Plasma polymerization and plasma treatment, J. Wiley & Sons, New York, 1984. [2] Strobel M., Lyons C.S., Mittal K.L. (Eds), Plasma surface modification of polymers: relevance to adhesion, VSP, Zeist, the Netherlands, 1994. [3] Occhiello E., Morra M., Garbassi F., Applied Surface Science, 47, pp. 235-242, 1991. [4] France R.M., Short R.D., Langmuir, 14 (17), pp. 4827-4835, 1998. [5] France R.M., Short R.D., J. Chem. Soc., Faraday Trans., 93, pp. 3173-3178, 1997. [6] Fernández-Blázquez J.P., Fell D., Bonaccurso El., del Campo A., Journal of Colloid and Interface Science, 357, pp. 234–238, 2011. [7] Balu B., Breedveld V., Hess D.W., Langmuir, 24, pp. 4785-4790, 2008. [8] Kaminska A., Kaczmarek H., Kowalonek J., European Polymer Journal, 38, pp. 1915-1919, 2002. [9] Van Der Mei H.C., Stokroos I., Schakenraad J.M., Busscher H.J., J. Adhesion Sci. Technology, 5, pp. 757-769, 1991. [11] Owen M.J., Smith P.J., J. Adhesion Sci. Technol., 8, pp. 1063-1075, 1994. [12] Morra M., Occhiello E., Marola R., Garbassi F., Humphrey P., Johnson D., J. Colloid & Interface Sci., 137, pp. 11-24, 1990. [13] Everaert E.P., Van Der Mei H.C., de Vries J., Busscher H.J., J. Adhesion Sci. Technol., 9, pp. 1263-1278, 1995. [14] Everaert E.P., Van Der Mei H.C., Busscher H.J., J. Adhesion Sci. Technol., 10, pp. 351-359, 1996. [15] Pascual M., Balart R., Sanchez L., Fenollar O., Calvo O., J. Mater. Sci., 43, pp. 4901-4909, 2008. [16] Occhiello E., Morra M., Cinquina P., Garbassi F., Polymer, 33, pp. 3007-3015, 1992. [17] Strobel M., Dunatov Ch., Strobel J.M., Lyons Ch.S., Perron St.J., Morgen M.C., J. Adhesion Science & Technology, 3, pp. 321-335, 1989. [18] Hill J.M., Karbashewski El., Lin A., Strobel M., Walzak M.J., J. Adhesion Science & Technology, 9, pp. 1575-1591, 1995. [19] Israelachvili J.N., Intermolecular and Surface Forces, Third Edition, Elsevier, Amsterdam, 2011.

Abstract #014

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CAPILLARY RISE IN MICROCHANNELS WITH SMOOTH AND PATTERNED WALLS

Glen McHALEa, Christophe L. TRABIa, Haadi JAVEDb, Michael I. NEWTONb, FOUZIA O. OUALIb a

Faculty of Engineering & Environment, Northumbria University, Ellison Place, Newcastle upon Tyne NE1 8ST, UK b School of Science & Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, UK. E-mail: [email protected]

Micro-channels find many applications in various fields, e.g. in diagnostic testing and DNA manipulation and in micro-reactors. Imbibition into such channels can be 1,2. In forced or free via the phenomenon of capillarity the latter case, surface chemistry controls the hydrophobicity/ hydrophilicity of wall, but imbibition also depends on surface area. In this work, we focus on the inter-play of surface structure and surface chemistry in determining how capillary rise and imbibition occurs. Micro-channels (130-140µm depth and 400-600µm wide) were fabricated in SU-8 on glass substrates using photolithography. Imbibition and capillary rise of polydimethylsiloxane PDMS oils of varying viscosities were investigated using a high speed camera. The position of the meniscus of the liquid was measured using image analysis software. Single “smooth” open channels and “rough” channels (saw-tooth type walls to give increased surface area, but with the same average channel volume for flow) were investigated. Here an “open” channel means the oil contacted the base and side walls of the channel, but the oil’s upper surface was free to air and not in contact with a solid wall. The equation describing imbibition in a vertically mounted capillary is,

1 d ⎛ dx 2 ⎞ ⎛ dx ⎞ ⎜⎜ ⎟⎟ = b − gx − ax⎜ ⎟ 2 dt ⎝ dt ⎠ ⎝ dt ⎠

(1)

where a and b are viscous and capillary coefficients, 1-3 respectively .

Fig. 1: The rise the main meniscus of a 19.2 m.Pa.s viscosity PDMS oil in a 600µm wide and 130µm deep channel. Dots show experimental data, solid lines are a numerical fit to eq. (1) and red dashed lines a fit to the analytical visco-gravitational eq. (3). The dotted curve is the expected rise using the nominal device parameters for a and b.

30

For rectangular cross-section open-channels these are given by,

a = 3η ρH 2ζ o (ε )

(2a)

b = γ LV [cosθ e (1 + 2ε ) − 1] ρh

(2b)

and

where H is depth and ε = H/W (W is the width of the channel) is the aspect ratio, ρ is the density, θe =0o is the Young’s law contact angle, η is the viscosity and γLV is the surface tension of liquid; ζo is a channel shape factor depending upon the aspect ratio. Equation (1) can be solved numerically or analytical solutions to 3,4 approximate forms can be used . For capillary rise in the long time limit, the inertial term (left hand) can be ignored and eq. (1) can be integrated to give the 4 visco-gravitational solution :

t=−

⎛ ab ⎛⎜ x x ⎞ ⎞ + ln⎜⎜1 − ⎟⎟ ⎟⎟ 2 ⎜ g ⎝ xe ⎝ xe ⎠ ⎠

(3) -2

where the equilibrium height is xe=b/g and g=9.81 ms . For plane parallel (“smooth”) walls, capillary rise followed the same trend as with capillary tubes. However, over time the meniscus was preceded by fingers of corner-running liquid along the internal corners defined by where the bottom of the channel 3,5 and a side wall meet .

Fig. 2: Effect of increased wall area (“roughness”) on the rise of main meniscus in open channels (W=600mm and H=130 mm. The inset shows the wall design (viewed from above the channels). The average volume for flow within the channel was kept constant.

Abstract #020

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The rise of the main meniscus followed a curve described by eq. (1) (Fig. 1). Observed equilibrium heights were smaller than predicted probably due to the corner-running liquid fingers. Eq. (1) and eq. (3) could be fitted to the data using parameters (a, b, to); rise rate was slower than predicted due to a dynamic contact angle in the initial phase of capillary rise. When the walls were parallel but saw-tooth shaped (“rough”) (Fig. 2 inset), the main meniscus could still be fitted to eq. (1) (also eq. (3)) (Fig. 3). The observed equilibrium height increased with increasing roughness (i.e. surface area for capillary pull) as expected. Increasing wall roughness also decreased the prominence of the corner-running fingers (Fig. 3).

600µm wide open channels with gradually decreasing roughness factor (r=3, 1.6, 1.4, 1.2 and 1 from left to right). In summary, capillary-driven imbibition into “smooth” open rectangular channels has been studied and compared to theory. “Rough” walls are found to increase the capillary pull and reduce corner-running fingers. References [1] Lucas, R., Kolloid Z 23, pp.15-22 (1918). [2] Washburn, E. W., Physical Review 17, pp. 273-283 (1921). [3] Ouali, F. F., McHale, G., Javed, H., Trabi, C., Shirtcliffe, N. J., and Newton, M. I., accepted Micro- Nano-fluidics (2013). [4] Fries, N., and Dreyer, M., Journal of Colloid and Interface Science 320, pp. 259-263 (2008); 327, pp. 125-128 (2008). DOI 10.1007/s10404-013-1145-5 [5] Bico, J., and Quéré, D., Journal of Colloid and Interface Science 247, pp. 162-166 (2002). Acknowledgments The authors’ acknowledge financial assistance from Engineering and Physical Sciences Research (EPSRC Grant No. EP/E063489/1). HJ would acknowledge Nottingham Trent University for support for a PhD.

the U.K. Council like to financial

Fig. 3: Different stages of flow of PDMS oil 98.6 mPas in

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SUPERSPREADING OF TRISILOXANE SURFACTANT SOLUTIONS – SCIENTIFICALLY FASCINATING AS WELL AS INDUSTRIALLY RELEVANT Joachim VENZMER Evonik Industries AG, Goldschmidtstr. 100, 45127 Essen, Germany. E-mail: [email protected]

In many industrial applications, wetting and spreading phenomena can be explained by simple concepts such as Young’s equation. This also holds true for most silicone surfactants, although they are somewhat special because of their exceptionally low surface tension and their surface activity even in oil-based systems. However, there is a class of trisiloxane surfactants called superspreaders which exhibit a quite peculiar behaviour on hydrophobic substrates: Their dilute aqueous solutions wet out completely (Fig.1C). Other, structurally quite similar trisiloxane surfactants do not show this “active” spreading process, but only a reduction of contact angle like it is to be expected from standard surface tension-reducing agents (Fig.1B). This fascinating phenomenon is being discussed in the scientific literature for more than 20 years now. Despite considerable efforts in several laboratories around the world, the mechanism of superspreading has not been fully elucidated yet [1]. This contribution will give an overview of the most important findings concerning the mechanism of superspreading from an industrial perspective. Whereas in academia the emphasis is more on the scientific proof of mechanisms and theoretical models, the main focus in industry is to develop hypotheses

32

which are able to explain the phenomena encountered during the practical application of superspreading surfactants. It will be demonstrated how the chemical structure, the phase behaviour and the spreading performance are related. In addition, by applying the physicochemical principles which have been shown to be crucial for superspreading, attempts to develop organic surfactant blends exhibiting similar properties as trisiloxane surfactants will be discussed.

Fig. 1: Photos taken 1 min after placing a 50 µL droplet onto PP; (A) water; (B) non-superspreading trisiloxane surfactant; (C) superspreading trisiloxane surfactant. References [1] Venzmer J., Superspreading – 20 years of physicochemical research, Curr. Opin. Colloid Interf. Sci. 16, pp. 335-343, 2011.

Abstract #025

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IMPINGEMENT DYNAMICS OF WATER DROPS ONTO FOUR GRAPHITE MORPHOLOGIES: FROM TRIPLE LINE RECOIL TO PINNING Paola G. Pittoni and Shi-Yow Lin* Department of Chemical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan E-mail: [email protected]

Impingement of liquid droplets onto dry surface substrates is a complex process that encompasses fluid dynamics, physics, and interfacial chemistry. Sundry parameters, such as drop size, impact velocity, liquid viscosity, surface tension, addiction of surfactants, and substrate morphology have been found intensely influencing the droplet impacting and spreading processes [1]. The aims of this study was analyzing the triple line dynamics, such as pinning, depinning or free triple line movements, during the spreading and the retraction phases of the drop impact, focusing especially on the influence of the substrate surface morphology. For this purpose, four different graphite substrates with very specific surface topographies (Figure 1) were prepared [2], and droplet impingement experiments at low Weber number (We=7.61) were conducted. A similar apparatus of the droplet impingement system and measurement technique detailed in Wang, et al. [3] was used in this work. We then analyzed in detail the wetting behavior for pure water droplets impacting onto these four unlike graphite substrates. During the initial phase (up to t=~2ms), understood to be a totally inertial dominated regime during which viscous and surface tension forces are negligible, all the drops revealed the same behavior, achieving their maximum wetting diameter after the spreading phase (Fig.2 a, d). In these first instants, all the drops were observed generating a shoulder region, which wetted and advanced horizontally on the solid surfaces, and then assuming a rim-like region while the process continued. Although this phase was still inertially dominated, the maximum spreading diameter and the law governing the triple line position were not completely independent of the surface morphologies: a higher maximum wetting diameter was observed for graphite-90° and graphite-120° and decreased increasing the surface hydrophobicity. Moreover, after the first two milliseconds, the drops were observed spreading faster onto less hydrophobic surfaces than superhydrophobic surfaces. These different spreading behaviors could be explained by the viscous dissipations being amplified when increasing the substrates roughness. At t=3~4ms, the spreading phase ended and the different substrates started showing distinct behaviors (Fig.2 b, e). The morphologies characterized by a generally smooth surface with the presence of random cavities, namely

Fig. 1: SEM analysis of the four substrates characterized by different advancing water contact angles (θa): 90°, 120°, 140°, 160°, and unlike topographies. Graphite-90° (a, b) exhibits a predominantly smooth morphology typified by the presence of random deeper cavities. Graphite-120° (c, d) shows a generally mid-rough surface featured by the presence of irregular hollows. Graphite-140° (e, f) reveals the existence of a micron-scaled roughness. Graphite-160° (g, h), in addition to the micron-scaled topography, presents a nano-scaled roughness.

graphite-90° and graphite-120°, clearly presented a pinned behavior with the wetting diameter remaining constant (Fig.2 b, c). The irregular edges of the cavities, clearly visible in the SEM analysis (Fig.1 a, b, c, d), stopped the movement of the triple line and the drop remained fixed on these random defects, as modeled by Ramos and Tanguy [4]. On the contrary, the superhydrophobic graphite-160° showed a clear recoil phase with the wetting diameter decreasing monotonically with time and the drop assuming an oblong dull shape (Fig.2 e, f). The surface characterized by 140° advancing contact angles revealed a mixed behavior. Until t=~4ms the wetting diameter decreased monotonically, exhibiting an initial recoil phase. However, from t >~4ms, the drop

Abstract #030

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was observed to be pinned on the surface, assuming a cone-like shape. This change in behavior could be explained by a transition from Cassie-Baxter to Wenzel state, which the drop underwent [5]. This transition was probably due to the air trapped by the micro-scaled roughness being pushed away during the impact. The contact area increase due to this Wenzel state significantly raised the adhesion and prevented the triple line from retracting, so that the drop remained pinned. Due to its double micro- and nano-scaled roughness, the said transition did not appear for graphite-160° surface where a certain amount of air remained trapped by the nano-scaled roughness, maintaining the Cassie-Baxter state. X (mm) 1

4 50 Y (mm)

15 20 25 30

50

X (pixel)

X (mm)

80

15

1 20

e

60

Y (mm)

Y (pixel)

50

X (pixel) 59

2

47

3

41 35

23

30

35

80

4 X (mm)

53

3

40

3

20 23

4

60 55 50 45

4

10

X (pixel)

b

60

2

1 5

20

1 20

X (mm)

2

X (pixel)

Y (pixel)

10

20

d

3

5

Y (mm)

2

Y (mm)

a 50

29

30

20

1 20

50

0

4

X (pixel)

1

80

t (ms)

20

8

140

80

t (ms)

8 3

1 30

t (frame)

60

2

H (mm)

1

1

1

100

0

30

t (frame)

In summary, the analysis of the dynamic behaviors of water drops impacting and spreading at low Weber number on four distinctive graphite surfaces was conducted and the relations between the movements of the triple line and these specific substrates morphologies were investigated. During the initial phase, understood to be a totally inertial dominated regime in which viscous and surface tension forces are negligible, all the drops revealed almost the same behavior. At the end of the spreading phase, the drop impacting onto different substrates started showing distinct behaviors and three different trends were found: a pinned behavior for smooth surfaces with the presence of random cavities (graphite-90° and graphite-120°); a free triple line recoil for superhydrophobic surfaces (graphite-160°), characterized by a double micro- and nano-sized roughness; and, finally, a mixed free-recoil/pinned behavior, due to a transition from Cassie-Baxter to Wenzel state, for hydrophobic surfaces (graphite-140°), characterized by a micro-sized roughness.

3

Dw (mm)

angle (o )

Dw (mm)

3

H (mm) angle (o )

120

0

X (pixel)

4

f

c

20

50

0

the peculiar pinning due to random surface defects, which we just described in this study, is conceptually completely different. In fact, while the graphite-90° pinning was observed just for these peculiar substrates morphologies at low Weber numbers (or during rather slow dynamic processes as evaporation), the transition from Cassie-Baxter to Wenzel state was observed just for precise Weber numbers, and, specifically, during experiments conducted at higher impact velocities.

60

Fig. 2: Illustrations of the droplet shape, wetting diameter (Dw), drop height (H), and contact angle during the spreading onto the graphite surfaces characterized by the 90° (a, b, c) and 160° (d, e, f) contact angles, from frame 1 to 30 (a,d), and from frame 30 to 60 (b, e). The numbers indicate the sequence of the images after the impact.

From this analysis, it was evident how deeply distinctive graphite morphologies were critical factors for understanding and foreseeing different dynamics of the three phases contact line. Even though pinned behaviors due to random surface defects has been already analyzed theoretically and experimentally in literature, during evaporation or forced wetting experiments, to the best of our knowledge, it was the first time that this peculiar pinned state was described for an impinging droplet, and thus observable even during highly dynamic processes and small time scales.

References [1] Yarin A.L., Drop impact dynamics: splashing, spreading, receding, bouncing, Annu. Rev. Fluid Mech., 38, pp. 159-192, 2006. [2] Hong S.J., Li Y.F., Hsiao M.J., Sheng Y.J., Tsao H.K., Anomalous wetting on a superhydrophobic graphite surface, Appl. Phys. Lett., 100, pp. 121601.1-121601.4, 2012. [3] Lin S.Y., Chang H.C., Lin L.W., Huang P.Y., Measurement of dynamic/advancing/receding contact angle by video-enhanced sessile drop tensiometry, Rev. Sci. Instrum., 67, pp. 2852-2858, 1996. [4] Ramos S., Tanguy A., Pinning-depinning of the contact line on nanorough surfaces, Eur. Phys. J. E, 19, pp. 433-440, 2006. [5] Chen L., Xiao Z., Chan P.C.H., Lee Y.K., Li Z., A comparative study of droplet impact dynamics on a dual-scaled superhydrophobic surface and lotus leaf, Appl. Surf. Sci., 257, pp. 8857-8863, 2011. [6] Wang Z., Lopez C., Hirsa A., Koratkar N., Impact dynamics and rebound of water droplets on superhydrophobic carbon nanotube arrays, Appl. Phys. Lett., 91, pp. 023105.1-023105.3, 2007. [7] Tsai P., Pacheco S., Pirat C., Lefferts L., Lohse D., Drop impact upon micro- and nanostructured superhydrophobic surfaces, Langmuir, 25, pp. 12293-12298 , 2009.

It is also noteworthy that, despite the fact that the pinning characterizing graphite-140°, which is due to the transition from Cassie-Baxter to Wenzel state, has been already investigated in previous droplet impinging works for different superhydrophobic substrates [6, 7], Abstract #030

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WETTING OF SURFACES: AS INVESTIGATED BY 1H NUCLEAR MAGNETIC RESONANCE Totland┴ C, Lewis┴ RT, Steinkopf§ SL, Nerdal┴* W

┴

§

Department of Chemistry, University of Bergen, Allégaten 41, Department of Biomedical Laboratory Science, Bergen University College, N-5007 Bergen, Norway. E-mail: [email protected]

The properties of water in the vicinity of a surface are important in a wide range of phenomena in nature and knowledge about these is useful in many different areas of research. In medicinal research such information can be valuable as cellular water is associated with the cell membrane, and also the stability and dynamics of biological macro-molecules such as proteins largely depend on adsorbed water. Furthermore, information about liquid interactions with a solid surface is important in order to understand and improve the transport of fluids in porous media, such as oil and water in reservoir rocks. Despite numerous NMR studies, uncertainty still exists about properties of water in the vicinity of a solid surface. This is primarily due to the complex nature of the H-bonded water structure which is affected by both the solid matrix geometry and the properties of the solid surface. Due to the complexity, water is often treated as a neutral and non-interactive carrier when explaining surface behaviour and adsorption phenomena of different molecules, such as surfactants adsorbed on mineral surfaces or drugs interacting with a cell membrane. Therefore, the realization of water as a key factor is important to improve the current state of knowledge in such complex systems. However, molecular level details concerning adsorbed molecules, especially water, are difficult to obtain experimentally. Here we study water adsorbed on solid surfaces and how addition of the amphiphile molecule 1-heptanol affects the water properties at the silica surface, as well as how a carboxyl acid, an alcohol or crude oil affect adsorbed water on sandstone. Both grinded sandstone and colloidal non-porous silica particles (40 nm average diameters) were used in this study, because these represent both a realistic and a more idealistic environment, respectively. Information on molecular dynamics can be obtained from relaxation measurements. Characteristics of the liquid molecules and the solid surface produce an anisotropic environment for the molecular motion that influences the T1 relaxation and the corresponding Arrhenius relationship of the molecular correlation time. NMR spin-spin relaxation (T2) measurements are sensitive to surface interactions of the liquid molecules and can give information on molecular dynamics of a shorter time scale than spin-lattice relaxation. Immobilized liquids, such as water and hydrocarbons adsorbed on a rock surface will display solid-like NMR spectral features with considerable resonance broadening. This occurs due to insufficient molecular tumbling for achieving isotropic averaging of dipolar couplings as well as resonance broadening due to magnetic susceptibility mismatch between rock surface and fluid.

The silica particles used in this study have a high chemical purity making them suited for a homogeneous sample. In long-range-ordered media, where the dipolar interaction is not averaged out by fast molecular motions, the fine structure of the water proton resonance can be a doublet spaced around the water chemical shift. In such studies observation of the proton resonances as ”Pake” doublets will reveal further information about the water properties. In addition to the necessary restrictions in molecular mobility, such a doublet also confirms presence of somewhat isolated water molecules in the sample. When water and 1-heptanol are interacting with saturated colloidal and 1 non-porous silica particles the H NMR spectra reveal molecular details of the interaction [1]. Similarly, a water film in between glass plates and sand stone wetted with water as well as wetted with water after an initial wetting with heptanoic acid, 1-heptanol or crude oil can display spectral features originating in the interactions of the liquid(s) with the solid surface. Silica samples with a SiO2/liquid ratio (w/w) of 1.5 ± 0.2 were prepared by mixing silica particles with an excess of liquid in a sample tube. These silica particles were hydrated with either high purity water, water with dissolved 1-heptanol, or 1-heptanol (98 %, Sigma-Aldrich), referred to as the silica/water, silica/water/1-heptanol and silica/1-heptanol sample respectively. The 1-heptanol solubility is about 1 g/L in water, giving a total of about 1 ‰ 1-heptanol in the water/1-heptanol solution used. The samples were then equilibrated at 303 K for five days, and excess liquid was removed by high speed centrifugation at 18000 rpm. The centrifugation was repeated until no further liquid could be removed from the samples. Finally the samples were packed into 4 mm ZrO2 MAS (Magic Angle Spinning) rotors. Samples containing sandstone with water and heptanoic acid, heptanol or crude oil are prepared in a similar way, but with an equilibration temperature of 318 K. All NMR experiments were carried out on a Bruker Advance 500 Ultrashield spectrometer operating at 500 MHz for protons, with a 1 variable temperature control accurate to ± 0.2 K. H NMR experiments on non-spinning (static) samples were carried out in a MAS probe head or in a flat coil probe head. In order to get resolved spectra, relaxation measurements on the silica/1-heptanol sample were carried out using a MAS spinning rate of 5 kHz. The resolved spectra made it possible to measure T1 relaxation of each individual resonance from the 1-heptanol molecule. The pulse sequence used for the T2 measurements is not selective to any resonance and gives an average relaxation value for the molecule as a whole.

Abstract #035

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Recorded proton spectrum

Simulated proton spectrum

10

5

0

-5

[ppm ]

1

Fig. 1: Recorded (top) and simulated (middle) H NMR spectra of a thin film of water between glass plates in a stack 2 of eight 0,75 cm plates. The top spectrum is recorded using a flat coil probe head. The two bottom simulated spectra show the individual peaks that make up the combined simulated spectrum (number three from the bottom). 1

Fig. 1 shows H NMR spectra of thin films of water between glass plates.

258 K

-2.5

0 Frequency (kHz) 2.5

278 K

273 K 263 K 260 K

-2.5

0 Frequency (kHz)

2.5

258 K

Fig. 2: Spectra of the silica/water/1-heptanol sample at various temperatures. Both the signal intensity and Δv1/2 are constant down to 263 K with an average value of Δv1/2 = 1160±15 Hz. Enlargement of the water peak at 258 K reveals a Gaussian lineshape. The position of the isotropic chemical shift was normalized to unity in all the spectra. 1

H NMR spectra of the Fig. 2 shows silica/water/1-heptanol non-spinning (static) sample at various temperatures. The silica/water/1-heptanol sample shows that the resonance intensity is constant down to 263 K in Fig. 2 and at 260 K the resonance intensity is reduced by 89% and at 258 K by 99.6 % compared to the resonance intensity at 278 K. This indicates that about 90% of the water molecules in the 36

silica/water/1-heptanol sample have similar properties and freeze at about 260 K. The free surface energy of water molecules in the vicinity of the surface/water interface may be reduced further due to adsorption interactions, and might explain why ~10% of the water freezes at temperatures below 260 K. Regarding the sand stone samples wetted with water as well as wetted with water after an initial wetting with heptanoic acid, 1-heptanol or crude oil show significantly reduced water mobility in presence of one of the three mentioned compounds in that a tenfold increase in the 1 H NMR linewidth of water is found. In the case of adsorbed water the system apparently consists of water in two different environmental states (data not shown), one “bound” water layer and another layer further from the silica surface. Water molecules in both environments give rise to a Pake doublet, thus implying reduced intermolecular interactions and a non-random orientation of the water molecules in both states. Dissolving 1 ‰ 1-heptanol in the water prior to adsorption on the silica surface (Fig. 2) reduces the differences in relaxation rates between water in the two environments at the silica surface. Furthermore, presence of 1-heptanol seems to primarily affect the water molecules in the adsorption layer closer to the surface, where the water molecules experience reduced translational freedom accompanied by increased rotational freedom. However, a 35 % increase in linewidth compared to the silica/water sample resonance indicates an overall reduced mobility of the sample water when 1 ‰ 1-heptanol is present. 1 H NMR spectra of thin films of water between glass plates suggest a possible hypothesis on the origin of the two peaks at about 4.7 ppm and at 1.5 ppm. They could correspond to the chemical shift of ordinary h-bonded water and to a different surface induced water structure, respectively [2]. The low chemical shift of the latter suggests that the electronic density around the two proton nuclei in water is significantly enhanced. 1 Further H NMR experiments of thin films of water between glass plates with various amounts of hydrophobic as well as hydrophilic compounds are in progress. Similarly, NMR experiments to detect a possible altered wettability of sand stone initially exposed to heptanoic acid, 1-heptanol or crude oil with time are carried out. References [1] Totland C., Steinkopf S.L., Blokhus A.M., Nerdal W. Water structure and dynamics at a silica surface: Pake doublets in 1H NMR spectra, Langmuir 27, pp. 4690-4699, 2011. [2] Gun´ko V.M., Turov V.V., Bogatyrev V.M., Zarko V.I., Leboda R., Goncharuk E.V., Novza A.A., Turov A.V., Chuiko A.A., Unusual properties of water at hydrophilic/hydrophobic interfaces, Adv. Colloid Inter. Sci. 118, pp. 125-172, 2005.

Abstract #035

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EFFECT OF ANIONS AND CATIONS ON THE SURFACE TENSION AND WETTING BEHAVIOR OF IONIC LIQUIDS S.N. Asare-Asher*, J.N. Connor and R. Sedev Ian Wark Research Institute, University of South Australia, Mawson Lakes, SA 5095, Australia E-mail: [email protected]

Ionic liquids (ILs) are organic salts with low melting o points (below 100 C) [1]. They are made up of organic cations and organic or inorganic anions. Commonly used cations are usually asymmetric and large. ILs are known to have negligible vapour pressures and therefore they are suitable for situations where any detectable volatility of the solvent is undesirable[2]. ILs are chemically diverse and it is important to know how different combinations of anions and cations affect their properties. With the emergence of ionic liquids as new solvents and as suitable replacement for conventional liquids (eg in synthesis and catalysis)[2], there is a need for fundamental studies of how they interact with common solid surfaces[3]. Three groups of ionic liquids were studied based on their composition: (i) ILs with the same NTf2 anion but varying alkyl chain length of the imidazolium cation (Cnmim.NTf2), (ii) ILs with the same NTf2 anion but varying cations (X.NTf2) and (iii) ILs with the same C4mim cation but varying anions (C4mim.X). The surface tension of the ionic liquids and their contact angles on three common polymer surfaces: (i) Teflon AF1600 (AF1600) (ii) Polystyrene (PS) and (iii) Polymethylmethacrylate (PMMA) were measured. It was observed that both anions and cations have similar contribution towards the overall surface tension of the IL and its wetting behaviour. This study improves the understanding of how ILs composition affects their surface and interfacial energies and also gives useful information for applications where interfacial properties play a significant role. Surface tension (ST) is the reversible work per unit area to increase the surface. For liquids, their fluidity makes the measurement of surface tension easy as stretching creates a new surface. Solids however are structured; their atoms occupy fixed positions in their lattice. Stretching causes re-orientation of the atoms in their lattice, and it may take a very long time for the solid to equilibrate. The surface energy (SE) of a solid is therefore different from its ST (unlike liquids) because its bulk property differs from the surface properties. For solids, the contact angle measurement is a basic measure of the wetting behaviour with a given liquid. Similar liquids wet or do not wet different surfaces depending on their varying surface energies. The contact angle (CA), depends on the interfacial tensions at the three-phase contact at a solid-liquid-vapour junction (Young’s equation). Surface roughness, surface heterogeneity (by design or by contamination), evaporation, adsorption and surface reorientation, may obscure the measurement of the SE of a solid. The above notwithstanding, using a series of probe liquids (often homologous alkanes) and extrapolating the results to complete wetting (contact

angle of zero) gives an empirical way to estimate a characteristic of the solid surface called critical surface tension (CST). Zisman and co-workers estimated the critical surface tension of many polymers using this method[4]. The modern theory of surface tension components (Good et al.[5]) postulates that the surface tension is a sum of the van der Waals (non-polar) and the acid-base (polar) interactions between the solid and the liquid. The choice of probe liquids is therefore extremely important and common organic solvents offer a rather limited choice. Complications of wetting behaviour on solid surfaces will be reduced as ILs practically do not evaporate. The Cnmim.NTf2 group had increasing alkyl chain length of the imidazolium cation from 2, 4, 6 and 10 carbon atoms (purchased from IoLiTec). The anions, denoted by X, combining with the C4mim cation were OS, NTf2, FAP, PF6, BF4 and DCA (obtained from Merck). The cations, X, in the X.NTf2 group were N8881, P14666, Hpy, and C4mpyr (Merck). All liquids were used as obtained. The ST of the ILs was measured using the Wilhelmy plate method at 25 °C. For the wetting studies, Teflon AF1600 was chosen because of its low SE and the non-polar interactions it shows with liquids. PS and PMMA have relatively higher SEs and show both polar and non-polar interactions with liquids. In preparing the polymer surfaces, AF1600, PS, and PMMA were dissolved in Fluorinert (FC-75), toluene and acetone respectively. The polymers solutions were spin coated onto clean glass slides. The coated glass slides were then dried to remove residual solvent in an oven. Wetting behaviour of the various groups of ILs on the polymers was studied by depositing small amounts of the ILs (groups (I) and (iii)) on the polymer surfaces. The receding and advancing static contact angles of the ILs were measured from side profile pictures. The ST of the Cnmim.NTf2 group decreased with increasing the value of n. The value of the surface tension of this group and all the ILs with longer alkyl chains approached the value of the ST of the longest chain liquid alkane (hexadecane, ST = 28 mN/m). For the C4mim.X group of ILs the ST increased in the order OS Mt, the behavior changes drastically: It is then governed by Marangoni flow, and unexpected phenomena like noncoalescence of sessile drops can be observed. References [1] H. Riegler, P. Lazar, Delayed coalescence behavior of droplets with completely miscible liquids, Langmuir 24, pp. 6395-6398 (2008). [2] S. Karpitschka, H. Riegler, Quantitative experimental study on the transition between fast and delayed coalescence of sessile droplets with different but completely miscible liquids, Langmuir 26, pp. 11823-11829 (2010). [3] S. Karpitschka, H. Riegler, Noncoalescence of droplets with different miscible liquids: Hydrodynamic analysis of the twin drop contour as self-stabilizing travelling wave, Phys. Rev. Lett. 109, pp. 066103 (2012). [4] A. Leenaars, J. Huethorst, J. van Oekel, Marangoni drying: a new extremely clean drying process, Langmuir 6, pp. 1701-1703 (1990). [5] J. Marra, J. Huethorst, Physical principles of Marangoni drying, Langmuir 7, pp. 2748-2755 (1991). [6] O. Matar, R. Craster, Models for Marangoni drying, Phys. Fluids 13, pp. 1869-1883 (2001). [7] M. Sellier, V. Nock, C. Verdier, Self-Propelling coalescing drops, Int. J. Multiphase Flow 37, pp. 462-468 (2011).

Abstract #094

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STATIC AND DYNAMIC PROPERTIES OF NANOMENISCI

Dupré de Baubigny Julien a,b, Buchoux Julien c, Delmas Mathieu a, Legros Marc a, Aimé Jean-Pierre c, Ondarçuhu Thierry a a

CEMES – CNRS 29 rue Jeanne Marvig BP 94347 31055 TOULOUSE Cedex 4 b INSA Toulouse 135 avenue de Rangueil 31077 Toulouse Cedex 4 c CBMN UMR 5248 allée de St Hilaire Bât B14 33600 Pessac E-mail: [email protected]

Fluid properties at the nanometer scale are an emerging field. Fundamental questions have been raised for a long time, but modern techniques of microscopy give now the opportunity to probe the physical properties of liquid interfaces at the nanometer scale [1]. One of the main issue concerns the structure and the dynamics of meniscus near the contact line which controls the dynamics of spreading, and more generally nanofluidics. The physics of nanomenisci is also an inherent issue to AFM imaging under ambient condition. The method we used is to dip an unconventional tip of an atomic force microscope (AFM) (carbon nanotube, nanocylinder) at the free interface of a liquid. This geometry allows to investigate properties of nanometric size meniscus and the behaviour of the liquid close to the contact line (Fig. 1a). Static results have been obtained with low stiffness AFM cantilever on which is attached a carbon nanotube [2]. Capillary force measured gives access to the contact angle, and the static spring constant of the meniscus. It also allows us to investigate anchoring of liquid on individual nanometer defects at the surface of the nanotube, mechanism behind contact angle hysteresis [3].

(a)

(b)

(a)

(b)

(c)

Fig.1: (a) Sketch of the experiment dipping nanosized carbon tip into a liquid interface. (b) Different contributions of dissipation during oscillation into the liquid.

We extend the measurements to dynamic processes using the oscillating AFM frequency modulation mode (FM-AFM) implemented on a Bruker Picoforce microscope equipped with a phase lock loop module (EasyPLL – Nanosurf). The tips used are nanocylinders with diameter ranging from 15 nm to 55 nm (Team Nanotec) or cone nanotube (homemade). The tip is dipped in and withdrawn from a liquid bath or droplet (ranging from 20 µm to 3 mm diameter) with a constant -1 velocity of the order of 1 µm.s . In order to avoid 58

evaporation issues we used ionic liquids (Solvionic). This mode gives different information which allows a systematic study of nanomeniscus and contact line dynamics. An example of curves obtained simultaneously with a 35 nm nanocylinder and 3 different oscillation amplitudes is reported in Fig. 2.

Fig. 2: Data curves obtained by FM-AFM with a 35 nm cylindrical tip dip into an ionic liquid. (a) Cantilever deflection as a function of tip position; (b) frequency shift; (c) dissipation signal. In black: static mode; in color: frequency modulation mode with a forced oscillation of 7 nm (red), 14 nm (blue), 21 nm (green). Insert: SEM image of the tip, scale bar: 400 nm.

- The deflection of the cantilever gives the capillary force exerted by the liquid (Fig. 2a) It provides local information on the contact line [4]: contact angle hysteresis, pinning on defects [3]. - Measurements of the frequency shift (Fig. 2b) are

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directly related to the effective stiffness of the meniscus, and inform us about its elastic properties. Interestingly, the dynamic meniscus spring constant is systematically larger than the static one, which may result from a new characteristic size, the thickness of the viscous layer δ (Fig. 1b), which plays a key role in oscillating regimes [5]. - The dissipation signal (Fig. 2c) is directly related to dissipative processes at work during the tip oscillation [6]. A precise analysis of the curves allows to evaluate the contributions coming from the viscous layer (slope), the nanomeniscus (z=0) and those from anchoring defects (peaks). Using different tips, we observe different behaviours depending on the pinning of the contact line on the tip. An interesting situation is provided by carbon nanotips which allow to investigate the dynamic of pinning on individual nanometric defects, mechanism which is largely unknown. This range of behaviours may allow to assess the different sources of dissipation considered in the models of dynamic of wetting: Cox-Voinov, De Gennes, molecular kinematic, etc. Systematic studies are performed for different liquids (alcanes, water, glycerol, ionic liquids), and tips (cylinders of different diameters, needles, carbon

nanotubes) to get a full picture of the static and dynamic properties of nanomeniscus and the basic mechanisms in the vicinity of the contact line which control the dynamic of spreading. Acknowledgements: this work is partially supported by the Laboratory of Excellence NEXT, the Train² project and the ANR project CANAC. References [1] Ondarçuhu T., Aimé J.P. Eds., Nanoscale liquid interfaces, Pan Stanford Publishing, 2013. [2] Allouche H., Monthioux M., Chemical vapor deposition of pyrolytic carbon on carbon nanotubes, Carbon, 43 (6), pp. 1265-1278, 2005. [3] Delmas M. Monthioux M., Ondarçuhu T., Contact Angle Hysteresis at the Nanometer Scale, Phys. Rev. Lett., 106 (13), pp. 136102, 2011. [4] Fabié L., Durou H., Ondarcuhu T., Capillary Forces during Liquid Nanodispensing, Langmuir, 26 (3), pp. 1870-1878, 2010. [5] Landau L., Lifshitz E., “Course of theoretical physics: fluid mechanics”, Elsevier Ltd, Oxford 1987. [6] Jai C., Aime J.P., Mariolle D., Boisgard R., Bertin F., Wetting an oscillating nanoneedle to image an air-liquid interface at the nanometer scale: Dynamical behavior of a nanomeniscus, Nano Lett, 6 (11), pp. 2554-2560, 2006.

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1st Int. Workshop on Wetting and evaporation: droplets of pure and complex fluids Marseilles, France, June 17th to 20th, 2013

WETTING OF A CARBON NANOTIP: CONTACT ANGLE HYSTERESIS AT THE NANOMETER SCALE

Thierry Ondarçuhu, Mathieu Delmas, Julien Dupré de Baubigny, Marc Monthioux Nanosciences group, CEMES-CNRS 29, rue Jeanne Marvig, 31055 Toulouse (France), E-mail: [email protected]

Whereas thermodynamics predicts that the contact angle of a liquid droplet at rest on a solid surface is given by the Young-Dupré equation, experiments on real solid surfaces show that this contact angle is not univocal but depends on the droplet history, resulting in a contact angle hysteresis (CAH). Despite many theoretical and experimental studies devoted to this problem, a quantitative correlation between contact angle hysteresis and surface defects shape or repartition is still lacking. Since topography at molecular level and very small densities of defects are sufficient to create appreciable CAH, a precise description of the pinning on individual defects, down to nanometer scale, is essential to fully describe the mechanisms responsible for the occurrence of the CAH. We developed an original method to address this challenging issue [1]. We measured by atomic force microscopy (AFM) the capillary force exerted by the liquid on a carbon nanoneedle, in a nanoscale replica of the classical Wilhelmy balance technique (Fig. 1a) [2]. The structure of the nanocone tips suits the needs for our study because they present a clean surface with a very small density of defects with sizes ranging from nanometer to tens of nanometers. Moreover, the quasi-1D geometry of these nanoneedles is well adapted to probe individual nanometric defects. (a)

(b)

Fig. 1: (a) Sketch of the experiment: a carbon nanotip is dipped in a liquid interface. The capillary force F measured by AFM is recorded as a function of the tip displacement z during extension and retraction of the piezoelectric element, corresponding to advancing and receding contact lines, respectively; (b) Example of force curve measured with a nanocone tip with a 120 nm long nanotube protruding at its extremity. The extension and retraction curves are represented, showing localized hysteresis cycles.

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The carbon tip was positioned above a microdroplet (20-100µm in diameter) and carefully lowered using the step motor of the AFM. A sudden attractive force indicated the contact of the tip with liquid and the creation of a liquid nanomeniscus around the tip extremity [3]. The tip/liquid interaction was measured during extension-retraction cycles of the piezoelectric tip support with defined amplitude (ranging from 50 nm to 5µm) and velocity (from 10 nm/s to 1 µm/s). The accuracy of force measurement was about 5 pN. An example of force curve is reported in Fig. 1b, in the case of the tip shown in Fig. 1a dipped in heptadecane. For easier comparison with models, the attractive force due to the meniscus is considered as positive. After contact with the liquid interface (z ≥ 0), a short plateau corresponding to the cylindrical nanotube is observed. The force then increases as soon as the contact line reaches the conical part of the needle. When tip motion is reversed, the force curve follows approximately the same path, both on the conical and nanotube portions. An increase of the force is always observed at the end of the curve for negative z value. It is characteristic of the meniscus stretching when the contact line is pinned at the tip extremity before snap off [2]. The main features of the force curve can therefore be interpreted by comparing with the needle shape. The curve reported on Fig. 1b is rather different from a typical experiment with a Wilhelmy balance for which advancing and receding curves are clearly separated, allowing a determination of advancing and receding contact angles. In our case, advancing and receding curves are superposed on portions of the nanoneedle surface and hysteresis cycles only appear locally. We attributed these cycles to the pinning of the contact line on individual (or a small number of) defects of the tip surface. In the geometry we used, the contact line is only a few tens of nanometers in length. The surface can thus be perfectly defined at this length scale, leading to portions with no hysteresis. The other advantage is that this short contact line can only interact with one or a small number of defects at once. An interesting situation is shown on Fig. 2a which corresponds to a zoom on a force curve (tip motion amplitude 100 nm). Two qualitatively different behaviors are evidenced. On the right part of the curve (z > 50 nm), a modulation of the force amplitude gives rise to a hysteresis cycle between the advancing and receding curves. On the contrary, on the left part, a smaller modulation of the force without any noticeable difference between both curves is observed. This latter case demonstrates that not every surface defect does

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1st Int. Workshop on Wetting and evaporation: droplets of pure and complex fluids Marseilles, France, June 17th to 20th, 2013

necessarily induce a CAH. Some defects induce a local change in the contact angle whose related force is fully reversible.

(a)

(b)

Fig. 2: (a) Zoom on a portion of the force curve where the contact line interacts with two defects with different natures, and calculated force curve for two different gaussian defects. (b) Plot of the dissipated energy W as a function of the defect force F0; inset: schematic representation of the pinning on a strong defect, in the simplified model. k is the spring constant of the meniscus.

Since it was established early that the CAH originates in the pinning of the CL on surface defects, the single defect situation attracted much attention. A pioneer paper by Joanny and de Gennes described the case as a balance between the elastic response of the CL and the force due to a local heterogeneity of the surface (assumed gaussian) [4]. Two cases can be distinguished depending on the relative values of the line spring constant and the gradient of defect force: (i) in the weak heterogeneity regime, for any tip position, only one equilibrium position of the CL exists. The contact angle is thus locally modified but in a fully reversible way; (ii) on the contrary, for strong heterogeneities, three equilibrium points may exist: the equilibrium point follows two different branches depending on the motion direction of the CL, leading to a hysteresis cycle. Figure 2b shows the expected force curves for two successive Gaussian defects with different forces leading to different situations. Depending on the defect strength, either a reversible modulation (as in the left part of the curve in Fig. 2b) or a hysteresis cycle (as in the right part of the curve in Fig. 2b) is observed. These two situations qualitatively describe the experimental results. The two defects of Fig. 2a therefore correspond to weak and strong defects, respectively, according to Joanny-de Gennes’s definition. To our knowledge, this is the first direct experimental evidence of the weak regime on an individual defect. In order to quantitatively investigate the strong defect regime which is the most frequent situation, we proposed a simplified model for the pinning on single defect. Considering the case of a defect with small dimension and sharp edges where F0 and a are the force and lateral extension of the defect respectively,

2 the dissipated energy per defect is given by W  F0 2k with k the meniscus (or contact line) spring constant. Both the pinning force F0 and the dissipated energy W were measured experimentally as the jump height and the area of the local hysteresis cycle, respectively, for a whole set of different events attributed to individual defects, for various tips dipped in heptadecane. The results evidence a quadratic relationship between W and F0 over 4 orders of magnitude in energy, compatible with the expression given above. The single defect case is therefore quantitatively described by a simple model. Interestingly, this description assuming a hookean elasticity accounts for pinning forces as small as 10 pN and dissipated -20 energies in the range of 10 J. For such values close -21 to the thermal energy kBT = 4.10 J, thermal fluctuations may play an important role. The minimal defect size necessary to obtain hysteresis was estimated by comparing the dissipated energy on the defect to kBT. It leads to a value comparable with the size of liquid molecules, compatible with previous results [5], which explains why it is so challenging to obtain hysteresis-free surfaces.

By its ability to probe the CL response at nanometer scale, the new experimental procedure we propose may open the way to systematic studies of the elementary processes occurring at the contact line during liquid spreading. It is important to extend our study to dynamic processes whose investigation should be possible by using dynamic AFM modes. In particular, the mechanisms of dissipation associated with the contact line motion, which remain largely unknown, are available with the frequency modulation FM-AFM mode [6]. Preliminary results will be presented. Acknowledgements Financial support by the ANR programs HD-Strain and CANAC, the CNRS specific support for technology transfer and by the LABEX NEXT are acknowledged. References [1] M. Delmas, M. Monthioux and T. Ondarçuhu, Contact angle hysteresis at the nanometer scale, Phys. Rev. Lett., 106, 136102, 2011. [2] A. H. Barber, S. R. Cohen and H. D. Wagner, Static and dynamic wetting measurements of single carbon nanotubes, Phys. Rev. Lett., 92, 186103, 2004. [3] JP Aimé, T. Ondarçuhu, R. Boisgard, L. Fabié, M. Delmas, C. Fouché, Nanomeniscus mechanical properties, in « Nanoscale liquid interfaces », Eds T. Ondarçuhu, J.P. Aimé (Pan Stanford Publishing), pp 307-359, 2013. [4] J. F. Joanny and P.G. de Gennes, A model for contact angle hysteresis, J. Chem. Phys., 81, pp.552-562, 1984. [5] T. Ondarçuhu and A. Piednoir, Pinning of a contact line on nanometric steps during the dewetting of a terraced substrate Nano Lett., 5, pp.1744-1750, 2005. [6] Jai C., Aimé J.P., Mariolle D., Boisgard R., Bertin F., Wetting an oscillating nanoneedle to image an air-liquid interface at the nanometer scale: Dynamical behavior of a nanomeniscus, Nano Lett, 6 (11), pp. 2554-2560, 2006.

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LIQUID NANODISPENSING: A NEW TOOL FOR STUDYING WETTING AT SUB-MICRON SCALE

Thierry Ondarçuhu1, Laure Fabié1, Erik Dujardin1, Julien Arcamone2, Francesc Perez-Murano2 1

Nanosciences group, CEMES-CNRS, 29, rue Jeanne Marvig, 31055 Toulouse (France) 2 CNM-IMB (CSIC), Campus UAB, 08193 Bellaterra ,Spain. E-mail: [email protected]

A liquid nanodispenser, called NADIS, was recently developed to answer the need of deposition techniques for nanosciences [1]. The deposition is realized with an original atomic force microscope (AFM) tip including a nanochannel drilled at its apex by Focused Ion Beam. The liquid transfer is performed by capillarity through this channel during contact of the tip with the substrate (Fig. 1). It has been previously shown that, by tuning the tip properties, the size of the deposited patterns can be controlled down to 70 nm in diameter corresponding -18 to volume in the attoliter range (10 L) [2]. Molecules, nanoparticles or proteins in solution could be patterned, with similar resolution, proving the versatility of this method [3]. Here, we show that, in addition to its interest for surface patterning and molecule deposition, NADIS is a unique tool to probe capillarity and wetting at nanoscale. In particular, we present studies on the dynamics of spreading at sub-micron scale and on the evaporation of femto-droplets.

Fig. 1: (left) Scanning electron microscope image of the apex of a NADIS tips with a 35 nm aperture. (right) AFM image of an array of ionic liquid nanodroplets and schematic representation of the NADIS tip.

We first studied the dynamics of the nano-dispensing process which is ruled by liquid spreading on the substrate [4]. We focused on the two main writing processes used in patterning i.e. spots and lines. The spot deposition was performed by AFM in force spectroscopy mode with imposed maximum contact force (5 nN), vertical tip velocity (1 µm/s) and adjustable contact time. The lines were created by moving the tip on the surface, at controlled velocity (ranging from 0.1 to 580 µm/s), with a nanopositioning table incorporated to an AFM [5]. The AFM close-loop was used to maintain a constant force (5 nN). We showed that both experiments give access to the same spreading dynamics R(t) which is defined over more than three orders of magnitudes in timescale as revealed in Fig. 2, where R-R0(t) is plotted in normal and logarithmic scale, R0 being the radius of the wetted part of the tip which is found to be larger than the aperture size. The two examples shown on Fig. 2, and 62

the other conditions tested experimentally, exhibit a common evolution with two different regimes: at short time scale (less than two second), the feature size follows a power law R-R0~t with α = 0.26 ± 0.04, defined over more than two orders of magnitude. The size then saturates and reaches an equilibrium value which depends on the tip and surface properties. The analysis of the growth mechanism in the NADIS case is therefore a way to study spreading dynamics R(t) with unprecedented spatial resolution (down to 100 nm) and for time values down to milliseconds. α

Fig. 2: (a) R-R0(t) curve for a 760 nm aperture tip before (diamonds) and after (squares) functionalization by dodecanethiol. (b) Same in logarithmic scale. Empty (filled) symbols result from spots (lines) experiments respectively. Solid lines are fit by the proposed model.

In order to interpret this dynamics which was not yet reported, we considered a liquid droplet spreading from a source with a radius R0 situated at a height h above the surface (see inset Fig.2). The main characteristic of this non-conventional geometry is that the volume of the liquid meniscus is not constant since it can be fed from the reservoir located on the cantilever. Indeed, from a previous study [6], we found that, for apertures larger than 200 nm, the pressure inside the meniscus is fixed by the Laplace pressure due to the curvature of the reservoir droplet. This gives the relationship linking θ and R, which reads, in a crude approximation, as θ =h/(R-R0). Combining this equation with the Cox-Voinov equation which gives the expression of the dynamic contact

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angle θ as a function of the contact line velocity V, one gets the temporal evolution of the radius R which shows two asymptotic behaviours: a R − R0 ∝ t1 / 4 law at short timescale followed by a saturation at longer times. The full solution determined numerically with a Matlab routine adjusted to the measured data is reported on Fig. 2. The model we proposed reproduced quantitatively the experimental results for a large variety of experiments changing tip or surface properties (not shown here). The geometric parameters R0 and h used to adjust the model with the experimental data were consistent with the dimensions of the tips used and followed coherent trends when changing tip size or surface chemistry. We also used NADIS to address the question of the evaporation of droplets with diameters in the sub-µm range [7], which correspond to volumes of femtoliters and smaller, a significant downsizing compared to most published data obtained in the microliter range. We used the NADIS technique to deposit such droplets on an ultra-sensitive nanomechanical device (resolution 10 fg) constituted by a polysilicon quad-beam resonator (QBR) (fig. 3). Alignment with the resonator is performed using a nanopositioning table incorporated in the sample holder of our AFM set-up [5]. Droplets with diameters ranging from 1 to 5 µm were reproducibly deposited on the resonators by adjusting the contact time. During evaporation, we monitored the resonance frequency shift of the QBR. Using a calibration curve, the temporal evolution of the droplets mass was determined down to 10 fg (10 attoliters volume) resolution. Examples of results obtained on glycerol droplets with initial volumes ranging from 0.2 fL to 20 fL are shown on fig.3.

mass sensor and schematic representation of the droplet. These experimental data do not show any deviation from the macroscopic models based on diffusion controlled process, whereas droplets dimension becomes comparable with the mean free path of molecules in air, ca. 100 nm. As a conclusion, NADIS is a unique tool for manipulation of ultra-small liquid quantities which provides new opportunities to perform experiments on wetting at sub-micron scale. References [1] A. Meister, M. Liley, J. Brugger, R. Pugin and H. Heinzelmann, Nanodispenser for attoliter volume deposition using atomic force microscopy probes modified by focused-ion-beam milling, Appl. Phys. Lett., 85, pp.6260-6262, 2004. [2] A. Fang, E. Dujardin and T. Ondarcuhu, Control of droplet size in liquid nanodispensing, Nano Lett., 6, pp.2368-2374, 2006. [3] E. Dujardin, T. Ondarçuhu, L. Fabié Manipulation of liquid nanodrops, in « Nanoscale liquid interfaces », Eds T. Ondarçuhu, J.P. Aimé (Pan Stanford Publishing), pp. 441-491, 2013. [4] L. Fabie and T. Ondarcuhu, Writing with liquid using a nanodispenser: spreading dynamics at the sub-micron scale , Soft Matter, 8, pp. 4995-5001, 2012. [5] T. Ondarcuhu, L. Nicu, S. Cholet, C. Bergaud, S. Gerdes and C. Joachim, A metallic microcantilever electric contact probe array incorporated in an atomic force microscope Rev. Sci. Instrum., 71, pp.2087-2093, 2000. [6] L. Fabie, H. Durou and T. Ondarcuhu, Capillary forces during liquid nanodispensing, Langmuir, 26, pp.1870-1878, 2010. [7] J. Arcamone, E. Dujardin, G. Rius, F. Perez-Murano and T. Ondarcuhu, Evaporation of femtoliter sessile droplets monitored with nanomechanical mass sensors, J. Phys. Chem. B, 111, pp.13020-13027, 2007.

Fig. 3: (symbols) Evolution of the mass as a function of time for droplets with initial volumes ranging from 0.2 fL to

20 fL; (lines) Fit by a constant contact angle model, (inset) Scanning electron microscope image of the Abstract #101

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SPREADING OF A VOLATILE DROPLET ON A SOLUBLE COATING: GLASS TRANSITION EFFECT Julien Dupas1, Marco Ramaioli2, Laurence Talini1, Emilie Verneuil1 Laurent Forny2, François Lequeux1 1

UMR7615 UPMC/CNRS/ESPCI ParisTech, Paris, France 2 Nestlé Research Center, Lausanne, Switzerland E-mail: [email protected]

The dissolution of a soluble powder is a paramount process for several consumer goods applications, including food [1], pharmaceuticals and detergents. Wetting is the first step in such process, enabling the dissolving liquid and the solid to come to an intimate contact. Few previous studies have uncovered the complexity inherent to wetting a soluble polymer by a droplet of a volatile liquid solvent [2, 3, 4]. Indeed, several simultaneous mass transfers take place, namely: evaporation of the solvent, absorption and diffusion of the solvent in the soluble substrate, as well as dissolution and diffusion of the polymer in the wetting droplet. The solvent uptake by the polymer surrounding the droplet modifies locally its interfacial energy, improves the substrate wettability and in turn prevents the existence of an equilibrium contact angle of the solvent droplet.

units. Its molecular mass is 2500 g.mol−1, the dextrose equivalent is 29 and the polydispersity index 4.9. The experiments are conducted at room temperature and humidity is set at different levels, using saturated salt solutions (see schematics in Fig. 1a). The droplet spreading velocity and dynamic contact angles are measured using a lateral camera (Fig. 1b), while another camera images a top view. In that top vue appear (Fig. 1c) the colorful Newton Hues created by the interferences of the light reflected by the wafer, through the thin polymeric layer. The latter allows the measurement of the local swelling of the polymer and its local solvent uptake. In another contribution [5], we use the same experimental approach to understand the hydration processes at stake in the vicinity of the contact line. At room temperature, maltodextrin undergoes a glass transition upon varying water content, which results in a two-order-of-magnitude change in water diffusion coefficient, as shown by NMR measurements of solutions at different water volume fractions [6, 7]. Based on these measurements and assuming that the water diffusion coefficient is one order of magnitude higher at glass transition than in the glassy state, the mass fraction of water at glass transition and the corresponding water activity are respectively:

φ g = 18% aWg = 0.6

Fig.1: (a) Experimental set-up for droplet spreading experiments. (b) Side-view showing the determination of the dynamic contact angle. (c) Top view of a spreading drop.

We study the spreading of a droplet of water, deposited on a thin layer of a hydrosoluble polymer. At room temperature, the polymer undergoes a glass transition in water content. We evidence the effect of glass transition on the spreading dynamics of the solvent onto the polymeric layer. The polymer layer is prepared by spin coating a polymer solution on a silicon wafer, followed by evaporation of the solvent. The polymer used is a maltodextrin, a polysaccharide consisting in D-glucose 64

During a typical spreading experiment, the dynamic contact angle decreases with the progressive slowing down of contact line speed, as illustrated by all the curves reported in Fig. 2. The results reported in this figure are obtained by varying the coating thickness (e), and setting the initial water activity (aw) at two different levels (Fig. 2a, aw = 0.75; Fig. 2b, aw = 0.43). The contact angles always increase with the coating thickness, in agreement with the results obtained by Tay et al. [2]. While the dynamic contact angle profiles are smooth if the initial aw is higher than the water activity at the glass transition (Fig. 2a), a clear kink appears if the initial aw is lower than the water activity at glass transition (Fig. 2b). The coordinates of the kink are called θg and Ug. Ug decreases with the coating thickness e, while θg remains roughly constant at a given humidity. For contact line speed below Ug, the droplet spreads easily (low contact angle) on a melt

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substrate, while above Ug it spreads on a glassy substrate.

comparison is not reported here for sake of brevity (see [6, 7]).

Fig. 3: Predicted Ug/K versus experimental Ug.

We show that glass transition in a polymeric coating can condition its wettability during a spreading experiment, in the particular case where the glass transition itself is caused by the absorption of the volatile spreading liquid. This effect is caused by the drastic changes of the diffusion coefficient of the solvent at glass transition. When spreading occurs on a polymer melt, the hydration is accelerated, thus increasing the wettability of the substrate. Fig. 2: Contact angle versus contact line speed for droplets of water spreading on maltodextrin coatings of varied thickness e, at two different humidities or water activities: (a) Curves g g obtained at aw = 0.75 > a w are smooth. (b) At aw=0.43< a w kinks are highlighted with arrows.

The water volume fraction in the coating can be derived based on the equations reported in the article by Tay et al. [3]. The difference in water fraction between the kinks (at glass transition) and the initial substrate can be expressed as:

where: - Dv is the diffusion coefficient of water in air; -

csat is the maximal concentration of water in air; ρ is the liquid density; D p is the diffusion coefficient of water in the polymer; L is the distance from the droplet over which the

coating is hydrated. Assuming a constant logarithmic term, this equation allows predicting well Ug and interpolating the approximating constant K from the experimental data g obtained at different aw< a w, as shown in Fig. 3. Ug is also predicted to scale with 1/e, in good agreement with the results reported in Fig. 2b, although a detailed

References [1] Forny L., Marabi A. and S. Palzer, Wetting, disintegration and dissolution of agglomerated water soluble powders, Powder Technology, 206, pp. 72-78, 2011. [2] Tay A., Bendejacq D., Monteux C. and F.Lequeux, How does water wet a hydrosoluble substrate?, Soft Matter, 7, pp. 6953–6957, 2011. [3] Tay A., Monteux C., Bendejacq D. and F. Lequeux, How a coating is hydrated ahead of the advancing contact line of a volatile solvent droplet. EPJE, 33, 3, pp. 203–210, 2010. [4] Monteux C., Tay A., Narita T., Wilde Y. D. and F. Lequeux, The role of hydration in the wetting of a soluble polymer, Soft Matter, 5, pp. 3713–3717, 2009. [5] Dupas J., Verneuil E., Talini L., F. Lequeux, Ramaioli M., and L. Forny, Spreading of volatile droplets on a soluble substrate, 1st International Workshop on “Wetting and evaporation: droplets of pure and complex fluids”, Marseilles (FR), June 17-20th, 2013. [6] Dupas J., Ramaioli M., Forny L., Verneuil E., Van Landeghem M., Bresson B., Talini L. and F. Lequeux, Fast spreading of volatile droplets onto a soluble coating: glass transition effects, in prep. [7] Dupas J., Wetting of soluble polymers, PhD thesis UPMC, 2012.

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STUDY OF THE CORRELATION BETWEEN SURFACE WETTABILITY OF LIQUID AND THE MUCOADHESIVE POLYMERS M. Rojewska1, M. Olejniczak-Rabinek2, A. Snela2, A. Biadasz3, K. Prochaska1, J. Lulek2

1

Poznan University of Technology, Institute of Chemical Technology and Engineering, M. Skłodowskiej-Curie 2, Poznan, Poland 2 Poznan University of Medical Sciences, Department of Pharmaceutical Technology, Grunwaldzka 6, 60-780 Poznan, Poland 3 Poznan University of Technology, Institute of Physics, Molecular Physics Division, Nieszawska 13a, 60-965 Poznan, Poland E-mail: [email protected]

Mucoadhesion involves the attachment of a natural or synthetic polymer to a biological substrate. It is a practical method of drug immobilization or localization and an important new aspect of controlled drug delivery. In recent years there has been an increased interest in mucoadhesive polymers for drug delivery [1,2]. Mucoadhesion also increases the intimacy and duration of contact between a drug-containing polymer and a mucous surface. It is believed that the mucoadhesive nature of the device can increase the residence time of the drug in the body. The combined effects of the direct drug absorption and the decrease in excretion rate allow for an increased bioavailability of the drug with a smaller dosage and less frequent administration [3]. Several theories have been used to explain the uncomprehended mystery of the mucoadhesion phenomenon. The surface tension of the mucus and the mucoadhesive polymer in the wetting theory correlates with its ability to spread on the mucus layer [4-6]. The contact surface between the polymeric matrix with active substance and cell membrane is crucial from the perspective of biomedical applications. The mechanism by which this occurs is that of polymer adsorption at an interface, where polymers will naturally collect to reduce the surface energy. They can then bind by the formation of many weak bonds, mimicking the natural role of mucins in saliva [6]. But adsorption process is preceded by the wetting process on the surface. Therefore, the wetting process needs to be taken into account in consideration to the surface properties of polymers. The main aim of the study is to determine and characterize the wetting properties of selected mucoadhesive polymers and their mixtures using the contact angle method. The polymers studied are widely used in pharmaceutical formulations as a binder and film-coating agent for tablets and capsules, and in oral solutions and suspensions [6-8]. The materials investigated were polymers showing different physicochemical properties and belonging to the group of mucoadhesive polymers: Noveon AA-1 (polycarbophil, acrylic acid polymer crosslinked with divinyl glycol), HEC (cellulose 2-hydroxyethyl ether), HPMC (hydroxypropyl methylcellulose), Carbopol 974P (carboxy polymethylene), Kollidon VA 64 (poly[1-(2oxo-1-pyrrolidinyl)ethylene]). Moreover, mixed systems of polymers with components at different molar ratios were considered: Kollidon VA 64:Carbopol 974P (2:1), Kollidon VA 64:Noveon AA-1 (2:1), Kollidon VA 64:Noveon AA-1:HEC (1:1:1) and HPMC:Kollidon VA

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64 (2:1). Contact angle measurements using double distilled water as a liquid was performed on the compressed discs of mucoadhesive polymers in order to characterize the hydrophilicity. Measurements of advancing contact angle of liquid on the polymers and their mixtures were carried out using the sessile drop method with the instrument Tracker, I.T. Concept. Contact angle measurement was repeated for each solution–model surface system six times. The curves shown represent the average of the six measurements taken. The accuracy of the measurement is ±1.5 [deg]. A drop of the volume equal to 3 µl was automatically pushed out of the capillary and was deposited on a stationary surface. The strategy employed was to fit the meridian of the experimental drop to the theoretical drop profile according to the Young–Laplace equation. Images of the liquid drop were collected using a video–based contact angle tensiometer. All measurements were carried out at 294 K. In order to characterize the polymeric powders and their mixtures, discs 8 mm in diameter were prepared by direct compression of 200 mg powder at 200 psi using hydraulic press for 1 minute (ICL). The compacted discs were placed in a sample holder and a liquid drop with a given volume was placed on each sample and observed by a video camera. In the first stage of the study, the contact angle of double distilled water on the mucoadhesive polymers were analyzed. Fig. 1 shows the dynamics of contact angle of double distilled water on different mucoadhesive polymer surfaces. The wetting process of material by water were observed in short time i.e. about 30 s. The polymer matrixes should be rapidly wetted in order to stick fast to the point (e.g. oral or nasal cavity, eye, vagina) where the drug will be released. One can observe that most of the polymers studied show hydrophilic properties. Consequently, from the experimentally obtained curves θ=f(t), the worst hydrophilic properties shows HPMC surface while the best Kollidon VA 64 surface. It is worth noting that drops of water placed on the Kollidon VA 64 surface are characterized by different the dynamics of contact angle comparing the dynamics for other polymers. In the initial stage of wetting by liquid rapid spreading of water on Kollidon VA 64 surface is observed, while on Noveon AA-1 surface as well as Carbopol 974P surface the values of contact angle are stable. In the case of wetting HEC material with water rapid swelling of the pressed substance was observed. This effect prevented to measure the contact angle by drop shape method.

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On the other hand, the Kollidon VA 64:Noveon AA-1 (2:1) matrix indicated worse hydrophilic properties than the surfaces of individual components, which may suggest that addition of HEC to polymeric matrix strongly influences the character of material surface.

Fig. 1: Dynamic contact angle of double distilled water on polymeric surface: ( ) Kollidon VA 64, ( ) Carbopol 974P, ( ) Noveon AA-1, ( ) HPMC.

It is obvious that a significant influence on the wetting process have the composition of material and type of liquid [9]. Firstly, the contact angle of water on mixed polymers surfaces has to be examined in order to study the effect of composition of material on wetting properties. Fig. 2 shows the dynamics contact angle of water on surfaces of individual polymers and their mixtures of different composition.

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Fig. 3: The confocal micrpscopy images (size 0.85x0.85mm) : polymers (1) HEC, (2) Kollidon VA 64+Noveon AA-1+HEC (1:1:1).

Fig. 3 shows the confocal microscopy images for the individual polymers surfaces and their mixture. On the basis of the confocal images one can observe significant differences in the structural properties of the surfaces of materials studied. Our research conducted indicates that the polymers examined show various wettability depending on the type of polymers and their composition. When analyzing the results, it should be noted that for most of the material considered it was found to be of a hydrophilic nature. From the viewpoint of the biological application of mucoadhesive polymers the next part of our work will be devoted to analyze the influence of temperature and biological fluids (e.g. simulated: saliva, gastric and vaginal fluid) on the wetting properties of polymeric materials. Acknowledgements The research was financially supported by DS–PB 32/067/2013, DS 62–213/2013 and 502-14-03314429-09228 and 502-14-03314425-09818. References

Fig. 2: Dynamic contact angle of double distilled water on polymers surfaces: ( ) Kollidon VA 64, ( ) Carbopol 947P, ( ) Noveon AA-1, ( ) HPMC and their mixtures: a) ( ) Kollidon VA 64:Carbopol 974P (2:1), ( ) HPMC:Carbopol 974P (2:1) b) ( ) Kollidon VA 64:Carbopol 974P, ( ) Kollidon VA 64:Noveon AA-1 (2:1), ( ) Kollidon VA 64:Noveon AA-1:HEC (1:1:1).

When analyzing the results, it should be noted that polymeric matrix of HPMC:Carbopol 974P (2:1) showed wetting properties as a consequence of the properties of the individual components. On the other hand, when comparing the dynamics contact angle of water on the mixed polymers surface (Fig. 2b), one can conclude that Kollidon VA 64:Noveon AA-1:HEC (1:1:1) surface showed strong hydrophilic character after 20 sec. Moreover, the effect of synergism in the wetting properties was observed for Kollidon VA 64:Noveon AA-1:HEC (1:1:1) surface wetted by water, because the water wets the surface that is being analyzed much better than the surfaces of their individual components.

[1] Peppas N.A., Buri P.A., Surface, interfacial and molecular aspects of polymer bioadhesion on soft tissues, J. Control. Release, 2 pp. 257-275, 1985. [2] Duchene D., Touchard F., Peppas N.A., Pharmaceutical and medical aspects of bioadhesive systems for drug administration, Drug Dev. Ind. Pharm., 14 pp. 283-318, 1988. [3] Huang Y., Leobandung W., Foss A., Peppas N.A., Molecular aspects of muco- and bioadhesion: Tethered structures and site-specific surfaces, J. Control. Release, 65, pp. 63-71, 2000. [4] Kharenko E.A., Larionowa N.I., Demina N.B., Mucoadhesive Drug Delivery Systems, Pharm. Chem. J., 43, pp. 200-208, 2009. [5] Khutoryanskiy V., Advances in Mucoadhesion and Mucoadhesive Polymers, Macromol. Biosci., 11, pp. 748-764, 2011. [6] Smart J.D., The basic and underlying mechanism of mucoadhesion, Adv. Drug Deliver. Rev., 57, pp. 1556 -1568, 2005. [7] Nafee N.A., Ismail F.A., Boraie N.A., Mortada L.M., Mucoadhesive delivery systems. I. Evaluation of muco– adhesive polymers for buccal tablet formulation, Drug. Dev. Ind. Pharm., 30 (9), pp. 985-993, 2004 [8] Wahlgren M., Christensen K.L., Jȍrgensen E.V., Svensson A., Ulvenlund S., Oral-based controlled release formulations using poly(acrylic acid) microgels, Drug. Dev. Ind. Pharm., 35 (8), pp. 922-929, 2009. [9] Emel'yanenko A.M., Boinovich L.B., Analysis of wetting as an efficient method for studying the characteristics of coatings and surfaces and the processes that occur on them, An review Inorg. Mater., 47 (15) , pp. 1667-1675, 2011.

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INFLUENCE OF SURFACTANT CONCENTRATION AND ROUGHNESS ON THE DYNAMICS CLOSE TO ADVANCING AND RECEDING CONTACT LINES Daniela FELL, Manos ANYFANTAKIS, Marcel WEIRICH, Elmar BONACCURSO, Hans-Jürgen BUTT, Günter K. AUERNHAMMER Max Planck Institute for Polymer Research, Mainz, Germany Email: [email protected]

We investigate dynamic wetting of surfactant solutions in a rotating drum setup and thin capillaries. The presence of minor amounts of surfactants (typically well below the critical micelle concentration) in the wetting liquid induces pronounced modifications especially in the dewetting behavior. In a few examples, dynamic contact angles and flow profiles will be discussed. Forced wetting and dewetting of polymer surfaces in aqueous solutions containing cationic surfactant cetyltrimethylammonium bromide (CTAB) has been studied with a rotating cylinder half immersed in the solution. The receding contact angle decreases with faster withdrawing speeds [1]. This decrease is enhanced when adding CTAB (Fig. 1). The addition of salt to the CTAB solution further enhances the effect but does not have a significant effect alone. We interpret this strong dependence of the contact angle on the flow velocity as a consequence of flow-induced Marangoni stresses. Comparison between surfactants of different nature (cationic, anionic, non-ionic) showed that the velocity-dependent contact angle depends strongly on the critical micelle concentration.

unaffected by the presence of the barriers. Dynamic contact angles are, therefore, not only influenced by short-range effects like Marangoni stresses close to the contact line, but also by long-range transport processes (like diffusion and advection) between the regions close to the receding and advancing contact lines.

Fig. 2: Hindering the surfactant transport either over the surface or through the bulk of the liquid changes the velocity dependent contact angle (adapted from [2]).

We compare these experiments to the time-dependent dewetting behavior of dilute surfactant solutions of CTAB during forced flow in fluorinated ethylenepropylene (FEP) microtubes. The dynamic receding contact angle of the solution at a given velocity decreased as the solid-liquid contact time increased [3]. Kinetics with long relaxation time of several hundred seconds led to a final state displaying a 0° dynamic receding contact angle.

advancing(

receding(

Fig. 1: Velocity dependent contact angle of various CTAB solutions (adapted from [1]).

The influence of local and nonlocal transport processes of CTAB molecules on dynamic contact angles and contact angle hysteresis was also studied in the rotating drum setup. The influence of long-range surfactant transport was analyzed by hindering selectively the surface or the bulk transport via movable barriers. With increasing hindrance of the surfactant transport, the receding contact angle decreased at all withdrawing velocities in the presence of CTAB [2] (Fig. 2). The control experiment with pure water was 68

Fig. 2: Hindering the surfactant transport either over the surface or through the bulk of the liquid changes the velocity dependent contact angle (adapted from [3]).

Time dependency of the contact angle was absent in

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the case of 2-propanol. To illustrate the influence of surfactants on the wetting and dewetting behavior, we discuss the changes observed in the flow profile in the vicinity of the contact line.

References [1] Fell D., Auernhammer G. K., Bonaccurso E., Liu C., Sokuler M., Butt H.-J., Langmuir 27, pp. 2112-2117, 2011. [2] Fell D., Pawanrat N., Bonaccurso E., Butt H.-J., Auernhammer G. K., Colloid Polymer Sci., 291, pp. 361 – 366, 2013. [3] Anyfantakis A., Fell D., Butt H.- J., Auernhammer G. K., Chem. Lett. 41, pp. 1232-1234, 2012.

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EFFECT OF SURFACTANT ON THE WETTING DYNAMICS OF A COLLOIDAL PARTICLE Javed ALLY, Michael KAPPL, Hans-Jürgen BUTT Max Planck Institute for Polymer Research Ackermannweg 10, 55128 Mainz, Germany Email: [email protected]

In this study, we consider the wetting of a particle at the interface of a droplet of surfactant solution. Particle wetting at the interfaces of droplets and bubbles is relevant to applications such as mineral flotation, cleaning processes, and producing particle-stabilized emulsions. Although particle wetting and adhesion have been studied extensively, the dynamics of the wetting process and subsequent disturbances of the interface have only been considered recently [1][2]. When a solid particle makes contact with the interface of a droplet or bubble, it ‘snaps in’ – the particle is pulled into the interface from the initial contact to an equilibrium position (Fig. 1). For small particles with negligible weight and buoyancy, the equilibrium position is a function of the particle wettability and surface tension of the interface. We are interested in the dynamics of a particle snapping into an interface, in the first milliseconds after the particle makes contact. The characteristic time scale for this process has been estimated as ~0.1 ms [1].

Considering, for example, a 20 µm diameter spherical particle with a contact angle of 90º, the average speed during a 0.1 ms snap-in would be 0.1 m/s, with 2 instantaneous acceleration of up to 500 m/s . The -3 capillary number in this case is ~1×10 . In the context of particle wetting, this is higher than the threshold -5 value of ~1×10 , indicating that during snap-in, viscous forces may also be significant. As the curvature of the interface must change during snap-in for the contact line to move up the particle, this may cause additional force on the particle due to Laplace pressure. As in other cases of dynamic wetting, the motion of the contact line on a particle snapping into a liquid interface may be affected by flows induced in the liquid phase. Similar to a spreading droplet, wetting of a particle is driven by the balance of interfacial tensions at the contact line. The addition of dynamic forces to this balance means the dynamic contact angle varies from the equilibrium value, and that the force on the particle cannot simply be calculated from the equilibrium contact angle, and dynamic effects must be considered. In addition to reducing the air-liquid interfacial tension, surfactants can lead to surface tension gradients and so-called Marangoni forces. When an interface with surfactant is deformed rapidly, the change in area produces a local surfactant concentration gradient in the deformed region, resulting in a surface tension gradient. The variation in surface tension can lead to liquid flow at the surface. This gradient persists until it is overcome by surfactant diffusion. As the adsorption of a particle to an interface results in a large and fast deformation of the interface, surface tension induced flows and fluctuations may have a significant effect on the wetting process.

Fig. 1: Stages of particle wetting and corresponding contact angles – (a) initial contact; (b) dynamic wetting – unknown contact angle and perturbed surfactant concentration at the interface; (c) equilibrium position, contact angle, and surfactant distribution. This study focuses on the dynamics resulting from the particle going from positions (a) – (c).

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To study the dynamics of particle wetting, we used atomic force microscopy coupled with high-speed data acquisition. An atomic force microscope (AFM) consists of a microscopic silicon cantilever probe, an optical lever system for measuring the cantilever deflection, and a scanner for moving the sample under study relative to the probe. We chose to use an AFM for this measurement because it provides high resolution force measurements as well as the potential for much higher speed measurements than other techniques e.g. high speed imaging. An AFM also allows us to use microscopic particles and to perform measurements over the entire length and time of the snap-in. The disadvantages of using an AFM are that it does not provide direct information about the particle contact angle and interface position, and that the

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dynamics of the AFM cantilever must be considered as well as the particle motion, as the particles are attached to the cantilever for force measurement.

could be that flow caused by the perturbation of the surfactant at the interface reduces the viscous resistance to the contact line motion.

To measure particle interactions with droplet interfaces, 20 µm diameter silica particles were mounted on AFM cantilevers using epoxy to make colloidal AFM probes. The colloidal probes were mounted in the liquid cell of a MultiMode PicoForce AFM. The liquid cell was used in order to limit droplet evaporation. Measurements were performed at the interface of ~70 µL droplets in a glass and stainless steel holder mounted on the AFM stage. Measurements were performed at approach speeds of 𝑝 1 + 𝑢!! v! → 𝜑! = 0 , ! v! → 𝜑! = 1 𝛾! < 𝑝 1 + 𝑢!! where 𝑝 denotes 𝑝 scaled by the characteristic pressure 𝛾!" ∆𝐴 𝑣! ∆𝑉 ~ 𝛾!" 𝑟. Assuming to apply these conditions only to cells adjacent to the dry-wet interface, these conditions correspond to the conventional IP model without a tapping rule for rigid ! systems: 𝑢!! = 0, [5]. In order to investigate cohesionless elastic materials, we adopted the following function as the elastic energy density, ! 1 1 1 ! 𝐾 𝑢!! + 𝐺 𝑢!" − 𝑢!! 𝛿!" , 𝑓! 𝑢!" = 𝑔 𝑢!! 2 2 2 where 𝛿!" is the Kronecker's delta and −𝑥 !!! for 𝑥 < 0 (compression) 𝑔 𝑥 = . 0 for 𝑥 ≥ 0 (expansion) ν > 1 is required for continuity. The bulk modulus and rigidity for compressive states are proportional to 𝑔 𝑢!! 𝐾 and 𝑔 𝑢!! 𝐺 , respectively.

ℎ 𝐺 𝐾 , where ℎ(𝑥) is an increasing function of 𝑥. The condition that the cracking-like invasion occurs can be explained by considering the free energy and local dissipation. In drying processes, the layer shrinks vertically to resist drying until the pressure increases beyond a threshold 𝑝~1. Such uniaxial compressive states are quasi-stable. The first invasion of air occurs at a cell with the smallest 𝛾! ≅ 1 − ∆γ on the top surface. If cracking-like invasion develops following the first invasion, wet cells in a region surrounding the crack changes their states to an approximately isotropic state, and the amount by which the free energy decreases must be larger than local dissipation for the invasion of air. We evaluated this Griffith-like condition and found that, for a crack of the initial length of 𝐿 cells, unstable growth occurs if 𝐿 ≥ 𝑐 𝐿 𝛤.𝑐 𝐿 is determined from the lattice properties and increases monotonically from approximately 0 to a value less than 1 as 𝐿 increases. The parameter 𝛤 was derived from the ratio of the energy required for crack creation and the released energy. We note that 𝛤 is proportional to 𝛥𝛾 because the Griffith energy in this system corresponds to an additional energy required for drying when the first invasion has occurred already. As 𝐿/𝑐 𝐿 generally has a minimum, if 𝛤 is smaller than the minimum value, the Griffith length vanishes and then crack-like invasion appears spontaneously in a uniform layer with no initial crack, as suggested by our numerical results. In conclusions, drying contraction can induce cracking in cohesionless elastic porous systems with small 𝛤, which is determined by the elastic properties, the heterogeneity, and the size of constituent particles. The fast drying and the effect of plasticity may change the fracture condition significantly [6]. Extension of this criterion to such cases is important issues in future studies. The author acknowledges A. Nakahara, Ooshida T, T. Mizuguchi, S. Tarafder, T. Dutta, L. Goehring and C. Urabe for useful discussions. This research was started with H. Ito for her master thesis, and supported by two Grants-in-Aid Scientific Researches (KAKENHI C 23540452 and KAKENHI B 22340112) from JSPS, Japan. References

Fig. 2: Dependence of the invasion type on the parameters.

We investigated the case of third order elasticity (𝜈 = 2) in our numerical simulations and found that air invasion of the conventional IP model changes to cracking-like invasion as 𝐾 decreases and 𝐺 increases, as depicted in Fig. 2. Cracking-like invasion also occurs as the heterogeneity ∆𝛾 decreases. Our results suggest that the invasion type is determined by

[1] Kitsunezaki S., Cracking Condition of Cohesionless Porous Materials in Drying Processes, to be published in Phys. Rev. E, 2013. [2] Wood D.M., Soil Behaviour and Critical State Soil Mechanics (Cambridge Univ. Press), 1990. [3] Griffith A.A., The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. London A 221, pp.163-198,1921. nd [4] Lawn B., Fracture of Brittle Solids 2 ed. (Cambridge Univ. Press), 1993. [5] Wilkinson D. and Willemsen J.F., Invasion percolation: a new form of percolation theory, J. Phys. A 16, pp. 3365-3376, 1983. [6] Kitsunezaki S., Crack Growth and Plastic Relaxation in a Drying Paste Layer, J. Phys. Soc. Jpn. 79, 124802, 2010.

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a single non-dimensional parameter 𝛤 ∝ (𝑟𝐾)! ∆𝛾/ Abstract #068

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INVERSE PATCHY COLLOIDS: CLUSTERS, SHEETS, AND GELS

Gerhard KAHL1, Emanuela BIANCHI1, Silvano FERRARI1, Christos N. LIKOS2 1

Institut für Theoretische Physik and CMS, TU Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria 2 Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Wien, Austria E-mail: [email protected]

Patchy particles, i.e., colloids with heterogeneously patterned surfaces, are a relatively new class of colloidal particles that have raised a remarkable amount of interest in the scientific community during past years [1, 2]. In the synthesis process of these particles regions (so-called patches) are created on the colloidal surfaces with suitable chemical or physical processes; as a consequence these patches differ in their interaction behavior from the untreated, naked surface. Via these patches, the particles are able to form selective and highly directional bonds with other particles, making them thereby to ideal building entities that bring about complex self-assembly scenarios in soft matter physics [3, 4]. With suitable experimental techniques, the patch number, their spatial extent as well as their shape can be suitably tailored [5]. Recently we have introduced a novel class of patchy particles [6], which we have termed inverse patchy colloids (IPCs). The motivation for these particles came from a colloidal system where negatively charged, spherical colloids are covered by adsorbed, positively charged polyelectrolyte stars [7]. If two such stars adsorb onto the colloidal surface, they occupy the two polar regions of the colloid, while the rest of the charged surface remains uncovered. The resulting macromolecule is a heterogeneously charged particle with positive polar patches and a negative equatorial region (see right top in Figure 1). As a consequence of the repulsion between the like-charged and the attraction between unlike-charged surface regions the effective interaction between such colloidal particles can be both attractive and repulsive, according to the relative orientation of the two particles: both the polar as well as the equatorial regions are mutually repulsive, while polar and equatorial regions attract each other. This competition between repulsion and attraction (which is not encountered in conventional patchy systems) promises an even richer self-assembly scenario than encountered for their conventional counterpart. Using the standard formalism of electrostatics and making use of the Debye-Hückel theory, the interaction between a pair of such IPCs can be calculated analytically [6]. However, the resulting expression is highly complex and not amenable to investigate the properties of an ensemble of IPCs, e.g. via computer simulations or via other statistical mechanics based methods. In an effort to investigate these IPCs on the level of ‘effective particles’ we have mapped these complex, orientationally dependent interactions via a suitable mapping procedure on an effective pair potential which can be expressed via simple analytic

expressions. The basic idea was to represent both the colloid as well as the attached stars by interaction spheres (shown, respectively, as grey and yellow spheres in the left panel of Figure 1). The effective interaction between two IPCs can then be written as a sum over overlap volumes of the three types of

interaction spheres, weighted by respective energy factors. These weight factors are suitably determined via a faithful coarse-graining scheme from the original, analytic expressions of the effective interactions (for details cf. [6]). Fig. 1: Schematic visualization of an IPC. Left top panel: monomer resolved picture; left panel: adsorbed polyelectrolyte stars and the central colloidal particle are replaced by effective interaction spheres (grey and yellow spheres, respectively); bottom right panel: representation of the interaction spheres alone.

Based on this effective interaction we have investigated (and currently are investigating) different aspects of the self-assembly scenarios for IPC systems [8]. The parameters that specify the particles are the overall charge (i.e., charges of the patches minus the charge of the colloid), the opening angle of the patches and their interaction range. The system is characterized by the density and the temperature. The methods we use are standard computer simulations and integral-equation theories. Using optimization techniques based on genetic algorithms we have identified the ordered equilibrium structures that such systems form at vanishing temperature [8]. A broad spectrum of rather unexpected structures emerges, that contains – apart from conventional fcc lattices – layered structures and lattices that are characterized by relatively large internal voids or even channels. These ordered structures have been used when studying the phase diagram of these systems.

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Investigations were carried out by computer simulation based evaluations of thermodynamic potentials and via thermodynamic integration schemes. Finally, coexistence between these ordered equilibrium structures and the disordered liquid phase are identified via common tangent constructions. We find that in addition, to the above mentioned structures, a plastic fcc lattice emerges as a stable structure: here the particles occupy the positions of a regular fcc lattice, while their spatial orientations are random [9]. Particular emphasis was put on large scale computer simulations of IPC systems for the disordered phases. Apart from the usual gas and liquid phases, particular interest was devoted to arrested states, i.e., glass- or gel-like structures. A typical simulation snapshot of a system of IPCs is shown in Figure 2 (simulation cell in the top panel and enlarged view in the bottom panel) indicate that the system is prone to form droplet- (or cluster-)like aggregates which themselves form a network throughout the simulation cell. In simulations of other parametrizations of IPC particles the formation of stable, extended, planar (i.e., sheet-like) structures has been observed. The complex interplay of the directional, both attractive and repulsive interactions leads to a broad variety of structures that are currently analysed: both spatial and orientational correlation functions are calculated from these computer simulations for a broad variety of particle parameters (which fix the interactions between the particles) and system parameters (such as density and temperature). Currently we are summarizing the results in a comprehensive discussion of the system.

Fig. 2: Simulation snapshot of a three dimensional system of IPCs (top panel); enlarged view of a spatial region where the system forms cluster-like (or droplet-like) structures.

Current investigations are dedicated to investigate how IPCs self-assemble under the influence of an external electric field. To this end the system is confined between two parallel plates: while the upper one is neutral (and thus hinders the escape of particles) the bottom plane is charged (assuming different values of sign and strength of charge with respect to the polar regions). The distance between the walls is limited to a value which prevents the particles to sit on top of each other. The emerging structures are highly intricate and reflect the complex energetic competition ensuing from the different charges. Furthermore we investigate the stability of isolated, droplet-like clusters formed by IPC: we study the influence of the system parameters (charge, patch width, interaction range) on the cluster size and on its stability. This work has been financially supported by the FWF (both via a Lise-Meitner Fellowship under project number M1170-N16 as well as by the SFB ViCoM under project number F41) and by the Marie-Curie ITN-COMPLOIDS (Grant Agreement No. 234810). References [1] Pawar A.B., Kretzschmar I., Macromol. Rapid Commun. 31, pp. 150, 2010. [2] Bianchi E., Blaak R., Likos C.N., Phys. Chem. Chem. Phys. 13, pp. 6397, 2011. [3] Doppelbauer G., Bianchi E., Kahl G., J. Phys.: Condens. Matter 22, pp. 104105 (2010). [4] Doppelbauer G., Noya E.G., Bianchi E., Kahl G., Soft Matter 8,pp. 7768, 2012. [5] Kraft D.J., Groenewold J., Kegel W.K., Soft Matter 5, pp. 3823, 2009. [6] Bianchi E., Kahl G., Likos C.N., Soft Matter 7, pp. 8313, 2011. [7] Likos C.N., Blaak R., Wynveen A., J. Phys.: Condens. Matter 20, pp. 494221, 2008. [8] Doppelbauer G., PhD Thesis TU Wien, 2012. [9] Noya E.G., Kolovos I., Bianchi E., Doppelbauer G., Kahl G., in preparation.

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CRACK FORMATION IN DROPLETS AND RECTANGULAR SAMPLES OF LAPONITE GEL DRIED UNDER AN ELECTRIC FIELD Tajkera KHATUN1*, Tapati DUTTA2, Sujata TARAFDAR1, Akio NAKAHARA3, So KITSUNEZAKI4, Chiyori URABE5, OOSHIDA Takeshi6, Nobyasu ITO7 1

Physics Department, Jadavpur University, Kolkata 700032, India Physics Department, St. Xavier’s College, Kolkata 700016, India 3 College of Science and Technology, Nihon University, Funabashi 274-8501, Japan 4 Research Group of Physics, Division of Natural Sciences, Faculty of Nara Women’s University, Nara 630-8506, Japan 5 FIRST, Aihara Innovative Mathematical Modelling Project, Japan Science and Technology Agency, Japan 6 Department of Mechanical and Aerospace Engineering, Tottori University, Tottori 680-8552, Japan 7 Dep. of Applied Physics, Graduate School of Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, Japan *E-mail: [email protected] 2

Droplets of complex fluids often crack on drying [1,2,3]. In sessile drop of blood drying under various circumstances, cracks also form [4,5]. We show that small droplets of aqueous laponite gel may not crack when dried, but in the presence of an electric field they show characteristic patterns of cracks. We apply a radial DC electric field to droplets of aqueous laponite gel (figure 1 A, B). When the center terminal is positive, cracks appear from the center of the droplet as seen in figure 1C. Figure 1D shows the situation with the center negative. In this case short cracks appear at the periphery, but the central region is free of cracks.

Fig. 1: (A) and (B) show schematically, the set up for drying droplets under a radial field with center positive and center negative respectively. (C) and (D) show the corresponding experiments with 5.3 V. For the center positive - (C), cracks grow from the center. With the center negative – (D), cracks grow from the periphery. The field is kept on throughout the experiment. The scale in the figure shows mm graduations.

Crack formation depends on the duration of exposure to the field and on the voltage applied. Larger samples show similar trends. Systematic recording and classification of observations are easier on larger samples. We present a detailed study of crack patterns on droplets as well as in large rectangular samples of drying laponite gel exposed to electric fields of various strengths for different time durations.

Laponite RD used for the experiments, forms a gel when stirred in water. We use acrylic substrate for the experiments. 0.625g of laponite RD is added to 10 ml of distilled water containing a trace of crystal violet dye (used to make the cracks easily visible) while it is on a magnetic stirrer. The mixture is stirred for 20-30sec and then a droplet of ~10 mm in diameter is placed on an acrylic sheet. To apply DC field to the droplet, an approximately circular ring made of aluminum wire for peripheral electrode is placed on the sheet. The droplet is then deposited inside the ring and another straight wire acting as central electrode of same material is placed at the centre of the droplet. After waiting for 4-5 minutes till the solution spreads out evenly and gels, the power is turned on. For studies in rectangular geometry the sample is prepared in the same method as in droplet but here 7.5g of laponite is added to 120 ml of distilled water. The solution is poured in a rectangular acrylic box of dimension 20 cm × 11.8 cm. Electrodes made of aluminum foils are fitted to opposite sides to have a field along the length of the box as desired, and connected to a DC power supply (figure 2 A). After waiting for 4-5 minutes till the solution spreads out evenly and gels, the power is turned on. Voltages of different strength (60V, 90V, 135V) with different exposure (2min, 10min, 1hr, throughout the experiment) times are applied length-wise. The results for droplets are similar to earlier observations on large circular samples of ~ 10 cm diameter [6,7]. Cracks always appear from positive electrode and propagate radially towards the counter electrode. We observe bubbles at the negative electrode. There appears to be some chemical reaction between the sample and the electrode which leaves a greenish-blue residue as seen in Figure 1(C-D). For the rectangular samples, results are as follows. When an electric field is applied, gel formation is initially observed at the positive end. The gel shrinks away from the electrode creating a narrow gap, before crack formation starts. Crack formation starts at the positive end and most of the subsequent cracks also appear at

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this end. Bubbles are observed at the negative electrode. In the case of exposure time τ=2min for different voltages, the cracks emerge from the positive electrode but there is some randomness in their further development (figure 2 B). As the time of exposure is increased, the cracks have a tendency to bend towards the two sides even though they always emerge from the positive electrode. Similar observations are recorded for τ= 10 minutes, 1 hour and ∞ for three different voltages. The number of cracks reaching the negative end is much less than the number initially formed at the positive end due to bending towards the sides. These are shown in figure 2 C, D. Some cracks are observed to grow from the negative electrode, but these are very few in number. Thinning of the gel is observed at the positive end of the layer and this is more pronounced for longer τ. The negative end of the gel is thicker by comparison.

This work is supported by an Indo-Japan collaborative project funded by DST and JSPS. Authors thank Y. Matsuo and T. Hatano for stimulating discussions. TK thanks CSIR for a research grant. CU is supported by the Aihara Project, the FIRST program from JSPS, initiated by CSTP. Special thanks to Rockwood Additives for gifting the sample of Laponite RD. References [1] Yakhno T.,Salt-induced protein phase transitions in drying drops, Journal of Colloid and Interface Science, 318, pp. 225-230, 2008 [2] Bardakov R.N., Chashechkin Yu.D., Shabalin V.V., Hydrodynamics of a Drying Multicomponent Liquid Droplet, Fluid Dynamics, 45(5),pp. 141-155,2010 [3] Tarasevich Yu.Yu., Pravoslavnova D.M., Segregation in desiccation sessile drops of biological fluids, Eur. Phys. J. E, 22, pp. 311-314, 2007 [4] Sobac B., Brutin D., Structural and evaporative evolutions in desiccating sessile drops of blood, Phys. Rev. E, 84( 011603), 2011. [5] Brutin D., Sobac B., Loquet B., Sampol J., Pattern formation in drying drops of blood, Journal of Fluid Mechanics, 667, pp. 85-95, 2011. [6] Mal D., Sinha S., Middya T.R., Tarafdar S., Desiccation crack patterns in drying laponite gel formed in an electrostatic field, Applied Clay Science, 39 , pp. 106–111, 2008. [7] Khatun T., Choudhury M.D., Dutta T., Tarafdar S., Electric-field-induced crack patterns: Experiments and simulation, Phys. Rev.E, 86(016114), 2012. [8] Nakahara A. and Matsuo Y., Transition in the pattern of cracks resulting from memory effects in paste Phys.Rev.E 74, 045102(R), 2006. [9] Pauchard L., Elias F., Boltenhagen P., Cebers A., Bacri J.C., When a crack is oriented by a magnetic field, Phys.Rev.E 77, 021402, 2008.

Fig. 2: (A) shows the schematic setup for the rectangular sample. (B), (C) and (D) show respectively the crack patterns for τ = 2minutes, 1hour and ∞ for a field of 90V. The arrow indicates the field (E) direction.

A ‘memory effect’ has been observed when desiccation cracks form in a paste to which a perturbation has been applied prior to drying. Such effects have been observed for different stimuli such as vibration or flow (Nakahara effect [8]) and magnetic fields [9]. In the present case of electrical perturbation we find something similar- that even a short duration of exposure to the field has a striking effect on the final crack pattern. We see in our experiment that unlike ‘Nakahara effect’ the field induced ’memory’ is not imprinted throughout the bulk of the sample. Due to the electrical perturbation cracks originate at the positive electrode. They continue to develop roughly along the field direction even after the field is switched off. This may be termed ‘persistence memory’. It is possible that very minute micro-cracks, not visible to the naked eye, begin to form within seconds of switching on the field. These continue to propagate after the field is switched off. 202

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CONCENTRATION DEPENDENCE OF COFFEE-RING FORMATION IN SESSILE DROPLETS OF SALINE SOLUTIONS

Virginie SOULIÉ(a), Stefan KARPITSCHKA(a), Florence LEQUIEN(b), Thomas ZEMB(c), Helmuth MOEHWALD(a), Hans RIEGLER(a) (a)

Max Planck Institute of Colloids and Interfaces, Am Mühlenberg 1, 14424 Potsdam-Golm, Germany Commissariat à l’Energie Atomique et aux Energies Alternatives (CEA), CEA/DEN/DPC/SCCME/Laboratoire d’Etude de la Corrosion Non Aqueuse, 91191 Gif-sur-Yvette, France (c) Institute de Chimie Séparative de Marcoule (ICSM), UMR 5257 (CEA/CNRS/UM2/ENSCM), Bagnols-sur-Cèze, France Email: [email protected] and [email protected]

(b)

The evaporation of a sessile droplet containing insoluble particles has been investigated intensively in the last decades after the pioneering publication of Deegan and coworkers [1]. When a droplet of colloidal fluid dries on a solid planar surface under controlled humidity, the non-uniform evaporation flux on the water-air interface drives any suspended particles towards the droplet edge. This mechanism is the origin of the “coffee-ring effect”. In some cases, it has been shown that drying of a sessile droplet involves different flows occurring inside the droplet. These flows can effectively reverse the coffee-ring effect such as Marangoni flow [2] or capillary flow [3]. Thus, the final deposit of the particles is determined by the competitive or cooperative interactions of these different flows.

angle remains approximately constant. In the range of NaCl concentrations studied, we identify two different evaporation regimes. (i) At very low sodium chloride -6 concentrations (below 10 M NaCl), the droplet radius decreases slightly with time while the contact angle -5 remains almost constant. (ii) Above 10 M NaCl, the droplet radius remains almost constant while the contact angle decreases linearly with time (Figure 1).

The influence of evaporation from a sessile droplet on the formation of crystallites has been investigated recently [4,5]. Salt initially dissolved in water crystallize when the local concentration is above “bulk” saturation (6.1M in the case of NaCl at room temperature). The morphology of the deposit from a saturated solution is affected by the repetitive humidity cycling [5]. Here, we investigate the effect of initial electrolyte concentration over six decades and osmotic stress, which controls the evaporation rate. We compare the different patterns finally formed. Experiments were performed by depositing a droplet (10 µl) onto a solid, planar and inert substrate with a syringe. Solutions of sodium chloride prepared with TM Millipore water are used at different concentrations -6 (10 M to 1M). As substrates, single-sided polished silica wafers are used. The evaporation is done in a closed chamber under controlled temperature and humidity. All experiments were carried out at T = (23.0 ± 0.5)°C, at different relative humidities (from 0% to 80%) and at constant gaseous flow of dry nitrogen and -1 water (2000 ml.min ). The droplet evaporation was analyzed by optical imaging from the top and the side simultaneously. The description of the experimental setup is given in the recent work by Karpitschka et al. [5]. Assuming that the droplet has a spherical cap shape during the evaporation process, the droplet radius and contact angle evolve independently depending on sodium chloride concentration. For pure water, the droplet radius decreases with time while the contact

Fig. 1: (a) The three evaporation modes identified: no pinning regime for pure water, partial pinning regime for very low NaCl concentration and complete pinning regime above -5 10 M NaCl. (b) Typical microscopy images of the final -3 -2 deposition patterns from droplets of 10 M NaCl, 10 M NaCl and 1M NaCl on silica wafer at T = 23°C and RH = 0% from the right to the left. Low NaCl concentrations droplets tended to form coffee-stain deposit, whereas high NaCl concentrations droplets formed fingering deposit, even crystals in the droplet center.

We show that as initial sodium chloride concentration increases, the final deposit evolves from coffee-ring deposition to formation of crystals in the droplet center.

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1 Int. Workshop on Wetting and evaporation: droplets of pure and complex fluids th th Marseilles, France, June 17 to 20 , 2013 -3

Below 10 M NaCl, a coffee-stain deposit is observed. -2 Above 10 M NaCl, at the very last stages of the evaporation, the complete droplet footprint is covered by micro-crystallites of different morphologies, including fingers, fractal aggregates, fractal branches and even, crystals, which appear in the droplet center. We propose following mechanism controlling the process: The vapor flux (diffusing from the free surface of the liquid into the surrounding air) diverges significantly at the droplet edge. This diverging flux causes a transport of the dissolved ions in the liquid towards the edge. The capillary force produces a local and transient excess concentration of sodium chloride at the droplet edge. Since chaotrope salts are depleted from the air-water interface, surface tension becomes higher at the droplet edge than in its center. Thus, there is a surface tension gradient along the droplet surface, which induces a Marangoni flow of solutes as shown on Figure 2. Marangoni flow favors the replenishment of ions toward the droplet edge.

Fig. 2: The capillary flow is induced by the divergence of the vapor flux, J(x). Due to the accumulation of sodium chloride at the droplet edge, the surface tension is higher in the edge than in the droplet center. Thus, Marangoni flow is induced by this surface tension gradient and is directed inward along the liquid surface.

This capillary force effect, in combination with a pinning of the droplet on a large area, favors the formation of a ring-like deposit at lower sodium chloride -5 -3 concentrations (10 to 10 M NaCl). The pinning of the edge rings is reinforced more and more by sodium chloride accumulation with the increase in NaCl concentration. However, the pinning of the droplet is not a necessary condition to obtain a coffee-ring -6 deposition. This is the case for 10 M NaCl droplet: the pinning is just partial because the droplet radius decreases very slowly during the evaporation. -2

At higher sodium chloride concentrations (10 to 1 M NaCl), the capillary flow as well as the Marangoni flow favor the formation of coffee-ring deposition. If the transient concentration reaches super-saturation, crystallization starts at the contact line. However, in the droplet center, the vapor flux is smaller than the droplet edge. Therefore, most of the ions still present in the droplet bulk are slowly enriched in the droplet center. Finally, the center dries fast, giving rise to dendritic structures.

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We also investigated the evaporation of sessile droplets of sodium chloride under different relative humidities. Increasing relative humidity reduces the vapor flux at the droplet edge. The coffee-ring deposition is wider (i.e. less focused to the droplet perimeter). Bigger crystals appear as the slow evaporation rate gives more time for diffusion and the growth is not diffusion-limited. When a sessile droplet of saline solutions evaporates at fixed temperature and relative humidity, the pattern formation seems to be primarily controlled by the initial salt concentration. Capillary flow and Marangoni flow both favor the ring deposits. Salt diffusion from high concentration regions to low concentration regions can create a competing flow away from the droplet edge. For sessile droplets of sodium chloride evaporating in higher relative humidity, the structure of the final deposit evolves in wider coffee-ring or bigger crystals, and our goal is to investigate if this is general. The influence of the initial electrolyte concentration and relative humidity on this final equilibrium morphology is still under study. In the present stage, the coffee-ring effect detected here is clearly different from the one observed with saturated solutions. The ultra-poor regime, when initial salt content in droplet is just enough to produce on average a monolayer of ionic crystals has still to be investigated. Also, during humidity cycling, i.e. cycling evaporation/recondensation, the salt stains remaining from one cycle should induce pinning in the next cycle, and the pinning regime should appear more frequently. Our final goal is to determine if a large number of drying-rewetting cycles (modeling the circadian cycle) will produce equilibrium morphologies of special electrochemical activity.

References [1] Deegan R.D., Bakajin O., Dupont T.F., Huber G., Nagel S.R., Witten T.A. Capillary flow as the cause of ring stains from dried liquid drops, Nature, 389, pp. 827-829, 1997. [2] Hu H., Larson R.G. Marangoni Effect Reverses Coffee-Ring Depositions, The Journal of Physical Chemistry B, 110, pp. 7090-7094, 2006. [3] Weon B.M., Je J.H. Capillary force repels coffee-ring effect, Physical Review E, 82 (015305), 2010. [4] Shahidzahed-Bonn N., Rafaï S., Bonn D., Wegdam G. Salt Crystallization during Evaporation: Impact on Interfacial Properties, Langmuir, 24, pp. 8599-8605, 2008. [5] Desarnaud J., Shahidzahed-Bonn N. Salt crystal purification by deliquescence/crystallization, A Letters Journal Exploring The Frontiers of Physics, 95 (48002), 2011. [6] Karpitschka S., Riegler H., Quantitative Experimental Study on the Transition between Fast and Delayed Coalescence of Sessile Droplets with Different but Completely Miscible Liquids, Langmuir, 26 (14), pp. 11823-11829, 2010.

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ACHIEVING A FLAT FILM PROFILE FOR APPLICATIONS IN P-OLED DISPLAYS Adam.D.Eales1, Alex.F. Routh1, Nick Dartnell2

1

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Department of Chemical Engineering, University of Cambridge, UK. Cambridge Display Technology Ltd., (Company number 02672530), UK. E-mail: [email protected], [email protected]

Polymer-Organic Light Emitting Diodes (P-OLEDs) are a technology where light is emitted as a function of the electrical operation. Unlike existing technologies, such as LCDs, they do not require a backlight with filters. For this reason they have the potential for much larger viewing angles and for use in the next generation of flexible electronics applications, such as bendable mobile telephones. During the manufacturing process of P-OLED displays a solvent containing polymer ink is dried. Depending on the processing conditions and ink properties a variety of different film profiles can be achieved. Typically the profile has some form of undulation, which results in a non-uniform emission profile and less than optimal efficiency and lifetime. The aim of this project is to model the dynamics of the drying process in order to predict the final shape of the deposit for given processing conditions and ink properties. It is hoped that the model will enable

prediction of situations that lead to 'flat' profiles. We have modeled the drop as an axisymmetric Newtonian fluid subject to uniform evaporation. Consolidation of polymer at the droplet edges leads to the well-known coffee-ring effect. We have developed a code to predict the final film profile as a function of the single dimensionless group – the Capillary number. Experimental studies have used white light interferometry to measure the given profiles of dried droplets as a function of various experimental parameters. The results show a strong effect of Capillary number and demonstrate that surface tension driven flow is controlling the droplet shapes.

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MEMORIES OF VIBRATION AND FLOW IN COLLOIDAL SUSPENSION VISUALIZED AS DESICCATION CRACK PATTERNS Akio Nakahara and Yousuke Matsuo Laboratory of Physics, College of Science and Technology, Nihon University, Funabashi, Chiba 274-8501, JAPAN E-mail: [email protected]

When a droplet of colloidal suspension is dried in room temperature, we often observe a formation of fascinating desiccation cracks patterns. Usually desiccation cracks emerge at the periphery of the droplet at the beginning, then these cracks propagate toward the center of the droplet and that process forms a radial desiccation crack pattern. You can easily find examples of such radial crack patterns on the HOME page of Droplets 2013. On the other hand, when a pond or a rice field is dried out in a hot and dry season, we observe only isotropic and cellular desiccation crack patterns without any directional ordering. The reason why we obtain directional crack patterns such as a radial one in the drying process of a droplet is the presence of a strong drying gradient from the periphery toward the center of the droplet [1].

with non-zero yield stress, the plasticity maintains a dome-shaped structure of the paste after it was poured into the container. After we pour the CaCO3 paste into a circular container, we vibrated the paste in an angular direction for 10 seconds to spread the paste homogeneously and flatly inside the container, and then stopped the vibration and dried the paste for two days. Then we got a beautiful radial desiccation crack pattern as is shown in Fig. 1(a).

Here, we find that we can get such regular crack patterns without any drying gradient. Not like the drying process of a droplet with a shape of a dome, we dry a flat colloidal suspension which is homogeneously distributed inside an acrylic container, so there is no drying gradient inside the container. To control the direction of crack propagation, we use memory effects of colloidal suspension. We find that a water-poor densely packed colloidal suspension with plasticity can remember the direction of mechanical forces applied to it, such as a vibration or a flow. Of course it is difficult to know what kind of mechanical forces the water-poor colloidal suspension had suffered in the past by just looking at it. The memory in the water-poor colloidal suspension can be visualized as the morphology of desiccation crack patterns which appear in the drying process. We also noticed that the memory effect of colloidal suspension can be applied to control desiccation crack patterns. By changing the memory inside the colloidal suspension, we can control and make various types of desiccation crack patterns [2]. Now let us explain our experimental results. We mix powder particles with small amount of water and make a water-poor densely packed colloidal suspension with plasticity, which is called as a paste. The diameter of solid powder particles is about few micrometers. When we mix 3000g of calcium carbonate (CaCO3) powder with 1500g of water, and pour the mixture into a circular acrylic container with 500mm in diameter, we get a pile of CaCO3 paste with a shape of a dome like a huge droplet. The reason why the pile takes a form of huge dome is not the effect of surface tension of the paste. Because the paste has plasticity

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Fig. 1: Desiccation crack patterns produced by memory of vibration in paste. The desiccation cracks propagate in the direction perpendicular to the direction of the vibration that the pastes had suffered before the drying process. The diameter of each circular container is 500mm. (a) Radial crack pattern. (b) Lamellar crack pattern.

At the beginning, we had thought that the radial crack pattern is induced by the circular shape of the container, but one day we noticed that we had vibrated the paste before drying. So, we decided to vibrate the paste in one direction horizontally for 10 seconds before drying, stopped the vibration and dried the paste for two days. Then we obtained a lamellar desiccation crack pattern. Since the direction of lamellar cracks are all perpendicular to the direction of the vibration we added to the paste two days ago before drying, we realized that CaCO3 paste can remember the direction of the vibration applied to it before drying. The key factor for

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the memory effect of vibration is the plasticity of the water-poor colloidal suspension. When we do the same experiment using a water-rich colloidal suspension with no plasticity, the water-rich colloidal suspension cannot remember any motions of the vibration added to it, so we only get an isotropic and cellular crack pattern. Of course, to imprint the memory of vibration into a water-poor colloidal suspension, we must vibrate it at a stress larger than the value of its yield stress. Otherwise, the water-poor colloidal suspension does not move at all relative to the motion of the container even under the vibration, thus it has no memory of the vibration. We tried to check whether other types of a water-poor colloidal suspension can remember the direction of a vibration, and could confirm the existence of memory of vibration in many types of water-poor colloidal suspension. One day we vibrated a water-medium colloidal suspension made of magnesium carbonate hydroxide. Here, the “water-medium” means that the colloidal suspension does not contain so much water to lose plasticity like a “water-rich” colloidal suspension, but it contains a bit more water than a “water-poor” colloidal solution which behaves as an elasto-plastic media like mud. Then the water-medium colloidal suspension of magnesium carbonate hydroxide is fluidized under the vibration, and once the water-medium colloidal suspension is fluidized, it comes to remember the flow direction. To visualize the memory of flow inside the solution, we dried it after we stop vibrating the container, then we got another type of a lamellar desiccation crack pattern with the direction of cracks all parallel to the direction of the flow motion [3]. Some people pointed out that the new type of lamellar crack pattern might be obtained by the mixed motion of a vibration and a flow, because we fluidized the water-medium colloidal suspension by vibrating the container. To realize a pure flow motion without any vibrations, we made an experimental setup described in Fig. 2. We stored the water-medium colloidal suspension of magnesium carbonate hydroxide in one side of the rectangular container, removed the plate vertically to let the suspension flow in one direction, and dried it for one week. We obtained a lamellar desiccation crack pattern shown in Fig. 2, the direction of which is parallel to the direction of the flow motion. We tried to check whether the water-medium CaCO3 colloidal suspension can remember a flow direction, but we found that it cannot. The reason why CaCO3 colloidal suspension cannot remember a flow direction is that the CaCO3 particles are charged in water and repel each other. The essence of plasticity is a formation of network structure of colloidal particles in water. When the water-medium CaCO3 colloidal suspension is fluidized, the network of charged particles is easily broken under the flow, thus it cannot remember flow direction. If we add sodium chloride to screen the Coulombic repulsion between charged particles, the water-medium colloidal suspension maintains its network structure even under a flow and it

gets the ability to remember flow direction [4]. Attempts to control the morphology of desiccation cracks using electric and magnetic fields are also successful [5-7]. We would like to combine all these methods to control crack formation more effectively.

Fig. 2: Desiccation crack pattern produced by memory of flow in paste. Desiccation cracks propagate in the direction parallel to the direction of flow that the paste had experienced before the drying process.

We would like to acknowledge Y. Shinohara, K. Hoshino and H. Nakayama for performing experiments with us and Ooshida Takeshi, M. Otsuki, S. Kitsunezaki, S. Goto, T. Matsumoto, S. Tarafdar, T. Dutta, N. Ito, S. Yukawa and F. Kun for valuable discussions. This work was supported by Grant-in-Aid for Scientific Research (KAKENHI) (B) 22340112 and (C) 23540452 and 24540404 of Japan Society for the Promotion of Science (JSPS). This project was also supported by JSPS and DST under the Japan-India Science Cooperative Program and by JSPS and HAS under the Japan-Hungary Research Cooperative Program. References [1] Allain C., Limat L., Regular patterns of cracks formed by directional drying of a colloidal suspension, Phys. Rev. Lett., 74 (4), pp. 2981-2984, 1995. [2] Nakahara A., Matsuo Y., Imprinting memory into paste and its visualization as crack patterns in drying process, J. Phys. Soc. Jpn., 74 (5), pp. 1362-1365, 2005. [3] Nakahara A., Matsuo Y., Transition in the pattern of cracks resulting from memory effects of paste, Phys. Rev. E, 74 (4), 045102(R), 2006. [4] Matsuo Y., Nakahara A., Effect of interaction on the formation of memories in paste, J. Phys. Soc. Jpn., 81 (2), 024801, 2012. [5] Mal D., Sinha S., Middya T.R., Tarafdar S., Desiccation crack patterns in drying laponite gel formed in an electrostatic field, Applied Clay Science, 39, pp. 106–111, 2008. [6] Pauchard L., Elias F., Boltenhagen P., Cebers A., Bacri J. C., When a crack is oriented by a magnetic field, Phys. Rev. E 77(2), 021402, 2008 [7] Ngo A. T., Richardi J., Pileni M. P., Do directional primary and secondary crack patterns in thin films of Maghemite nanocrystals follow a universal scaling law?, J. Phys. Chem. B 112(7), pp. 14409-14414, 2008.

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DRYING-INDUCED WRINKLING OF A NANOMETRIC GLASSY SKIN IN HYDROGELS Karine Huraux, Tetsuharu Narita, Bruno Bresson, Christian Frétigny and François Lequeux Laboratoire SIMM-PPMD, UPMC-ESPCI ParisTech-CNRS UMR7615, 10 rue Vauquelin, 75005 Paris, France E-mail: [email protected]

Drying of a droplet of a solution of glassy polymer can lead to intriguing complex shapes: under solvent evaporation, polymers accumulate near the air/droplet interface and may form a glassy skin, which bends as the volume of the droplet decreases [1]. In order to characterize this buckling instability which is strongly geometry-dependent, instead of a solution droplet (having very limited possibility for geometry), we used a chemically crosslinked hydrogel dried under different geometries and external constraints. It is known that hydrogels undergoing large volume change can show surface patterns induced by the thermodynamic and/or mechanical instabilities [2,3]. It is expected that these instabilities can occur during drying of the hydrogels, however, no detailed work has been reported. We found that the mechanical instability induces wrinkling of chemically crosslinked poly(vinyl alcohol) gel (PVA gel) surface during drying [4]. Here we show experimentally that glass transition plays an important role in wrinkle formation. We synthesized PVA gels by crosslinking chemically PVA aqueous solution with glutaraldehyde at acidic condition. Glass capillaries were used as mould to obtain a gel cylinder. The size of the gel at equilibrium swelling in water is about 5 cm in length, 1 mm in diameter. The equilibrium PVA concentration is about 15 %. Drying of PVA gel cylinders is performed under 2 geometries. (1) The gels are hung, or the upper end glued on a support, the lower end free. The gels are dried in a drying chamber under air flow under controlled humidity (16 – 90 %). Weight change of PVA gels is monitored by a balance. (2) The gels are fixed to the constant length (initial length) in order to study the effect of mechanical constraint on the morphology. The weight, diameter, traction force and surface morphology were monitored with time. The surface morphology of gels after drying is observed by atomic force microscopy (AFM) and scanning electron microscopy (SEM). Gravimetric measurements was performed to determine the solvent weight fraction as a function of the activity of the solvent (= relative humidity) [5]. In order to study the mechanical property of PVA gels surface under drying, we measured force-distance curves by AFM. The microscope is operated in contact mode at a scanning rate of 1 Hz using a cantilever tip with a force constant of 40 N/m. These curves give the deflexion of the cantilever as a function of its distance to the gel surface.

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Fig. 1: Surface morphology of PVA gels dried with a free extremity under different values of humidity ((a) 95%, (b) 66%, (c) 47% and (d) 16%) observed by SEM.

Fig.1 shows SEM images of PVA gel surfaces dried at different humidities, h. At high humidity, no particular surface morphology was observed. At low humidity, we observed labyrinth patterns due to wrinkling of the surface. The wavelength of the wrinkling is about 0.5 µm for h = 16 %, 1 µm for h = 47 %. The wrinkling has no specific orientation. We found the same tendency for gels dried at constant length (image not shown). We observed that the wrinkles are orientated along the direction of the applied strain. In general, wrinkling occurs under two conditions [6,7]: (1) when there is an upper stiff layer on a soft support, and (2) when this stiff layer is compressed in the in-plane direction. Drying can induce concentration gradient of the polymer and creates a concentrated polymer layer on the drying surface when the drying is faster than equilibration by diffusion of water/polymer. However, in our gel system, the outer layer of the gel is submitted to a tensile stress: as the outer layer is drier and contracts but the bulk is not yet, the outer layer is stretched in the in-plane direction (compressed in the thickness direction). Thus in order to compress the outer skin layer in the in-plane direction and in order to make it wrinkle, this tension has to be removed without any contraction of the skin. The only possibility is that the skin undergoes the glass transition (condition 3). The reference state of the deformation is reset and no tension is left. Then the drying of the bulk compresses the skin and it wrinkles. Here we discuss the three points concerning the proposed wrinkling mechanism of the PVA gel. (1) drying-induced glass transition: The glass transition

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water content of PVA gel is determined by quasi-stationary desorption measurement of water. The PVA gel showed the glass transition at 13 % of water, corresponding to the equilibrium humidity of 6%. This result agrees with the humidity dependence of wrinkle formation in Fig.1. (2) formation of a glassy skin on the soft bulk: According to the wrinkling theory [7], the skin thickness is related to the wavelength of the wrinkles and the moduli of the skin Es and bulk Em:

⎛ E ⎞ λ ≈ e⎜⎜ s ⎟⎟ ⎝ Em ⎠

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For our gels (Es = 2.1 GPa, Em =0,2 MPa) the skin thickness is estimated to be about 50 nm for 1 µm of wrinkle wavelength. In order to characterize this thin glassy layer, we measured AFM force-distance curves. We estimated the variation of stiffness of the drying gel surface as a function of drying rate. It is shown that the gel surface after 2 minutes of drying under air flow is as hard as that of the gel after complete drying. Then when the air flow is stopped, the gel surface is softened, indicating that the swollen bulk of the gel rehydrates the surface. (3) compression of the glassy skin and apparition of the wrinkles: Fig.2 shows time profiles of the retraction stress and evaporation flux of water from a PVA gel dried under constant length. We simultaneously observed decreasing in the slope of the force curve, sharp drop in the evaporation rate, and apparition of the wrinkles at about 15 min. We attribute the slow-down of the stress increase at about 15 min to the glass transition of the gel surface and the relaxation of the force. In summary, we observed a phenomenon of wrinkling appearing on the surface of PVA gels during drying. Fast drying (inducing a concentration gradient) at low humidity (inducing glass transition) is required for the gels to wrinkle. The value of the wavelength of the wrinkles is about 1 µm and increases with increase in the humidity. Since the wrinkles remain after drying, this morphology is the consequence of the formation of a glassy skin at the surface of the gel which undergoes a compressive stress induced by the drying of the bulk. Some evidence for the presence of a glassy skin essential to the formation of wrinkles has been produced: AFM experiments have shown that if the drying is fast enough, the gel is composed of a dry upper layer on a wet bulk and traction force measurements have revealed that wrinkles appear when the glass transition occurs.

References [1] Pauchard L., Allain C., Stable and unstable surface evolution during the drying of a polymer solution drop, Phys. Rev. Lett., 68, pp. 052801-052804, 2003 [2] Tanaka T. et al., Mechanical instability of gels at the phase transition, Nature, 325, pp. 796-798, 1987 [3] Matsuo E.S., Tanaka T., Patterns in shrinking gels, Nature, 358, pp. 482-485, 1992 [4] Huraux K., Narita T., Bresson B., Frétigny C., Lequeux F., Wrinkling of a nanometric glassy skin/crust induced by drying in poly(vinyl alcohol) gels, Soft Matter, 8, pp. 8075–8081, 2012 [5] Bouchard C., Guerrier B., Allain C. et al., Drying of glassy polymer varnishes: A quartz resonator study, J. Appl. Polym. Sci., 69, pp. 2235, 1998 [6] Groenewold J., Wrinkling of plates coupled with soft elastic media, Physica A, 298, pp. 32-45, 2001 [7] Cerda E., Mahadevan L., Geometry and Physics of Wrinkling, Phys. Rev. Lett., 90, pp. 074302-074305, 2003

Fig. 2: Time profile of the contraction force (triangles), and the evaporation flow (circles) and imaging of gel surface by optical microscopy during drying at h = 57%.

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HOW ROBUST IS THE RING STAIN FOR EVAPORATING SUSPENSION DROPLETS? Y. Msambwa, D.J. Fairhurst, F.F. Ouali*

School of Science and Technology, Nottingham Trent University, Nottingham, NG11 8NS, United Kingdom Emails: [email protected], [email protected] ,[email protected] The ring stain is commonly seen when droplets containing particles, such as coffee, are left to dry on a surface: a pinned contact line leads to outward radial flow, which is enhanced by the diverging evaporative flux at the contact line. As shown by Deegan et.al.1997 [1] particles are swept outwards in this flow and create a ring which grows according to a simple power law with time. If all the particles end up in the ring, its width and height should also be given by power laws of concentration, with exponent 0.5. In this work, we use suspensions of polystyrene particles in water with sizes ranging from 100 to 500 nm and initial concentrations c0 from 0.009% to 2%. We use humidity and reduced pressure (from 760 torr to 10 torr) to vary the drying rate from 0.5nl/s to 6nl/s, a range of substrates to vary the initial contact angle between 1.5° and 30°, and invert the droplets to change the direction of gravity. The evaporation of 1 µl droplets deposited on the substrates was carefully monitored and the flow rate was determined by dividing the initial volume of the drop by the total drying time. The final deposits were imaged using a CCD camera with IC Capture software. ImageJ was used to analyse the images and obtain a radial profile of the measured intensity across the deposit. This enables the width of the ring to be determined with accuracy but cannot be used to determine the deposit heights as it only gives a variation of relative intensity. The heights of the deposits were determined using a Dektat 150 surface profiler. The profiler records a line profile of each deposit with ~ 3 µm horizontal resolution and almost 10nm vertical resolution. For each droplet, six scans were taken along diameters, evenly spaced around the deposit. Average values for the ring height, but also for the droplet radius and width were determined from the sets. The measurements show that at low drying rates nearly all the particles are deposited in the ring, however there is a significant deposition of particles in the centre of the drops at the fastest drying rates (corresponding to 10 torr) (Figure 1). Moreover, we find that, at a given initial concentration, the height and width of the ring are independent of the drying rates when nearly all particles are in the ring, but that, not surprisingly, both width and height decrease at the highest drying rates when a significant fraction of the particles is in the centre of the drop (Fig. 1).

0.50± 0.05 (Fig. 2). However, the ring width, normalised by the initial radius, has an exponent closer to 0.30±0.03 (Fig. 2). This suggests that not all particles are deposited in the ring, and that at higher concentrations, more particles are deposited towards the centre of the droplet. Deposition in the centre appears to occur in the very latest stages of drying, when fluid velocities typically diverge, the droplet behaves more like a thin film, and the scaling laws are not expected to hold. To confirm whether this is the case, analysis of the surface profilometry data is underway to determine the fraction of the particles which ends up in the ring and its dependence on initial concentration and drying rates.

Fig. 1: Comparison of deposit profiles measured using surface profiler (solid black lines) and imaging (red dashed lines) at two different drying rates: 0.6nl/s (left) and 3.3nl/s (right). The two images are shown underneath. Both droplets contained 500nm particles at initial concentration c0 = 1%.

We also find that for both substrate orientations, all contact angles, microspheres sizes and drying rates, the variation of ring height with initial concentration follows the predicted power law, with exponent equal to 210

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Fig. 2: Power laws showing width and height of deposited ring-stain as a function of the initial droplet concentration. These data are average over particle size, drying rate and orientation. The exponent for the height is 0.5 and for the width is 0.3. References [1] R. Deegan, O. Bakajin, T. Dupont, G. Huber, S. Nagel, T. Witten, Nature 389 (1997) 827–829.

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WETTING DYNAMICS ON GELS: HOW THE GEL CHARACTERISTICS AFFECT THE CONTACT LINE? Tadashi KAJIYA, Adrian DAERR, Laurent ROYON, Tetsuharu NARITA, François LEQUEUX and Laurent LIMAT Laboratoire MSC, UMR 7057 CNRS, Universite Paris Diderot PPMD/SIMM, UMR 7615 CNRS, UPMC/ESPCIParisTech. Email: [email protected]

Gels are materials which are attracting continued interest as they are an intriguing state of matter in physical and chemical sciences [1] and they also have potentials in diverse fields of applications such as drug delivery and cell transplantation [2]. The understanding interfacial properties of gels are of crucial importance in such applications. Here, we are focusing on the wetting problem on gels. Wetting is still an active subject of research even on “hard” solid surfaces because we have to patch up classical hydrodynamics near the contact line. On gels, the situation would be more complex as the wetting liquid can cause a large deformation on the gel surface which successively affects the statics and dynamics of the contact line. The gel deformation is caused by two mechanisms: by the balance between the interfacial tensions and elastic resistance of the gel and by the volume exchange between the liquid and gel. Intuitively, the behavior of the contact line on gels might be understood in analogy with the wetting on soft surfaces like an elastomer [3-5] or with the wetting on permeable surfaces like porous media and polymer films [6,7]. However, as gels have an unusual nature between solids and liquids, the wetting on gels would be even more complex than those situations. In this conference, we will present our two experiments for studying the different aspects of wetting on gels: water sessile drops on hydrophilic gels (PAMPS-PAAM) and water drops on hydrophobic gels (SBS-Paraffin). Water drops on hydrophilic gel: Effect of liquid diffusion [8] Poly (2-acrylamido-2-methyl-propane-sulfonic acid -coacrylamide) (PAMPS-PAAM) gels were used for substrate, and distilled water (Milli-Q Integral; Millipore, USA) was used for liquid droplets. Figure 1 shows the setup for the drop-gel profiles measurement. The gel substrate was placed on a hollow stage, and a droplet was placed on the substrate with a micropipet. The initial volume of the droplet was fixed to 1 µl. To measure both the profiles of the droplet and of gel simultaneously, the grid projection method was used. In the grid projection method, the profiles are measured by tracing the distortion of grid lines between before and after the placement of the droplet. The original grid plate was located far from the observation system. The illumination light emitted from the 212

photodiode passed through the grid plate and was converted to a parallel light by an optical lens (f = 200 mm). Then the light was guided to the bottom of the substrate, and passed through a focus lens (TV lens f = 35 mm: Pentax, Japan). This focus lens projects the mirror image of the grid inside the gel substrate, which is set just below the droplet. With the use of the mirror image, the resolution of the grid lines increases up to 6 times of the original grid lines. The grid image was measured by a CCD camera (A101FC; Basler AG, Germany) which was located above the droplet. The example of the grid image obtained after the placement of droplet is also shown in fig. 1.

Fig. 1 Measurement method for drop-gel profiles. The original profile was reconstructed by tracing the light path which passes through each grid line. The shift of the grid line ds is related to the local slope of the interface tan α ( x, t ) between the mediums of different refraction ratios (medium A: air, medium B: water or gel). With geometrical optics, the relation between the shift and slope is given by the following three equations:

sinα = n sin β (1),

γ = α − β (2), tan γ =

ds (3), e

where α and β are the angles of the light path in mediums A and B with respect to the normal to the interface, γ is the angle of the light path in medium B with respect to the vertical axis, n is the refractive index of medium B (since the water volume fraction in the gel is considerably large, we used the value of water n =

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1.33). By solving eqs. (1) - (3) the local slope of the interface tan α was obtained from ds, and the whole profile was obtained by integrating tan α in a horizontal direction x.

by a CCD camera from the side of the droplet. As the SBS-paraffin gel is hydrophobic, there is no volume exchange between the drop and gel. However, the rheology of gel strongly affects the behavior of the moving contact line. The contact line exhibits three different regimes of motions (fig. 3). When the contact line advances at a high velocity, the contact line moves continuously with a constant contact angle. As the contact line slows down, it starts stick-slip: the contact line stays at a certain position, and then suddenly slips forward. With further decrease of the velocity, the contact line stops stick-slip and continuously advances again. We also found that the transitions of these motions can be characterized by the frequency of the contact line motion defined by the velocity v and drop radius R as f=v/R.

Fig. 2 (a) Cross sections of drop/gel profiles. (b) ,(c) Time evolutions of the droplet radius and the angles of droplet and of substrate. Figure 2 (a) shows the half cross sections of the profiles (the height against the radial position) of the droplet and gel substrate for 3 different time steps. During the diffusion process of the droplet into the gel substrate, both the profiles of the droplet and substrate vary. At the initial stage (t = 25 s), the contact line of the droplet is seen clearly, i.e., there is a discontinuity of the slope between the region of the droplet and substrate. As the water diffuses from the droplet into the substrate, the height of the droplet region decreases, while the height of the substrate close to the contact line increases (100 s and 200 s). Figure 2 (b) and (c) shows the drop radius and the angles of the drop and of substrate against the time. Here, the angles θdrop and θgel indicate the angles relative to the horizontal plane. By comparing fig. 2 (a) with (b), it is clearly seen that the motion of the contact line is strongly coupled with the variation of the angles. At the first stage when the contact line is pinned, there exists a large difference between θdrop and θgel. As the water diffusion proceeds, θdrop and θgel come close to each other, and it is only at the moment where these two angles almost corresponds that the contact line starts to recede. This result indicates that when a contact line recedes on a PAMPS-PAAM hydrogel, apparently it has a finite receding contact angle, but the actual receding angle on the deformed gel surface θdrop−θgel is almost 0ﾟ. Water drops on hydrophobic gel: deformation by the capillary force [9]

Effect

of

In this experiment, a water droplet was placed on a hydrophobic poly(styrene-butadiene-styrene)(SBS) -paraffin gel substrate. Then, the droplet was inflated at a constant volume rate by a syringe connected to a motor-pump. The behavior of the droplet was observed

From the comparison of the diagrams of contact line motions with the measurement of gel rheology, we conjectured that the observed transition indicates that on visco-elastic gels, the contact line exhibits both the aspects of wetting on elastic solids and wetting on viscous liquids depending on the characteristic frequency. At an intermediate regime where the substrate behaves neither like solid nor like liquid, the stick-slip motion appears.

Fig. 3 Images and a diagram of the motions of contact line advancing on a SBS-paraffin gel. A cross over frequency measured by rheometry is shown in diagram. References [1] M. Doi, J. Phys. Soc. Jpn. 78, 052001 (2009). [2] D. Kaneko, T. Tada, T. Kurokawa, J. P. Gong, and Y. Osada, Adv. Mater. 17, 535–538 (2005). [3] A. Carre, J. C. Gastel, and M. E. R. Shanahan, Nature 379, 432 (1996). [4] E. R. Jerison, Y. Xu, L. A. Wilen, and E. R. Dufresne, Phys. Rev. Lett. 106, 186103 (2011) [5] M. C. Lopes and E. Bonaccurso, Soft Matter 8, 7875 (2012). [6] A. Aradian, E. Raphael and P. G. de Gennes, Eur. Phys. E 2, 367 (2000). [7] A. Tay, F. Lequeux, D. Bendejacq, and C. Monteux, Soft Matter 7, 4715 (2011). [8] T. Kajiya, A. Daerr, T. Narita, L. Royon, F. Lequeux and L. Limat, Soft Matter 7, 11425 (2011). [9] T. Kajiya, A. Daerr, T. Narita, L. Royon, F. Lequeux and L. Limat, Soft Matter 9, 454 (2013).

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1 Int. Workshop on Wetting and Evaporation: droplets of pure and complex fluids th th Marseilles, France, June 17 to 20 , 2013

FROM MULTI-RING TO SPIDER WEB: PATTERN FORMATION FROM DRYING COLLOIDAL DROPS Xin YANG1, Christopher LI2, Ying SUN1

1

Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, PA 19104 2 Department of Material Science and Engineering, Drexel University, Philadelphia, PA 19104 E-mail: [email protected]

Deposition morphology of colloidal drops consisting of solution processed functional materials is crucial in applications such as inkjet and gravure printing, spray deposition of printable electronics, photovoltaics, and 1-3 micro-batteries . With the development of vastly available organic and inorganic ink materials containing nano-metallic particles, semiconductor quantum dots and nano-wires, conducting polymers of different 4-6 shapes and functionalities , the challenge now is to effectively assemble these nano-scale building blocks 7 into useful structures . In this work, the effects of the particle concentration and evaporation rate on the deposition morphologies of self-assembled nano-particles in an inkjet-printed evaporating colloidal drop are systematically studied. Inkjet-printed pico-liter drops containing 20 nm sulfate-modified polystyrene particles at concentrations of 0.1%, 0.25%, and 0.5% are printed on a very hydrophilic substrate of contact angle ~ 0°. The relative humidity is controlled at 20%, 40%, and 70% inside an environmental chamber during the printing experiments where the temperature is kept at 22°C. The deposition patterns of inkjet-printed colloidal drops with different particle volume fractions dried under 40% relative humidity are shown in Fig. 1 from multiple rings for the particle loading of 0.5% (Fig. 1a), to

spider-web-like deposit for the particle loading of 0.25% (Fig. 1b), and to radial spokes for 0.1% (Fig. 1c). Inside a drying colloidal drop, the transition from multi-ring (Fig. 1e) and spider web (Fig. 1f) to foam (Fig. 1g) and islands (Fig. 1h) from the drop edge to the drop center is also explored. The objective of this paper is to examine these phase transition criteria of nano-particle self-assembled morphologies under different deposition conditions. For a relatively high particle loading of 0.5% as shown in Fig. 1a, after the contact line depins from the drop edge and leaves a thick outmost ring, a series of thinner, concentric rings are assembled. Foam and island structures are then formed when the contact line moves near the drop center. The spider-web-like deposit is however observed between the multi-rings and foam for the case of 0.25% particle loading (Fig. 1b). These deposition phase transitions result from the competition between the receding velocity of the contact line, Ucl, and the particle deposition rate Up. Based on the mass conservation and the assumption that the particle concentration keeps constant during drop evaporation, the contact line receding velocity Ucl and particle deposition rate Up inside a drying drop follow Ucl ~ 1/R and Up ~ const, which are schematically shown in Fig. 1d. Here, R is the instantaneous radius of the contact line. For a drop with 0.25% particle loading

Fig. 1: Deposition morphologies inside colloidal drops dried under 40% relative humidity with different particle concentrations: a) 0.5%, b) 0.25%, c) 0.1%. The black scale bars in a), b) & c) are 20 µm. d) contact line receding velocity and particle deposition rate during drop evaporation. The deposition morphologies inside b) changes from the drop edge to the center: e) multi-ring, f) spider web, g) foam, h) islands. The white scale bars in e) ~ h) are 2 µm.

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(Fig. 1b), when the contact line depins from the outmost ring, Ucl >> Up. This fast particle deposition rate promotes the stick-slip motion of the contact line, and hence enables the formation of the multi-ring structure at drop edge shown in Fig. 1e. As the drop continues receding, the Ucl increases to be close to Up, where parts of the contact line maintain the stick-slip motion, while other parts continuously recede. As a result, the spider web deposition is formed as shown in Fig. 1f. 8 According to the theory of fingering instability , the wavelength of the spider web (the circumferential length of the gird) follows λ / R0 ~ R / R0 , where R0 is

Ucl keeps increasing, leading to the deposition phase transition from left to right in Fig. 2. For a drop with a higher particle loading, the deposition consequently shows multi-ring, spider web, foam, and islands from the drop edge to the center. For the case of lower particle loading, the deposition morphology transitions from spoke, to foam and islands.

the diameter of the outmost ring. Further contact line receding induces Ucl > Up, resulting in the deposited particles not having enough time to self-assemble into close packed structures. Foam structure is hence produced as shown in Fig. 1g. Once the contact line recedes to the deposition center, where Ucl >> Up, particles are deposited into isolated islands (Fig. 1h). Similar phase transition is also observed for the case of 0.1% particle loading. When the contact line starts to recede, the smaller deposition rate Up, resulted from a lower particle loading, does not lead to enough accumulation of particles to pin the entire contact line. Hence, parts of the contact line are pinned and the other parts keep receding, as a result of the fingering instability of the drying liquid front. The parts of the contact line that continuously recedes push the particles to accumulate in the originally pinned regions, and in turn enhance the contact line pinning in these regions. The radial spoke-like patterns of particle assembly are hence formed near the edge of the deposit as shown in Fig. 1c. As evaporation continues, the increasing Ucl and constant Up during contact line receding initiate the deposition transition from spoke into foam and islands from the edge to the center of the deposit. By tuning the relative humidity of the environment, the wavelengths of the spoke in different drops can be controlled following λ ~ 1 / 1 - RH , where RH is the relative humidity of the drop drying environment. The phase diagram of the deposition morphologies as a function of particle concentration and contact line velocity of a drying colloidal drop is summarized into Fig. 2. At a low contact line velocity, corresponding to the edge of the deposit, the morphologies of multi-ring, spokes or islands are observed inside different drops with decreasing particle concentration. For drops of high particle concentration, the faster particle deposition leads to a stick-slip motion of the contact line when drop recedes. This stick-slip motion produces the multi-ring structure and the spacing of the rings increases with the increasing concentration. For drops with a low particle concentration, the limited number of particles that deposit at the contact line can only partially (or not at all) pin the contact line, and the radial spokes result from fingering instability (or isolated islands) are formed.

Fig. 2: Schematic phase diagram illustrating the possible deposition morphologies: multi-ring, spoke, spider web, foam and islands, as a function of particle concentration and contact line velocity of an evaporating colloidal drop.

References [1] Krebs, F. C.; Gevorgyan, S. A.; Alstrup, J., A roll-to-roll process to flexible polymer solar cells: model studies, manufacture and operational stability studies. Journal of Materials Chemistry 2009, 19, (30), 5442-5451. [2] Tekin, E.; Smith, P. J.; Schubert, U. S., Inkjet printing as a deposition and patterning tool for polymers and inorganic particles. Soft Matter 2008, 4, (4), 703-713. [3] Pudas, M.; Hagberg, J.; Leppavuori, S., Roller-type gravure offset printing of conductive inks for high-resolution printing on ceramic substrates. International Journal of Electronics 2005, 92, (5), 251-269. [4] Hoth, C. N.; Choulis, S. A.; Schilinsky, P.; Brabec, C. J., High photovoltaic performance of inkjet printed polymer: Fullerene blends. Advanced Materials 2007, 19, (22), 3973-+. [5] Lee, H. H.; Chou, K. S.; Huang, K. C., Inkjet printing of nanosized silver colloids. Nanotechnology 2005, 16, (10), 2436-2441. [6] Rogers, J. A.; Bao, Z., Printed plastic electronics and paperlike displays. Journal of Polymer Science Part a-Polymer Chemistry 2002, 40, (20), 3327-3334. [7] Glotzer, S. C.; Solomon, M. J.; Kotov, N. A., Self-assembly: From nanoscale to microscale colloids. Aiche Journal 2004, 50, (12), 2978-2985. [8] Saffman, P. G.; Taylor, G., The Penetration of a Fluid into a Porous Medium or Hele-Shaw Cell Containing a More Viscous Liquid. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1958, 245, (1242), 312-329.

For a drop with given particle loading, as it evaporates,

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MARANGONI OR NOT MARANGONI? 3D PARTICLE TRACKING ON EVAPORATING COLLOIDAL DROPS Alvaro G. Marin, Robert Liepelt, Massimiliano Rossi, Christian J. Kähler Institute for Fluid Mechanics and Aerodynamics, Bundeswehr University Munich, Neubiberg, Germany. E-mail: [email protected]

Sessile evaporating droplets fascinate for the rich and complex behavior that hides behind their apparent simplicity. Since Deegan et al. [1] explained the evaporation-induced flow that drags suspended particles towards the contact line, an intensive research has been devoted to the flow that spontaneously takes place within evaporating droplets [2-5]. The basic phenomenon of the so-called coffee-stain formation can be explained by assuming thermal equilibrium. However thermal effects play an important role in the flow patterns within the droplet and in the deposits left on the substrate. Using water-based colloidal solution droplets on glass slides, Deegan et al. [6] already realized that an important amount of particles did not follow the path towards the contact line but moved instead towards the droplet’s zenith along the surface; they correctly identified such effect as Marangoni surface flows. In that case, the origin was due to the lower temperature at the drop’s zenith in comparison with the contact line’s, warmer for being closer to the solid substrate. Larson and Hu [7] performed a careful numerical study confirming the experimental observations by Deegan et al. for water drops on glass slides. Among their conclusions they pointed out that there should be a critical contact angle below which Marangoni flows would be overtaken by the capillary-driven flow towards the contact line. Ristenpart et al. [8] went further by pointing out the critical role played by the relative thermal conductivity liquid/substrate, and solved the temperature problem numerically to find a relationship between the critical contact angles and the thermal conductivity ratio. Besides the amount of theoretical and numerical predictions, careful experimental measurents of this phenomenon has been so far scarce. For example, Bodiguel and Leng [9] used a fast scanning confocal microscope to directly measure planar velocity components in the full volume of an evaporating droplet. Besides the time-scale resolution limitation due to the necessary time for scanning each plane, the authors showed a clear surface flow towards the droplet’s zenith for most of the droplet’s life. Due to the complication of the measurement techniques, most of the authors are only able to analyze the paradigmatic case of evaporation of water droplets on glass. There are two main reasons why the phenomenon has not been observed and measure clearly until now: First, water droplets get easily contaminated with contaminants that may have surfactant effect at the surface and hinder surface tension gradient along the surface. Second, the intrinsic difficulty involved in fully volumetric velocimetry techniques, since three-dimensional positions and the full velocity field 216

are required simultaneously to study the dynamics of particles on moving free surfaces. In the present work, we show fully three-dimensional, three-component and time resolved particle tracking measurements of particles suspended on sessile drops of liquids with different thermal conductivities, evaporating on substrates with different thermal conductivities. Our final aim is to give a definitive answer to the questions: Is there Marangoni surface flow in evaporating water droplets? How accurate are the critical contact angles predicted by different authors [7,8] for other liquids and surfaces?.

Fig. 1 – Particles and velocities close to the contact line of a water droplet evaporating on glass slide. The trajectories correspond to the first 15 minutes of evaporation. Particle diameter is 2µm and the droplet initial volume 4 µl. To fulfill this aim, we employ A-PTV [10,11] (astigmatic particle tracking velocimetry), which consist on the acquisition of astigmatic images of microparticles with well-known properties. By analyzing the astigmatic shape of the particle image we are able to determine the relative position of the particles along the optical axis. The technique only requires a single camera and standard illumination techniques. In this particular case we employed a low-power continuous laser (532 nm) for illuminating the fluorescent particles. Polystyrene latex particles, supplied by Microparticles GmbH and coated with a red fluorescent dye, were used in very diluted concentrations of circa 0.001% weight. The

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droplet is left evaporating on different types of transparent substrates: glass slides, vinyl slides and thin Polydymethilsiloxane (PDMS) films. The particles are observed using a Carl Zeiss Axio observer Z1 inverted microscope. In order to minimize the contamination of the droplets, triply-deionized water is employed for all the solutions, and droplets with volumes below 5 µl are normally used to minimize both the area exposed and the evaporation time. The droplets are protected from peripheral airflows with a large plastic recipient open on the top and are evaporated in an empty room at constant temperature of 20°C and 50% humidity.

These preliminary results will be completed with different liquids and substrates to cover a wider range of thermal conductivity ratios. The velocity measurements obtained will serve to make proper comparisons with the current models and simulations and estimate with unique accuracy the relative importance of the Marangoni flow in comparison with the main evaporation-driven flow responsible for the coffee-stain effect. It would be desirable to determine the temperature field within the droplet in order to confirm many of the facts studied here. In future experiments, by using thermo-liquid crystal microparticles [12], we intend to simultaneously track the three-dimensional particle position and its instantaneous temperature. References

Fig. 2- Velocity plot in the last minutes of water drop evaporation on glass. The contact angle is approximately 6°. Our results clearly show a surface flow oriented towards the droplet’s zenith in water droplets evaporated on glass substrates (see figures 1 and 2). Many authors have predicted the presence of a stagnation point not far from the contact line, where Marangoni flow balances the outward capillary-driven flow. On the contrary, no stagnation point has been identified at any contact angle between the contact line and the droplet’s zenith, and all particles start their path towards the drop’s zenith as soon as they reach the drop’s surface. This observation needs to be confirmed with further experimental data and better resolution. Larson and Hu [7] and Ristenpart et al. [8] actually predicted the existence of a critical contact angle below which all flow would be directed towards the contact line. The flow is indeed observed to be weaker or completely absent when the droplet is evaporated on a plastic substrate, with lower thermal conductivity and therefore lower capability of providing thermal energy towards the contact line. In ethanol/water mixtures evaporated on glass, the thermal gradient is expected to be reversed and therefore difficult to distinguish from the main flow towards the contact line. The experiments clearly demonstrate the presence of Marangoni flow in those cases where the thermal gradients are favorable. An interesting observation, also pointed out by other authors [1,9], is that the particles tend to accumulate and form large two-dimensional clusters at the drop’s zenith. If the effect could be enhanced, it could be well used by simply tuning the substrate temperature to promote deposition in different parts of the droplet surface.

[1] Deegan, R. et al. Capillary flow as the cause of ring stains from dried liquid drops. Nature, (1997). [2] Hu, H. & Larson, R. G. Evaporation of a Sessile Droplet on a Substrate. J. Phys. Chem. B 106, 1334–1344 (2002). [3] Fischer, B. J. Particle Convection in an Evaporating Colloidal Droplet. Langmuir 18, 60–67 (2002). [4] Popov, Y. Evaporative deposition patterns: Spatial dimensions of the deposit. Phys. Rev. E 71, 036313 (2005). [5] Gelderblom, H., Bloemen, O. & Snoeijer, J. H. Stokes flow near the contact line of an evaporating drop. J. Fluid Mech. 709, 69–84 (2012). [6] Deegan, R. et al. Contact line deposits in an evaporating drop. Phys. Rev. E (2000). [7] Hu, H. & Larson, R. G. Analysis of the Effects of Marangoni Stresses on the Microflow in an Evaporating Sessile Droplet. Langmuir 21, 3972–3980 (2005). [8] Ristenpart, W., Kim, P., Domingues, C., Wan, J. & Stone, H. Influence of Substrate Conductivity on Circulation Reversal in Evaporating Drops. Phys. Rev. Lett. 99, 234502 (2007). [9] Bodiguel, H. & Leng, J. Imaging the drying of a colloidal suspension. Soft Matter 6, 5451–5460 (2010). [10] Cierpka, C., Segura, R., Hain, R. and Kähler, C. J. A simple single camera 3C3D velocity measurement technique without errors due to depth of correlation and spatial averaging for microfluidics. Meas. Sci. Technol. 21 (2010). [11] Cierpka, C., Rossi, M., Segura, R. and Kähler, C. J. On the calibration of astigmatism particle tracking velocimetry for microflows. Meas. Sci. Technol. 22 (2010). [12] Segura, R. et al. Non-encapsulated thermo-liquid crystals for digital particle tracking thermography/velocimetry in microfluidics. Microfluid. Nanofluid . (2012). doi:10.1007/s10404-012-1063-y

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SEGGREGATION OF SILICA PARTICLES WITH DIFFERENT SIZE BY DRIVEN RECEDING CONTACT LINES Carmen L. Moraila-Martínez, Miguel A.Cabrerizo-Vílchez and Miguel A. Rodríguez-Valverde Biocolloid and Fluid Physics Group, Dept. of Applied Physics, University of Granada, Campus of Fuentenueva, E-1807, Spain Email: [email protected]

Since the thickness of the drop meniscus reduces gradually toward the contact line, particles transported by the flow created inside the drop are deposited at a position where the individual particle size matches the thickness of the local meniscus. Consequently, smaller particles are expected to move closer to the contact line compared to the larger ones, which leads to size-dependent particle separation. Hence, the “coffee ring” effect can result in size dependent nano/microparticle separation near the contact line region of an evaporating liquid drop. This enables for a simple chromatography technique for processing biological entities with minimal resource requirements [6]. In this work we present the results obtained of driven receding contact lines with particle suspensions using a methodology referred to as Controlled Shrinking Sessile Drop (CSSD) [1]. This methodology allows to standardize the contact line dynamics of an evaporating drop in a shorter time interval. Moreover, undesired effects due to the increment of the particle concentration during the loss of liquid are worded because the particle concentration in bulk during the entire CSSD process was constant. 218

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It is reported that small particles may be readily arranged at the vicinity of contact lines rather than larger particles due to the wedge shape of the solid-liquid-air interfacial region (hydrophilic substrates). Smaller particles provide a greater number concentration (at the same volume fraction), have a greater mobility and accumulate closer to the contact line rather than larger particles [6].

We found that ring-like deposits were obtained with the three different particle sizes. The main differences of the deposits obtained were the lengths of each deposit (the height, width and diameter of the ring). In Figure 1 we plot the profiles of the deposits acquired with a white light confocal microscope (PLµ, Sensofar Tech S.L.). As expected, the higher and wider ring was formed with the SiO2-1.16 µm suspensions. Thus, the height and width of the ring-like deposit directly depend on the size of the particle at fixed concentration.

R ing dia m e te r (m m )

It is known [4] that small particles may be readily arranged at the vicinity of contact lines rather than larger particles due to the wedge-like shape of the solid-liquid-air interfacial region (in hydrophilic substrates). Although segregation effects in coatings are undesirable in many industrial and scientific processes, the discrimination of particles with different size [5, 6, 7] on a substrate can be also fruitful.

In order to test the CSSD technique with particles of different size, we performed experiments with Silica © particles of 20nm (Klebosol ), 120nm and 1.16µm © (Microparticles ) of diameter. Particle suspensions were diluted at ΦV= 1 and 5% and pH2. Under these conditions, substrate-particle and particle-particle electrostatic interactions were minimal [5]. We employed polymethylmethacrylate (PMMA, 2mm-thick © sheets, CQ grade, Goodfellow ) as substrate for the deposit formation. This material was utilized due to its stable response in contact angle.

Z (µm )

The formation of solute deposits during the evaporation of sessile drops containing complex liquids (solid particles, polymeric dispersions, emulsions..) is a multivariable problem. The diversity in the deposit morphology is due to the complex mechanisms behind the transport of particles during drop evaporation. The morphology of the deposits is also influenced by properties of particle: volume number, contact angle [1], shape [2] and size [3].

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W (µm ) Fig. 1: Profile of the ring-like deposits obtained with CSSD experiments using SiO2-20nm, SiO2-120nm and SiO2-1.16µm suspensions on PMMA substrates at ΦV = 1% and pH2. The diameter of the ring-like deposits is plotted as function of the particle size (logscale).

To explore if the CSSD technique can be also used to separate mixtures of particles, we performed CSSD experiments on PMMA substrates with mixtures 1:1 and 5:1 of SiO2-120nm and SiO2-1.16 µm suspensions at pH2.

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In Figure 2, contact line dynamics of the

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mixture 1:1 is shown.

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1 pinning rc = 5 .7 5 m m

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rc (c m ) Fig. 2: Contact line dynamics during a CSSD experiment with a mixture 1:1 of SiO2-120nm and SiO2-1.16µm suspension at pH2 on a PMMA substrate. The arrows indicate the position the pinning events.

We found that a ring-like deposit was formed followed by branched deposits. These deposits were constituted only with SiO2-120nm nanoparticles followed by a stain. The stain is mainly formed by SiO2-1.16µm particles. Hence, the results obtained with the CSSD technique with different particle sizes are in agreement with the behaviour of an evaporating drop. The CSSD technique enables the nano/microparticle segregation near the contact line region. References [1] C. L. Moraila-Martinez, M. A. Cabrerizo-Vilchez, M. A. Rodriguez-Valverde, The role of the electrostatic double layer interactions in the formation of nanoparticle ring-like deposits at driven receding contact lines, Soft Matter 9 (2013) 1664–1673. [2] P. J. Yunker, T. Still, M. A. Lohr, A. G. Yodh, Suppression of the coffee ring effect by shape-dependent capillary interactions, Nature 476 (7360) (2011) 308–311, ISSN 0028-0836. [3] S. Biswas, S. Gawande, V. Bromberg, Y. Sun, Effects of Particle Size and Substrate Surface Properties on Deposition Dynamics of Inkjet-Printed Colloidal Drops for Printable Photovoltaics Fabrication, J. Sol. Energ. Eng. 132 (2) (2010) 021010–7. [4] J. Perelaer, P. J. Smith, C. E. Hendriks, A. M. J. van den Berg, U. S. Schubert, The preferential deposition of silica micro-particles at the boundary of inkjet printed droplets, Soft Matter 4 (2008) 1072–1078. [5] A. P. Sommer, M. Ben-Moshe, S. Magdassi, Size-Discriminative Self-Assembly of Nanospheres in Evaporating Drops, J. Phys. Chem. B 108 (1) (2004) 8–10. [6] T.-S. Wong, T.-H. Chen, X. Shen, C.-M. Ho, Nanochromatography Driven by the Coffee Ring Effect, Anal. Chem. 83 (6) (2011) 1871–1873. [7] C. Monteux, F. Lequeux, Packing and Sorting Colloids at the Contact Line of a Drying Drop, Langmuir 27 (6) (2011) 2917–2922.

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MICRODROPLETS AS CONFINED SYSTEMS: UNUSUAL ACCESS TO NUCLEATION 1

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GROSSIER Romain , HAMMADI Zoubida , MORIN Roger , VEESLER Stéphane 1

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Centre Interdisciplinaire de Nanoscience de Marseille, CNRS UMR7325 Campus de Luminy case 913, 13288 Marseille cedex – France E-mail: [email protected]

Experiments on nucleation process may be frustrating due to its stochastic nature: we do not know where and when an indefinite number of nucleation events will occur. Usually, this problem is addressed via a statistical analysis on a large sample of nucleation events: a large number of independent experiments must be realized to access nucleation mechanisms. Thus, droplets based techniques such as microfluidics have largely been employed, allowing one to repeat the exactly same experiment hundreds or thousands of times, giving rise to statistically relevant data. Despite this, our understanding and control of nucleation and subsequent material properties is still limited. We, here, propose another way of getting to the bottom of nucleation, in the framework of crystallization in solution, by using confined systems, i.e. finite volume systems which volume affect nucleation.

Due to this confinement effect, unexpected high supersaturation can be reached compared to bulk systems [2], resulting in a possible control on nucleation. In order to confirm our predictions, we present a simple fluidic device that generates single or arrayed microdroplets of controlled size ranging from nanoliter to femtoliter [3]. Droplets are generated on an oil covered plastic coverslip with the help of a glass capillary filled with an aqueous phase. Once this capillary touches the coverslip, depending on the pressure we apply and the velocity at which the capillary is displaced, lines of monodisperse microdroplets are generated (fig. 2). As water is slightly miscible in oil phases, it diffuses outside the droplet, thereby increasing the concentration of the dissolved species until nucleation and growth of a crystal occur.

We, first, reconsidered the impact of the microdroplet volume on both mechanism and conditions of nucleation. Using a simple thermodynamical model [1], we identified a clear window of parameters (supersaturation, solubility and volume of the droplet) where only one single critical cluster is allowed to nucleate. The key to reveal this window is to take into account the depletion of the solution during the nucleation process: supersaturation is not constant (it decreases) along the course of a cluster to reach its critical size. By doing so, critical size to reach increases, and if the reservoir (the droplet) is sufficiently tiny, solubility of the solution will be attained before a critical cluster could have nucleate. The more the droplet is small, the more the supersaturation have to be great to allow nucleation, which is illustrated in fig. 1.

50µm

Fig. 2: Microdroplets array in the picoliter range. Droplets are generated on a PMMA coated coverglass, using a glass capillary, with injection pressure P = 4000 Pa, and velocity varying from 0.1 (first line, diameter=12µm) to 1 mm s−1 (last line, diameter=31µm) by 0.1 mm s−1 step. From [3].

AgCl

Fig. 1: Minimal supersaturation of AgCl in a water droplet to allow nucleation of a single (red line) and two (blue line) critical clusters. If in nanoliter droplets a slight supersaturation (just above the solubility) is sufficient to allow nucleation to occur, consequent supersaturation (almost 2.5) have to be reached in femtoliter droplets in order to allow such an event.

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In this context, crystallization kinetics undergoing confinement will be shown to be more accurate to approach nucleation mechanism via induction time measurements. Thus, we demonstrate that confinement allow us to experiment "non-stochastic" nucleation: we control where and when one single nucleation event will occur [4]. This control represents a great improvement in studying factors influencing nucleation process and its underlying physics.

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References [1] Reaching one single and stable critical cluster through finite-sized systems Grossier, R. & Veesler, S., Crystal Growth & Design, 2009, 9 (4), pp. 1917-1922 [2] Ultra-fast crystallization due to confinement Grossier, R., Magnaldo, A. & Veesler, S., Journal of Crystal Growth, 2010, 312, pp 487 - 489 [3] Generating nanoliter to femtoliter microdroplets with ease Grossier, R., Hammadi, Z., Morin, R., Magnaldo, A. & Veesler, S., Applied Physics Letters, 2011, 98, 091916 [4] Predictive Nucleation of Crystals in Small Volumes and Its Consequences Grossier, R., Hammadi, Z., Morin, R., & Veesler, S., Physical Review Letters, 2011, 107, 025504

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WETTING KINETICS OF WATER NANO-DROPLET CONTAINING NON-SURFACTANT NANOPARTICLES: A MOLECULAR DYNAMICS STUDY 1,2 1 2 1 Gui LU , Han HU , Yuanyuan DUAN , Ying SUN Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, PA 19104, USA Key Laboratory of Thermal Science and Power Engineering of MOE, Beijing Key Laboratory of CO2 Utilization and Reduction Technology, Tsinghua University, Beijing 100084, P.R. China E-mail: [email protected]

Nanofluids are known to be able to significantly modify the transport properties of the base fluids and can hence be used for heat transfer enhancement, drag 1 reduction, among others . The wettability of nanofluids is of particular interest to microfluidic systems, in which surface tension plays an important role due to the relative small dimensions and high specific surface 2 areas of the micro-devices . The addition of nanoparticles makes the wetting kinetics of base fluids more complicated due to the particle-particle, particlesubstrate, and particle-fluid interactions. Self-assembly of nanoparticles within the bulk liquid, at solid-liquid and liquid-vapor interfaces, or in the vicinity of contact line region greatly affects the wettability of nanofluids. 3 Wasan et al. reported the enhanced spreading behavior (i.e., super-spreading) of nanofluids. A solid-like ordering structure of nanoparticle deposition was observed near the contact line region. This ordering structure, stemming from the settlement and assembly of nanoparticles, gives rise to an excess structural disjoining pressure in the vicinity of contact line, altering the force balance near the contact line and hence enhancing the wetting kinetics. In this paper, the dynamic wetting of water nano-droplet with non-surfactant gold nanoparticles was simulated using molecular dynamics (MD) simulations. The effects of particle loading and wettability on wetting kinetics and contact line mobility of nanofluid droplets are discussed. Cylindrical water droplets (d=10 nm, l=1.6 nm, 4500 water molecules) with gold nanoparticles of n=0, 9, 18, and 27 (corresponding to volume fraction φ=0%, 3.43%, 6.77% and 9.87%, respectively) spreading on a Au(100) surface 3 (60×1.6×1.6 nm , 9600 gold atoms) were simulated. 3 The gold nanoparticles (0.8×0.8×0.8 nm , 32 gold atoms per particle) were absorbed spontaneously by a water droplet and the combined nanofluid droplet was then equilibrated. Wetting simulations of nanofluid droplets were conducted until they stop spreading. The 4 was used for water-water TIP4P-Ew model 5 interactions and the embedded-atom method (EAM) was applied between gold-gold atoms. A 12-6 LJ potential with ε=0.05427 eV, σ=3.1 Å, and a cutoff distance of 9 Å was used to describe water-gold interactions. The spreading was simulated using LAMMPS under NVT ensemble at T=300 K. Snapshots of a pure water droplet and three nanofluid droplets with different particle loadings are shown in Fig. 1. It can be observed that the spreading radius decreases with increasing particle loading. The addition

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of nanoparticles inhibits rather than enhancing the wetting kinetics during the nano-second spreading process. For all three cases, nanoparticles distribute randomly inside the droplet within t = 10 ns. In contrast 3 to what is found in macroscopic experiments , no sign of solid-like ordering is observed in the vicinity of contact line when the nanofluid droplets fully spread. To further examine these different spreading behaviors, we estimated the diffusion timescale of nanoparticle by Einstein diffusion theory. The distribution coefficient was defined as D=kBT/3πηd, where kB is the Boltzmann constant, T the temperature, η the viscosity, and d the particle diameter. The transport time for one particle from the center of droplet to the interface is 2 t=πR /D=250 ns (R is the radius of the droplet), much longer than the entire spreading process of 10 ns. In other words, there is not enough time for nanoparticles to self-assemble into ordered structured in the contact line region. The dimensionless droplet spreading radii (R’=R/R0, where R0 is droplet radius before spreading) versus dimensionless time (t’=γt/µR0, where γ is the surface tension of water) is plotted in Fig.2a.

Fig. 1: Spreading of nanoscale water droplets with different particle loadings at t = 10 ns. (a) pure water, (b) particle volume fraction φ = 3.43% (number of particles n = 9), (c) φ = 6.77% (n = 18), and (d) φ = 9.87% (n = 27). Water molecules are set to be semi-transparent for better visualization of gold nanoparticles within the drop from (b) to (d).

To examine the role of surface tension, two NVT systems, one with two flat free surfaces and the other with only one bulk liquid were simulated. The time-averaged surface excess energies of these two systems (-) were calculated, leading to the surface tension ((-)/Ainterface) of pure water and nanofluids with different particle loadings as summarized in Table 1. The excess energy method gives γ=0.06793 N/m at T=300 K for pure water, close 6 to the experimental data of γ=0.072 N/m . The

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increasing in surface tension of water droplet with non-surfactant nanoparticles attributes to the stronger van der Waals interactions between particles at the L-V interface. Table 1 L-V surface tension based on free energy method. water n=9 n=18 n=27 φ 0 3.43% 6.77% 9.81% (eV) -1789.081 -2841.828 -3885.474 -4943.323 -1796.242 -2853.841 -3910.417 -4969.034 γlv(N/m) 0.06793 0.1002 0.1109 0.1175

MD simulations. The addition of non-surfactant nanoparticles hinders rather than enhancing spreading during the nano-second process. The contact line mobility decreases with increasing nanoparticle volume fraction and particle-water interactions, due to the increased surface tension and liquid-solid friction. a.

The spreading coefficient, S =γsv - γsl - γlv, can be used to characterize droplet spreading capability, where γ is the surface tension and subscripts s, v and l stand for solid, vapor and liquid, respectively. The contact line mobility is driven by the competition among the surface tension force, the adhesion force between solid and liquid phases, and the viscous stress. The spreading coefficient equals to the resultant force triggering the outspreading motion of contact line. The liquid-vapor surface tension increases with increasing nonsurfactant nanoparticle loading, leading to a smaller spreading coefficient. This reduced spreading coefficient corresponds to a slower contact line velocity and a smaller equilibrium spreading radius.

b.

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In the molecular kinetic theory (MKT) , the contact line mobility is a measure of the attachment or detachment of molecules to or from the substrate. The MKT theory gives the relation between the contact line velocity (U) and the contact angle (θ) following U/cosθ~γlv/ζ, where ζ is the liquid-solid friction coefficient. As shown in Fig. 2b, the relation between U and cosθ shows good linearity for t >3 ns (cosθ > 0.8). The slopes obtained from linear fitting of U~cosθ for pure water and nanofluids of different particle loadings give γlv/ζ=5.294±0.258. The resulting liquid-solid friction of pure water is 0.0143Pa·s, which has the same 8 magnitude reported by Blake et al. . Similar values of γlv/ζ for pure water and three nanofluids indicate that, the liquid-solid friction also increases with increasing liquid-vapor surface tension. Since the dissipation mechanism in the MKT theory discards viscous dissipation in the bulk liquid and only focuses on the local dissipation in the vicinity of the contact line region, the liquid-solid friction ζ defined in this approach is affected only by surface tension. Larger surface tension due to higher non-surfactant nanoparticles volume fraction leads to a larger liquid-solid friction for the dynamic wetting process. The effect of nanoparticle wettability on the dynamic wetting of nanofluid droplets is also examined by changing the particle-water interaction energy ε. With the increase of ε from 0.0271 eV to 0.0543 eV and to 0.0814 eV, the wettability of particles increases and the resulting droplet spreading kinetics suppresses due to stronger interactions between nanoparticles and water molecules. In conclusion, the dynamic spreading of water nano-droplets with non-surfactant is examined using

Fig. 2: Wetting kinetics and contact line mobility of nano-droplets of different particles loading. a) Dimensionless spreading radius versus dimensionless time and (b) contact line velocity versus contact angle. References [1] Choi U.S., Developments Appl. Non-Newtonian Flows, ASME, FED 231, pp. 99-105, 1995. [2] de Gennes P.G., Wetting: statistics and dynamics, Rev. Mod. Phys. 57(3), pp. 827-863, 1985. [3] Wasan D.T. and Nikolov A.D., Spreading of nanofluids on solids, Nature 423(6936), pp. 156-159, 2003. [4] Horn H.W., Swope W.C., Pitera J.W., Madura J.D., Dick T.J., Hura G.L., and Head-Gordon T., Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew, J. Chem. Phys. 120(20), pp. 9665-9678, 2004. [5] Daw M.S., Foiles S.M., and Baskes M.I., The Embedded-Atom Method - a Review of Theory and Applications, Mater. Sci. Rep. 9(7-8), pp. 251-310, 1993. [6] Gittens G. J., Variation of surface tension of water with temperature, J. Colloid Interface Sci. 30(3), pp. 406-421, 1969. [7] Blake T.D. and Haynes J.M., Kinetics of liquid/liquid displacement, J. Colloid Interface Sci. 30(3), pp. 421-423, 1969. [8] Blake T.D., The physics of moving wetting lines, J. Colloid Interface Sci., 299(1), pp. 1-13, 2006.

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FORMATION OF NANOPARTICLE STRIPE-LIKE DEPOSITS AT DRIVEN RECEDING CONTACT LINES Diego NOGUERA-MARÍN, Carmen L. MORAILA-MARTÍNEZ, Miguel A. CABRERIZO-VILCHEZ, Miguel A. RODRIGUEZ-VALVERDE Biocolloid and Fluid Physics Group, Applied Physics Department, Faculty of Sciences, University of Granada, 18071 Granada E-mail: [email protected]

In order to produce well-ordered structures via evaporation of colloidal suspensions [1], it is essential to control the evaporation flux, solute concentration, interaction between the solute and the substrate, etc. Several authors have reported that the pH of the solution modifies the final deposit pattern [2-4]. Bhardwaj et al. [2] explained the transition between different patterns by considering how the electrostatic and van der Waals forces (known as DLVO forces) alter the particle deposition process. Moraila-Martínez et al. [3] concluded that the morphology of the nanoparticle deposits is modulated to a different extent by the strength of the particle–particle repulsion, the substrate–particle wettability contrast and the substrate receding contact angle. However, nanoparticle patterning is ultimately ruled by contact line dynamics.

are able to decouple the evaporation from the motion of triple line and to explore separately certain effects. We used the minimum speed of liquid removal (6.9 µm/s) imposed by the microinjector (PSD3 Hamilton) and the 3 cell dimensions (Hellma 50 x 50 x 10 mm ). This way, we operated in the quasistatic regime of contact line motion (low capillary number). The relative humidity was ca. 50% and the temperature 25ºC. We monitored the contact line dynamics with a CCD camera (Qimaging Retiga 1300) coupled to an objective. The deposits found on the substrates were subsequently observed with white light confocal microscope (PLµ, Sensofar Tech S.L.). We measured the particle electrophoretic mobility as a function of pH value using a Zetasizer Nano device (Malvern) for all types of nanoparticles used in this study, at a concentration of 0.01% (v/v). The results are shown in Fig. 2. G la s s -‐2 5 nm P MMA -‐9 5 nm S iO 2 -‐9 0 nm

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Wettability contrast (difference between the receding contact angles of substrate and particle) promotes (or inhibits) the pinning of contact line, thus the accumulation of particles near the contact line is enhanced with positive wettability contrasts. Further, as greater wettability contrast, the contact line pinning should take longer time. In this work, we intend to examine the impact of the wettability properties of the substrate-particle system on the deposit morphology upon minimum electrostatic interactions. From the work of Moraila-Martínez et al. [3], the electrostatic double layer interactions were modified by diluting the nanoparticles in buffer solutions at different pH values. The set-up used (see Fig. 1) was similar to the device described by Bodiguel et al. [5]. With this device, we

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We confirmed that the contact line dynamics (see Fig. 3) and the final deposit depended on the solution pH. Although stick-slip events were optically found at pH2, stripe-like patterns were formed for both pH values (see Fig. 4). However, the pattern morphology changed as the medium pH. The DLVO scenario of interacting particles is described as a steady-state situation, where the particles freely diffuse through the liquid. In the problem of drying of particle suspensions, the particles are further driven by a convective flow. In general, the substrate-particle repulsion opposes to the particle diffusion towards the substrate. However, near the substrate, the particle-particle interaction of strongly charged particles may push the particles against the substrate where the particles are further driven by the evaporation-driven convective flow. Particle deposition is mitigated when the substrate-particle electrostatic repulsion is strong and the interparticle interaction is weak.

hysteresis (pinning time, stick-slip behavior) and receding contact angle (wedge-shaped region, evaporation-driven convective flow, height deposit) of the substrate. We applied three surface treatments 2 over glass slides (75x24 mm , Menzel-Gläser): cleaning (starting point), Argon RF plasma (full removal of organic pollutants), heating (removal of hydroxyl groups). These treatments produced smooth substrates with different wettability properties: plasma-treated glass (contact angle hysteresis=1.2º), clean glass (13º) and dehydrated glass (47º). Contact line dynamics (stick-slip behaviour) correlated to the wettability contrast and the substrate contact angle hysteresis (see Fig. 5). As expected, the stripe-like deposits formed were also dependent on the contact line motion (see Fig. 6) although the maximum height of the three deposits saturated over 1.0-1.3 µm. The main differences were found on the horizontal dimensions of each deposit and the stripe shape. This opens up a new method of controlling colloidal deposition patterns through the change of system electric properties and of wettability properties of the substrate. 1 .5

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This work was supported by the “Ministerio Español de Ciencia e Innovación” (project MAT2011-23339) and the “Junta de Andalucía” (projects P08-FQM-4325 and P09-FQM-4698).

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[1] N. Vogel, C. K. Weiss and K. Landfester, Soft Matter, 2012, 8, 4044–4061. [2] R. Bhardwaj, X. Fang, P. Somasundaran and D. Attinger, Langmuir, 2010, 26, 7833–7842. [3] C.L. Moraila-Martínez, M.A. Cabrerizo-Vílchez and M.A. Rodríguez-Valverde, Soft Matter, 2013,9, 1664-1673 [4] C. Hsueh, C.L. Moraila Martínez, F. Doumenc, M.A. Rodríguez-Valverde and B. Guerrier. Chemical Engineering and Processing (2012) doi: 10.1016/j.cep.2012.07.006. [5] H. Bodiguel, F. Doumenc and B. Guerrier, Eur. Phys. J. Spec. Top., 2009, 166, 29–32

For weak electrostatic interactions, we explored different values of wettability contrast between substrate and particle (self-pinning), contact angle Abstract #136

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PARTICLE FORMATION OF DRUG-LOADED POLYMER MICROPARTICLES PREPARED BY ELECTROSPRAYING USING MIXED SOLVENT SYSTEMS Adam BOHR 1,2,3, Feng WAN 2, Mohan EDIRISINGHE 3, Mingshi YANG 2

1

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Institut Galien Paris-Sud, Faculté Pharmacie, Université Paris-Sud, 5 rue J-B Clément 92290 Châtenay-Malabry, France. Department of Pharmaceutics and Analytical Chemistry, University of Copenhagen, Universitetsparken 2, Copenhagen 2100, 3 Denmark. Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK E-mail: [email protected]

Drug delivery systems based on polymeric micro-particle carriers continue to be of interest for formulation of large molecules and low solubility drugs. Such drug-carrier systems may help protect and stabilize the drug from the often harsh biological environments and provide controlled release of the 1 drug . Electrospraying is an attractive and relatively new technique for the preparation of carrier particles for drug delivery applications. The technique is based on the atomization of a liquid into small droplets under the influence of electrical forces and the subsequent drying of these droplets into particles. With electrospraying near-monodisperse particles are prepared in a one-step process without the use of elevated temperatures or surfactants, thus overcoming some of the limitations associated with other particle preparation techniques. Further, a broad range of materials can be used and characteristics such as size, morphology and surface chemistry of the particles 2 produced may be controlled to some extent . Yet, the process is complex due to the interplay between different interdependent parameters, which influence the characteristics of the resulting particles and the 3 particle formation process is still not fully understood . The solvent composition of the feed solution is an important process parameter and has a great effect on the particle formation and characteristics. The evaporation rate and solubility of the solvent(s) largely determine the precipitation of solutes in the droplets and their formation into particles. The objective of this study was to investigate binary solvent mixtures and their influence on the particle characteristics of poly(lactic-co-glycolic acid) (PLGA) particles loaded with the small molecule drug Celecoxib (CEL). All solutions of PLGA and CEL were prepared at a solute concentration of 5%w/v and a drug loading of 10%w/w using mixtures of the solvents acetone (ACE) and methanol (MeOH) at molar ratios 100:0, 90:10, 75:25 and 69:31 (ACE:MeOH). The particles were produced using a single nozzle electrospraying setup. The viscosity of the solutions were measured using an Ubbelohde viscometer (Cannon instruments). The evaporation profile of feed solutions were evaluated using thermogravimetric analysis (TGA) at 25 ºC. The morphology and size of the particles were determined using scanning electron microscopy (SEM) (JEOL JSM-6301F). The surface chemistry of the particles was measured and calculated using X-ray photoelectron spectroscopy (XPS) (Thermo Scientific).

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A

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D

Fig. 1: SEM images of microparticle samples, 10D100:0 (A), 10D90:10 (B), 10D75:25 (C) and 10D69:31 (D).

The intrinsic viscosity of PLGA in the mixed solvents decreased with increasing MeOH content (0.24-0.15 dL/g) indicating a reduction in solubility as a function of increased MeOH content. The polymer chain conformation was thus more compact for solutions containing MeOH while the polymer chain were more stretched out in the solution with pure ACE. The evaporation time was shorter for pure solvent mixtures than for the feed solutions and further the evaporation rate became slightly lower with increasing MeOH concentration. The indicates that the particle formation would be slower for samples with increasing MeOH concentration. SEM images showed that the microparticles had either smooth or grainy surfaces (see Fig. 1) depending on the solvent composition with increasing roughness as the MeOH concentration was increased. The particles were between 2-4µm in diameter and particles prepared in ACE/MeOH mixtures were smaller than those prepared with pure ACE with a fine correlation between MeOH concentration and particle size. This observation can partly be explained by the higher electrical conductivity of MeOH compared with 4 ACE resulting in smaller particles, a well-known effect . Although all particle samples were prepared with 10% CEL and 90% PLGA the surface chemistry measurements showed that the CEL concentration on the surface ranged between 20-41%. The surface CEL concentration gradually increased with increasing MeOH concentration. The notable difference observed in surface drug concentration indicates that phase separation may have taken place between PLGA and

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CEL at high MeOH concentrations. This work demonstrates that particle formation in the electrospraying process depended markedly on the solubility of the solutes, Celecoxib and PLGA and also on the evaporation rate of the solvents. The microparticles prepared from solvent mixures using electrospraying exhibited different size (2-4µm), surface roughness. Results from surface chemistry analysis showed the CEL was enriched on the particle surface with increasing MeOH concentrations indicating the importance of solvent properties on the migration of CEL and PLGA in the droplet during particle formation. There was a good correlation between the particle samples studied and the different characteristics evaluated. It is believed that better understanding on the influence of solvent systems on particles formation and on relevant particle characteristics can be exploited in particle engineering and lead to better performance of drug loaded particles References [1] Vehring R., Pharmaceutical particle engineering via spray drying, Pharmaceutical Research, 25(5), 999-1022, 2008. [2] Jaworek A., Sobczyk AT., Electrospraying route to nanotechnology: An overview. Journal of Electrostatics, 66(3-4), 197-219, 2008. [3] Park C., Lee L., Electrosprayed polymer particles: Effect of the solvent properties, Journal of Applied Polymer Science, 114, 430-437, 2009. [4] Gañan-Calvo A., Davila J., Barrero A., Current and droplet size in the electrospraying of liquids. Scaling laws, Journal of Aerosol Science, 28, 249-275, 1997.

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CONFINED DRYING OF COMPLEX FLUIDS DROP Laure DAUBERSIES, Jacques LENG, Jean-Baptiste SALMON LOF, UMR5258, 178 av. Schweitzer, 33608 PESSAC. E-mail: [email protected]

The elaboration of phase diagrams is an important day-to-day task in physical-chemistry with direct and economic implications in many industrial realms (cosmetics, foodstuffs, chemical enhanced oil recovery, etc.). Building such a diagram is in principle simple and tedious and consists of mixing chemicals, usually by hand, and monitoring the state of the mixture. Here, we present a simple method—drying of a drop of a complex fluid in a confined geometry, see fig. 1—that permits one to quantitatively reconstruct a phase diagram, and to estimate thermodynamic and kinetic information. This method allows the exploration of a given out-of-equilibrium route from dilute up to very concentrated regimes with great simplicity: it indeed consists of watching a solution or a dispersion left to dry between two circular and transparent wafers (typical diameter 8 cm). Confinement not only casts specific kinetics to evaporation but also facilitates the use of analytical tools for the observation. In that sense, this drying setup bypasses most of the difficulties related to the drying of sessile drops. Moreover, the precise analysis of such experiments, and its comparison with a recent model [1] describing the drying kinetics in such confined geometries, allows the estimation of both the activity of the mixture (i.e. the driving force of evaporation), and its mutual diffusion coefficient (that governs the relaxation of concentration gradients).

Fig. 1: (a) Schematic view of the confined drying cell, typical sizes: h = 100µm, volume of the drop 1µL, wafer diameter 8cm, initial droplet diameter 1-2mm. (b) Examples of the drying for a model colloidal dispersion (left, [2]), a copolymer solution (right, [3]).

In the present work, we show on a model complex fluid, a block copolymer solution (see Fig. 1(b) right), that the direct observation of the drying kinetics in such a confined geometry, which includes (i) the measurement of the volume of the drop against time, (ii) the monitoring of a series of nucleation events, and (iii) spatially-resolved Raman spectroscopic measurements of the solute concentration field within the drop, yield estimations of the complex fluid phase diagram, its activity and mutual diffusion coefficient against the solute concentration [3]. We also evidenced that the drying induces radial gradients of concentration in the confined drop, thus leading to differences of density orthogonal to the gravity that yield in turn buoyancy-driven flows. The magnitude of these buoyancy-driven flows in such a confined geometry can be estimated within the lubrication approximation by a balance between buoyancy and viscous dissipation. Astonishingly, we demonstrated that such flows have a negligible influence on the concentration gradient that generate them, and thus on the drying kinetics. Importantly, such flows yet exist and can transport efficiently larger solutes such as colloidal species dispersed in the mixture [4]. References [1] Daubersies L., Salmon J.-B., Evaporation of solutions and colloidal dispersions in confined droplets, Phys. Rev E 84, 031406, 2011. [2] Daubersies L., Leng J., Salmon J.-B., Confined drying of a complex fluid drop: phase diagram, activity, and mutual diffusion coefficient, Soft Matter 8, 5923 (2012) [3] Leng J., Drying of a colloidal suspension in confined geometry, Phys. Rev E 82, 021405, 2010. [4] Daubersies L., Selva, B., Salmon J.-B., Solutal Convection in Confined Geometries: Enhancement of Colloidal Transport, Phys. Rev. Lett. 108, 198303 (2012)

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EVAPORATION DYNAMICS AND SEDIMENT PATTERN OF A SESSILE PARTICLE LADEN WATER DROP

Guillermo HERNÁNDEZ-CRUZ1, Minerva VARGAS3, J. Luis LUVIANO1 J. Arturo PIMENTEL2, Gabriel CORKIDI2 and Eduardo RAMOS1 1

2

Renewable Energy Institute, Biotechnology Institute 2 Universidad Nacional Autónoma de México 3 Instituto Tecnológico de Zacatepec E-mail: [email protected]

The dynamics of the flow inside an evaporating sessile drop of water with polystyrene spheres of 1µm in diameter is described. The initial volume of the drops is in the range from 0.6 to 1µl and observations are made from the deposition, up to total evaporation. The flow is recorded in a sequence of images that are analyzed with a micro PIV system to extract quantitative information. The flow inside the drops has various stages with different time scales and according to preliminary observations, for large concentrations, it is possible to correlate the motion of the fluid inside the drop with the pattern of sediments. Three complementary optical techniques were used to obtain the images of the evaporation process of the droplet. The first was a phase contrast illumination set up under an inverted Olympus IX71 microscope with a UplanFL N 10x objective and a high speed camera Optronis 5000 running at a rate of 250 fps and with a resolution of 512 x 512 pixels. The light source was a 660nm wavelength Thorlabs USA M660L2 light emitting diode (LED). The effect of epi-fluorescence was used in the second observation procedure; for this purpose, the microscope was equipped with a 4900-ET-EGFP single band filter set in combination with a 470nm wavelength Thorlabs, M470L2 LED. The third technique was an alternating epi-fluorescence/phase contrast illumination procedure that was implemented by synchronizing with the high speed camera two high intensity LEDS (470nm and 660nm) at a frequency of 250Hz. Half wave positive cycles triggered the phase contrast illumination 660nm LED while half wave negative cycles triggered the 470nm epi-fluorescence LED. By this way, even images in the acquired sequence of images of the evaporation process registered the fluorescent particles while odd images registered the overall topography of the droplet under evaporation. With this method, it is possible to identify simultaneously the topographic image where features like membrane rupture regions show clearly and images of the fluorescent particles to be analyzed with a PIV system. In all observations the targets were distilled water drops with volumes in the range of 0.6 to 1.0 µl with fluorescent particles in suspension (Thermoscientific fluorescent microspheres coated with Firefli* Fluorescent Green (468/508nm)). Drops were deposited on a round VWR micro cover glass. The temperature was stabilized and controlled to 14 ºC with a Bipolar Temperature Controller CL-100

(Warner Instruments, USA) coupled to a Peltier device SC-20 series platform (Warner Instruments, USA) and a RE415 Cooling Thermostat (Lauda-Königshofen, Germany). The environmental relative humidity was 30% - 48%. We used the image analysis software Image-Pro v7.0 to trace semi-automatically the membrane's rupture contour while the droplet was evaporating. This was achieved by using the auto tracing edge detection procedure selecting at least two sample points in such border region, so the algorithm could follow the remaining contour of the breaking membrane automatically. The coordinates of the rupture contours were saved in text format to integrate them with the PIV results. The number of particles per unit volume was measured with a Neubauer chamber and a grain counting image analysis procedure that measures the total intensity of light emitted by the particles in a known liquid volume, subtracting the background light and dividing by the average light emitted by a single particle. The drops with volumes of 1µl have initial footprints of approximately 1 mm in diameter and the suspensions 5 6 used have 3.2 X 10 to 5.67 X 10 micro-spheres per µl . For the PIV analysis, we use interrogation areas of 16 X 16 pixels and 25% overlap. In the range of volumes explored, the evaporation processes last typically several minutes with the exact duration depending on the relative humidity in the room. The process can be divided in four parts. In the first, the drop takes the shape of a spherical cap and the velocity of the fluid inside the drop is very slow and difficult to resolve but particles emigrate steadily towards the contact line and build up to start forming the coffee ring. The general motion pattern, as calculated with numerical models, has been suggested to be a convective cell with radial symmetry around the vertical axis, but experimental observations are not conclusive since counter-flowing streams are difficult to resolve in plane views. Also, random motions of tracers reduce substantially the signal to noise ratio. In this stage, the slow radial velocity allows the particles that pile up at the rim of the drop (coffee ring) to accommodate in crystalline arrangements (Marín et al. (2011)). Analysis of the structure of the outer layers of the coffee ring indicates that its height is approximately one micron and that the structure is ordered. This first part of the evaporation takes up to 80% of the total

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time.In the second part of the evaporation process, the drop is almost flat and the velocity field inside the drop is mostly radial to compensate for the preferential evaporation near the contact line. The radial velocity can be estimated by making a mass balance and it is found that the radial velocity grows as a function of time as an hyperbola, i.e. vr ∼ 1/(t-to), Deegan et al. (2000). This process continues up to the point when the thickness of the drop is reduced to a layer with a thickness of few microns with a rapid accumulation of the particles near the contact line which results in a quick thickening of the coffee ring with particles piling up in a disordered pattern. In these two first stages, the edge of the drop remains pinned and can be well approximated by a circle. The third part of the process starts when the liquid film is sufficiently thin and rips off from the coffee ring and a complicated interaction of surface tension which pulls the liquid to reduce the area and evaporation, determine the internal flow. In the initial stages of this part a transient formation of a secondary coffee ring slows down the motion of the retracting contact line forming relatively thick sediment segments with the shape of short circular arcs. Subsequently, the geometry of the outer boundary of the drop becomes unstable and small perturbations modify its local curvature to generate a time dependent non-circular edge.

thin radial segments of sediments. This situation prevails until the liquid totally evaporates. The time scale of parts three and four can be estimated by considering that the motion is promoted by the force (per unit distance) produced by the surface tension as the evaporation makes subsequent positions unstable. Assuming radial symmetry and making a balance between the force per unit distance given by Young-Laplace equation and the local acceleration we 3 1/2 get t ∼(ρ/γr ) . The corresponding radial velocity scale 1/2 is vr ∼(γ/ρr) i.e., for a given material, the velocity growth is proportional to the inverse of the square root of the radius. In Figure 1, an example of the last three stages of evaporation is shown.

Fig. 2: Radial velocity averaged over a circles of radii: 0.8R (green line), 0.5R (blue line) and 0.3R (red line), where R is the radius of the contact line. Thin lines are data from 15 averaged PIV velocity fields. Thick lines are local smoothing using 30 points.

Fig. 1: Illustration of the last three stages of the evaporation process. The initial footprint of the drop is 1 mm in diameter. Upper row: Inverse Optical microscope images. In the lower row, the velocity field occurring inside the drop is shown in plan view. Left column: Second part of the evaporation process; the liquid fills the whole circular area inside the coffee ring, the internal flow is mostly radial and drags particles toward the edge. Central column: Third part of the evaporation process; relatively thick, circular arcs of sediment indicate the formation of secondary coffee rings. Right column: Fourth part of the evaporation process; surface tension dominates the flow, the drop becomes almost circular and thin radial sediment segments are generated. During the fourth part of the process, local irregular features of the drop edge are smoothed out by surface tension. For large concentrations, this effect generates fast inward radial flows which sweep particles forming 230

In Figure 2, we show the radial velocity averaged over rings of various radius as functions of time. The tracers show a maximum that is displaced towards larger times for smaller radii. The gradual acceleration is consistent with the hyperbolic growth predicted for the second part of the evaporation process. The velocity readings from rings with large radii drops earlier than those with smaller radii indicating, as expected, that the dry zone grows from the contact line inwards. The traces for r = 0.5R and smaller display a double maximum which results from a not symmetric process and that the averaging over fixed rings is not representative of the whole process. Observations made with low particle concentration revealed that once the drop brakes loose from the coffee ring, the shape of the liquid zone is strongly asymmetric and depends critically on local effects. These effects include partial attachment of the membrane to the coffee ring, zones with non uniform accumulation or depletion of spheres, and others. References [1] Deegan R. D., Bakajin O., Dupont T.F., Huber G., Nagel S.R., and Witten T.A. Phys. Rev. E, Volume 62, pp. 756-765, 2000. [2] Marín A.G., Gelderblom H., Lohse D. and Snoeijer J. H., Order-to-disorder transition in ring-shaped colloidal stains, Phys. Rev. Rev., Volume 107, 085508, 2011.

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WETTABILITY CONTROL OF SILICON BY CREATING SUB-30 NM NANOPILLARS VIA SELF- ASSEMBLED BLOCK COPOLYMER TEMPLATES AND POLYMER BRUSH DEPOSITION Parvaneh Mokarian-Tabari1,2, Ryan Enright 2,3 and Michael A. Morris1,2

1

Department of Chemistry, University College Cork and Tyndall National Institute, Cork, Ireland, Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN), Trinity College Dublin, Dublin, Ireland. 3 Thermal Management Research Group, Efficient Energy Transfer (ηET) Dept., Bell Labs Ireland, Alcatel-Lucent Ireland, Blanchardstown Business & Technology Park, Snugborough Rd, Dublin 15, Ireland. E-mail: [email protected] 2

Superhydrophobic surfaces in the so-called Cassie or non-wetting state display extreme wetting behavior through a combination of surface texture and hydrophobic surface chemistry that can cause water droplets to roll or bounce off, carrying away dust particle and other contaminants in the process. Potential applications for these surfaces range from self-cleaning surfaces to water condensation surfaces for enhancing energy efficiency in power generation and water desalination. In nature, we find biological systems that combine material properties and texture to achieve specific functionality. Examples include the anti-wetting and self-cleaning properties of the Lotus leaf, the anti-dew properties of the Dog’s Bane leaf and the anti-reflective properties of insect’s eyes. These examples highlight that designing functional surfaces often requires the geometrical control of surface feature shape, size and periodicity at nanometric length scales. However, fabricating increasingly smaller nanostructures (below 30 nm), while maintaining precise geometric control over large areas presents a significant challenge. Structure length scale has been shown to be especially 1,2 important in structure-enhanced condensation. It has been shown that, beyond the typical thermodynamic criteria for Cassie or Wenzel (complete) wetting states, there is a structure-length-scale dependent wetting 2 criterion dictated by the droplet nucleation density. So far, this criterion has limited the maximum heat flux that can be sustained by structure-enhanced condensation surfaces before transition to the Wenzel state due to 1 increasing droplet densities [Miljkovic et al]. Thus, our aim is to study droplet formation and growth rates during water condensation on sub-30 nm features and extend the Cassie-to-Wenzel transition to larger heat fluxes. Lithography is a fundamental process in the manufacture of complex geometries, but is rapidly approaching its physical resolution limits. Here we demonstrate the fabrication of periodic sub-30 nm silicon nanopillars using a block copolymer pattern transfer technique. The ability of block copolymers to self-assemble into well-defined, periodic arrays with sub 100 nm dimensions provide ideal mask etch templates for nanolithography purposes. In combination with chemical functionalization, the silicon features, etched using the block copolymer pattern

transfer technique, are used to modify the apparent wettability of the surface. Block copolymers consisting of two covalently bound, but otherwise immiscible, polymer chains self-assemble into well-defined, ordered arrays with characteristic length scales from 1-100 nanometers. We used polystyrene-block-poly ethylene oxide (PS-b-PEO) block copolymer purchased from Polymer Source with average molecular masses of blocks MPS = –1 –1 42 kg mol and MPEO = 11 kg mol . 30 nm thin PS-b-PEO films were spun cast from toluene solution onto bare silicon substrates and exposed to toluene at 3 50 °C (vapour pressure of 12.3 kPa) for 45 minutes. The samples were quenched at room temperature and imaged with AFM (tapping mode). Figure 1 shows the topographic AFM image of well ordered domains of PS-b-PEO with periodicity of 38 nm. To increase the etch contrast, the iron oxide inclusion method was 4 applied. The samples were then immersed in ethanol for 15 hours. After removal from ethanol, a dilute iron oxide solution was spun cast on the polymer films to allow iron oxide to diffuse into the ethanol-activated PEO domains. The film was then exposed to UV ozone for 1 hour to remove the matrix polymer (polystyrene). The template was pattern transferred onto the silicon substrates via ICP/RIE (inductive coupled plasma/reactive ion etching). This resulted in silicon nanopillars with iron oxide on top of the pillars. To remove the iron oxide, the sample was immersed in oxalic acid solution for 3 hours. Figure 2 shows an SEM image of dense, rough arrays of nanopillars (solid fraction, φ ≈ 0.22, roughness, r ≈ 3.4) on a large area of silicon. We functionalized the pillars with hydroxyl terminated polydimethylsiloxane (PDMS-OH). A solution of 1% PDMS-OH (with average molecular –1 masses of 5300 kg mol ) in toluene was prepared. The Silicon substrates were cleaned in Piranha solution. The PDMS solution was spin cast on the silicon substrates (with nanopillars) immediately after piranha cleaning. The samples were then annealed at 180 °C for 5 hours. After removing the samples from the oven, they were sonicated in toluene for 15 minutes. This step ensured that a 2-6 nm thick PDMS brush layer formed on the surface since all non-chemically bonded PDMS chains would be dissolved in toluene and removed from the surface. Water contact angles on the samples were measured

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at each processing step. The unprocessed silicon substrates used (with a native oxide layer on top) had a contact angle of approximately 26º. On the non-functionalized silicon nanopillars, a contact angle of 53º was measured. Interestingly, while this is consistent with a droplet encountering energy barriers 5 in the advancing Wenzel state on a surface not 6 satisfying the imbibition condition, we calculated the -1 critical imbibition angle to be θc = cos [(1 - φ)/(r - φ)] ≈ 76º; much larger than that measured on the smooth SiO2 substrate. Meanwhile, on the smooth PDMS-coated silicon sample, we measured contact angles of 108º. On the PDMS-coated nanopillars increased the contact angle to 127º, which is significantly lower than the expected Cassie angle of 148º. In summary, we have realized sub-30 nm pillar features in silicon using a block copolymer mask technique. The observed wettability of the fabricated and functionalized surfaces has demonstrated anomalous wetting behavior with respect to the nominal surface feature geometry realized. Ongoing work is exploring droplet hysteresis and condensation behavior, surface preparation procedures and surface defects to explain the preliminary results obtained thus far.

Figure 1: AFM topographic images showing well defined arrays of dots in a hexagonal forming PS-b-PEO film. The inset shows the FFT image indicating a periodicity of 38 nm.

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1 mm

500 nm Figure 2: SEM of the silicon surface fabricated using PS-b-PEO block copolymer as a mask template. The etched pillar structures were 23±6 (2σ) nm in diameter, 63±20 (2σ) nm high and spaced 47±9 (2σ) nm silicon nanopillars. The inset shows a deposited water droplet with a static contact angle of 127° on the PDMS coated silicon nanopillars. References 1. Miljkovic, N.; Enright, R.; Nam, Y.; Lopez, K.; Dou, N.; Sack, J.; Wang, E. N., Jumping-Droplet-Enhanced Condensation on Scalable Superhydrophobic Nanostructured Surfaces. Nano Letters 2013, 13 (1), 179-187. 2. Enright, R.; Miljkovic, N.; Al-Obeidi, A.; Thompson, C. V.; Wang, E. N., Condensation on Superhydrophobic Surfaces: The Role of Local Energy Barriers and Structure Length Scale. Langmuir 2012, 28 (40), 14424-14432. 3. Mokarian-Tabari, P.; Collins, T. W.; Holmes, J. D.; Morris, M. A., Cyclical “Flipping” of Morphology in Block Copolymer Thin Films. Acs Nano 2011, 5 (6), 4617–4623. 4. Ghoshal, T.; Maity, T.; Godsell, J. F.; Roy, S.; Morris, M. A., Large Scale Monodisperse Hexagonal Arrays of Superparamagnetic Iron Oxides Nanodots: A Facile Block Copolymer Inclusion Method. Adv. Mater. 2012, 24 (18), 2390-2397. 5. Raj, R.; Enright, R.; Zhu, Y. Y.; Adera, S.; Wang, E. N., Unified Model for Contact Angle Hysteresis on Heterogeneous and Superhydrophobic Surfaces. Langmuir 2012, 28 (45), 15777-15788. 6. Bico, J.; Tordeux, C.; Quere, D., Rough wetting. Europhysics Letters 2001, 55 (2), 214-220.

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Topic 5 Use of external forces

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DYNAMIC MEASUREMENT OF THE FORCE REQUIRED FOR MOVING A LIQUID DROP ON A SOLID SURFACE Dominik W. PILAT, Perikles PAPADOPOULOS, David SCHÄFFEL, Doris VOLLMER, Ruediger BERGER, Hans-Juergen BUTT Max Planck Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany E-mail: [email protected]

We measured forces required to slide sessile drops over surfaces. The forces were measured by means of a vertical deflectable capillary stuck into the drop. The Drop Adhesion Force Instrument (DAFI) allowed the investigation of the dynamic lateral adhesion force of water drops of 0.1 to 2 µl volume at defined velocities. On flat PDMS surfaces the dynamic lateral adhesion force increases linearly with the diameter of the contact area of the solid/liquid interface and, in accordance with molecular kinetic theory, linearly with the sliding velocity. The movement of the drop relative to the surfaces enabled us to resolve pinning of the three

phase contact line to individual defects. We further investigated a three-dimensional superhydrophobic pillar array. Depinning of the receding part of the rim of the drop occurred almost simultaneously from 4-5 pillars, giving rise to peaks in the lateral adhesion force. References Pilat D.W., Papadopoulous P., Schäffel D., Vollmer D., Berger R., Butt H.-J., Dynamic Measurement of the Force Required to Move a Liquid Drop on a Solid Surface, Langmuir, 28, pp.16812, 2012.

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INFLUENCE OF GRAVITY LEVELS ON HYDROTHERMAL WAVES IN ALCOHOL DROPLETS Florian CARLE, Marc MEDALE, David BRUTIN IUSTI Laboratory, UMR 7343 CNRS, Aix-Marseille University, 5 rue Enrico Fermi, 13453 Marseille cedex 13, France E-mail: [email protected]

Thermocapillary instabilities develop during the evaporation of volatile fluids when the surface tension gradient is strong enough. When the surface of the fluid is static, instabilities appear as a response to temperature gradients due to the relation between temperature and surface tension. This experimental study aims to have a better understanding of the parameters that influence the creation, the number and the size of these instabilities. To achieve this goal, droplets of pure alcohols (ethanol, methanol and propanol) were evaporated onto heated substrates for various levels of gravity (from microgravity to hypergravity) during parabolic flight campaigns in Bordeaux Merignac, France.

It is known that, during evaporation, a temperature gradient develops from the apex of the drop to the contact line, resulting in a gradient of surface tension, generating in most cases instabilities. Hydrothermal waves (HTWs) flow radially around the apex where most of the evaporation takes place. They are spaced by an almost constant angle along the axial symmetry of the triple line. However, one can notice that the HTWs do not develop inside the propanol (see Fig. 1) whereas a large number develop in ethanol and twice as much in methanol. The link between the fluid nature and the number of HTWs is foreseen and will be presented. µg

1.8g

1.8g

1200

1000

Heat Flux (W/m 2 )

The evolution of the drop is following by a high definition camera on the side to observe the evolution of the geometric parameters (diameter, height and contact angle) and an infrared camera on the top of the substrate in order to observe the thermal motion inside these semi-transparent fluids. A heat flux-meter measures the heat flux absorbed by the drop and the substrate temperature [1].

800

600

400 Propanol Methanol Ethanol

200

0

-10

-5

0

5

10

15

20

25

30

40

time (s) Fig. 2: Heat flux absorbed by three droplets of alcohols to evaporate at onto a substrate at temperature of 40°C

All the substrates are regulated at constant temperature. Figure 2 shows the heat flux absorbed by the droplets of the three tested alcohols, created at t = 0s on during the microgravity phase (in white). Fig. 1: Alcohol droplets evaporating onto a nuflon substrate at 45°C, average drop diameter is 8 mm, Ta = 20°C and Pa = 835 mBars

Figure 1 shows typical thermal motion inside droplets in each configuration (fluids and gravity levels). The droplets are created by injecting fluid through the substrate to have their diameters below the capillary length. However, in some case, the sphericity of the droplet is disturbed due to the vibrations the flight of the aircraft resulting in a significant jitter in the level of microgravity.

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The fluids physical properties play a major role in the behaviour of the HTWs. For the evaporation of similar volume droplets, the energy need is the lowest for propanol; indeed, this fluid has the highest value of latent heat of all the alcohols tested in this study. Therefore, the evaporation dynamics is mainly done by conduction and diffusion and does not induce turbulent motion inside the fluid. On the other hand, methanol and ethanol have a lower value of latent heat and evaporate quickly. In the 22 seconds phase of microgravity, it was possible to completely evaporate two droplets of methanol (increase of the heat flux in Figure 2 at t = 15s in blue).

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These behaviours are evidenced with the Marangoni number calculation. The effective Marangoni number (depending only of the kinematic viscosity, density, surface tension and effussivity of the fluids) is plotted as a function of the substrate temperature (see Figure 3). The high value of the Marangoni number for the methanol indicates an intense turbulent flow inside the droplets that is well observed by the infrared visualisation. Ethanol and Propanol has an effective Marangoni number of a same order of magnitude. However, it is interesting to see that, with the temperature increasing, Marangoni numbers of propanol become higher than ethanol (for a threshold of 45°C). This reversal of the trend has unfortunately not been evidence experimentally. 6 2 x 10

Ethanol Methanol Propanol

Effective Marangoni number

1.8

1.4

1.2

1

0.8

25

30

35 40 45 Temperature (°C)

50

55

Fig. 4: Number of hydrothermal waves plotted as a function of the dimensionless time of evaporation [3]

Microgravity experiments show the same power law evolution. Three more levels of gravity (0.16, 0.38 and 1.8g) have been added to this study to complete this investigation. Using fast Fourier transform (FFT) on the infrared images of the droplets, the spatial wavelength of the HTWs is investigated. On a side note, this study has a double interest: scientific but also technological. This experience is the test phase of the IMPACHT project funded by CNES.CAS, whose purpose is to evaporate volatile fluid droplets in a scientific satellite whose launch is planned in 2015-2016 to deepen the study of the dynamics of the evaporation in microgravity. The experimental cell, which flies during the parabolic flight campaigns, is the prototype of the one that will fly in the satellite. These campaigns have enabled us to correct the technical problems that have not been taken into account in its design, like improving of the injection and flushing system, as well as optical adjustments of the infrared windows. [4]

1.6

0.6 20


60

Fig. 3: Effective Marangoni numbers for the three alcohols as a function of the temperature

Due to the high roughness of the substrate, the evaporation of the drops occur at pinned contact line (constant wetting diameter) forcing the contact angle to decrease. Therefore, the rolls that develop at the vicinity of the contact line due to the intense thermal gradient are more and more confined inside the fluid and strongly depends of the height of the drop. This aspect will be investigated more in details during a numerical study based on the Navier-Stokes equation. [2] Most of the time, instabilities have been found to form concentric torus around the apex rotating in the same direction from hot to cold area. The external torus is smaller but more intense due to the system configuration. A shear phenomenon appears between the two torus where instability develops and get dragged in the flow. This leads to a detachment of the thermal plume, well visible on the infrared visualisation. Due to this height-dependency, and since height decreases over time, the number and behaviour of the HTWs also evolves over time. We have observed a power law decay of the number of instabilities with a substrate temperature and volume of the drop influence as shown on Fig. 4. [3]

Acknowledgements

The authors would like to thanks the "Centre National d'Etudes Spatiales" for their financial support and the parabolic flight campaigns and the European Space Agency and Novespace for the 2nd Joint European Partial-g Parabolic Flights (JEPPF) campaign on Decembre 2012. References [1] D. Brutin, Z. Zhu, O. Rahli, J. Xie, Q. Liu, and L. Tadrist, Evaporation of Ethanol Drops on a Heated Substrate Under Microgravity Conditions, Microgravity Science and Technology, 22, 387 (2010) [2] M. Medale and B. Cochelin, A parallel computer implementation of the Asymptotic Numerical Method to study thermal convection instabilities, Journal of Computational Physics, Volume 228, Issue 22, 8249-8262 (2009) [3] F. Carle, B. Sobac, and D. Brutin, Hydrothermal waves on ethanol droplets evaporating under terrestrial and reduced gravity levels, J. Fluid Mechanics, 712, 614–623 (2012) [4] G. Pont, D. Brutin, F. Carle, D. Bruno, L. Bernabé, Steps towards the development of a payload dedicated to the study of the evaporation of a sessile droplet, 63th IAC - Naples (2012) [5] F. Carle, B. Sobac, and D. Brutin, Experimental evidence of the atmospheric convective transport contribution to sessile droplet evaporation, Applied Physics Letters, Volume 102, Issue 6, 061603 (2013).

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INTERFACE LOCALIZED LIQUID DIELECTROPHORESIS

Glen McHALEa, Carl V. BROWNb, Michael I. NEWTONb, Gary G. WELLSb, Naresh SAMPARAb, Christophe L. TRABIa a

Faculty of Engineering & Environment, Northumbria University, Ellison Place, Newcastle upon Tyne NE1 8ST, UK b School of Science & Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, UK. E-mail: [email protected]

In electrowetting a conducting liquid droplet acts as one electrical contact on a hydrophobic surface which is separated from a conducting surface by a thin insulator. This capacitive structure includes both interfacial and electrostatic energies and so the equilibrium contact area and contact angle of the droplet depends on the voltage. Berge recognized that this could be a method to create voltage controlled reversible hydrophilicity on 1,2 a hydrophobic surface , and that this was a powerful method to control and manipulate droplets of liquid. Since then electrowetting (on-dielectric) has been 3,4 5 and applied to optical devices , displays 6,7 microfluidics . Electrowetting contains a number of limitations including requiring a conducting liquid and a direct electrical contact (at least in principle). It has also been difficult to achieve low contact angles for droplets in air. Another electrostatic method of manipulating 8,9 liquids is to use liquid dielectrophoresis (LDEP) . When a liquid is composed of dipoles then a non-uniform electric field can produce a net force. Normally, this is considered as a bulk liquid effect. In our work, we use an electric field that decays with distance from the solid surface. We show how the effects of liquid dielectrophoresis can be localized to liquid-air, liquid-solid and liquid-liquid interfaces thus providing a powerful method to control the wetting of surfaces and the shapes of liquid interfaces.

can be brought together in a single notational form by using the value of voltage, VTH, at which complete 13 wetting, i.e. cosθ(VTh)=1, is predicted to occur ,

⎛ V cos θ e (Vo ) = cos θ e (0) − [cos θ e (0) − 1]⎜⎜ o ⎝ VTh

2

⎞ ⎟⎟ (3) ⎠

We conducted droplet experiments using 1, 2 propylene glycol in air on a substrate fabricated with parallel planar interdigitated electrodes of finger width and gap spacing of 80 µm coated with a hydrophobic 2 µm thick SU-8 film to prevent accidental damage to the device. The effect of this film is to slightly reduce the 10 strength of the non-uniform field in the droplet . The electrodes create a decaying electric field with distance from the substrate, but also introduce a periodic modulation of the field in the direction across the electrodes. A 10 kHz peak-to-peak voltage caused the liquid to spread along the electrodes giving a stripe droplet configuration. A side view profile revealed a circular arc cross-section from which a contact angle could be measured. The data (Fig. 1) shows some contact angle hysteresis, but is very consistent with the predictions of eq. (2).

For a uniform layer of a dielectric liquid of depth h on a solid surface with an electric potential that decays with depth of penetration into the liquid, i.e. V(z)=Voexp(-2z/δ), where δ is a penetration depth, the electrostatic energy 10,11,12 , per unit contact area, wE, stored in the liquid is

wE = −

ε oε lVo2 2δ

⎡ ⎛ − 4h ⎞ ⎤ ⎢exp⎜ δ ⎟ − 1⎥ ⎠ ⎦ ⎣ ⎝

(1)

For a dielectric droplet in air with a maximal height>>δ, the effects of liquid dielectrophoresis are then effectively localized to the solid-liquid and solid-air interfaces. For a thin dielectric liquid film with hδ remains valid. Similar effects with a focus on liquid lens applications have been published for axisymmetric droplets in 14-16 . In our own liquid-liquid systems by Yang et al preliminary work on liquid-liquid systems using the stripe droplet format, we have observed an initial

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response corresponding to a centering motion of the droplet, followed by a linear relationship between the square of the voltage applied and the cosine of the contact angle. In our work the ratio of slopes from this curve for droplets of different liquids (with ε2 and ε3) in the same immiscible immersion liquid (with ε1) appears to follow the ratio (ε2-ε1)/(ε3-ε1) of the droplets as would be expected from the two-liquid analogue to eq. (2). The effects of non-uniform electric fields are not restricted to the equilibrium wetting, but can also alter the dynamics of spreading. When a droplet is first deposited on a substrate it is in an out-of-equilibrium shape. Subsequently, it will spread until the dynamic contact angle tends to the equilibrium one, i.e. θ(t) → θe(Vo). Since the driving force is γLV[cos θe(Vo)- cosθ(t)] the rate of spreading will depend on the applied voltage. Starting from eq. (3) three regimes can be predicted: i) an exponential approach to equilibrium (VVTh). Recently, we demonstrated experimentally that three regimes exist with dynamics consistent with these expectations. Importantly, regime three provides a demonstration of the ability to induce super-spreading 13 using a voltage and without the use of surfactants . When a non-uniform electric field is used with a constant thickness thin film of dielectric liquid, rather than a droplet, the decay of the electric field can be incomplete at the upper liquid interface. As a consequence static wrinkles can appear on its surface. Theory predicts that the fundamental sinusoidal mode 11,19 has an amplitude, Α, related to the applied voltage,

⎛ ε (ε − 1)Vo2 ⎞ − 4h ⎞ ⎟⎟ exp⎛⎜ A ∝ ⎜⎜ o l ⎟ γ LV ⎝ δ ⎠ ⎠ ⎝

(4)

We confirmed this relationship using a thin 3 µm film of 1-decanol on a substrate with interdigitated electrodes of pitch 20 µm. We also used this effect to create a 11 voltage programmable diffraction grating .

Fig. 2: Amplitude phase grating in transmission mode (λ=543 nm) using a 3 µm thick film of 1-decanol. [Data from ref. 11].

Acknowledgments The authors’ acknowledge the financial support of the UK EPSRC (grant EP/E063489/1). NS acknowledges Nottingham Trent University for the provision of PhD studentship funding and GW acknowledges the EPSRC/COMIT Faraday Partnership and Kodak (European Research) Ltd for funding. References [1] Berge, B., “Electrocapillarity and wetting of insulator films by water,” Comptes Rendus de l’ Academie des Sciences Serie II 317 (2), pp. 157-163, 1993. [2] Vallet, M., Berge, B. and Vovelle, L., “Electrowetting of water and aqueous solutions on poly(ethylene terephthalate) insulating films,” Polymer 37 (12), pp. 2465-2470, 1996. [3] Berge, B. and Peseux, J., “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3 (2), pp. 159-163, 2000. [4] Kuiper, S. and Hendriks, B. H. W., “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85 (7), pp. 1128-1130, 2004. [5] Hayes, R. A. and Feenstra, B. J., “Video-speed electronic paper based on electrowetting,” Nature 425 (6956), pp. 383-385, 2003. [6] Pollack, M. G., Fair, R. B. and Shenderov, A. D., “Electrowetting-based actuation of liquid droplets for microfluidic applications,” Appl. Phys. Lett. 77 (11), pp. 1725-1726, 2000. [7] Fair, R. B., “Digital microfluidics: is a true lab-on-a-chip possible?,” Microfluid. Nanofluid. 3 (3), pp. 245-281, 2007. [8] Jones, T. B., Gunji, M., Washizu, M. and Feldman, M. J., “Dielectrophoretic liquid actuation and nanodroplet formation,” J. Appl. Phys. 89 (2), pp. 1441-1448, 2001. [9] Jones, T. B., “On the relationship of dielectrophoresis and electrowetting,” Langmuir 18 (11), pp. 4437-4443, 2002. [10] McHale, G., Brown, C. V., Newton, M. I., Wells, G. G. and Sampara, N., “Dielectrowetting driven spreading of droplets,” Phys. Rev. Lett. 107 (18), art. 186101, 2011. [11] Brown, C. V., Wells, G., Newton, M. I. and McHale, G., “Voltage-programmable liquid optical interface,” Nature Photonics 3 (7), pp. 403-405, 2009. [12] Brown, C. V., McHale G. and Mottram, N. J., “Analysis of a static wrinkle on the surface of a thin dielectric liquid layer formed by dielectrophoresis forces,” J. Appl. Phys. 110 (2), art. 024107, 2011. [13] McHale, G., Brown, C. V. and Sampara, N., “Voltage induced spreading and super-spreading of liquids,” accepted, Nature Communications (2013). [14] Yang, C-C., Yang, L., Tsai, C. G., Jou, P. H. and Yeh, J. A., “Fully developed contact angle change of a droplet in liquid actuated by dielectric force,” Appl. Phys. Lett. 101 (18), art. 182903, 2012. [15] Yang, C-C., Tsai, C. G., and Yeh, J. A., “Dynamic behavior of liquid microlenses actuated using dielectric force,”J. Microelectromech. Syst. 20 (5), pp. 1143-1149, 2011. [16] Yang, C-C., Tsai, C. G., and Yeh, J. A., “Variable focus dielectric liquid droplet len,” Optics Express 14 (9) pp. 4101-4106, 2006. [17] Tanner, L. H., “Spreading of silicone oil drops on horizontal surfaces,” J. Phys. D: Appl. Phys. 12 (9), pp. 1473-1484, 1979. [18] McHale, G., Newton, M. I., Rowan, S. M. and Banerjee, M. K., “The spreading of small viscous stripes of oil,” J. Phys. D: Appl. Phys. 28 (9), pp. 1925-1929, 1995. [19] Brown, C. V., Al-Shabib, W., Wells, G. G., McHale, G. and Newton, M. I., “Amplitude scaling of a static wrinkle at an oil-air interface created by dielectrophoresis forces,” Appl. Phys. Lett. 97 (24), art. 242904, 2010.

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WATER DROPLETS ON SUPERHYDROPHOBIC SURFACES: COLLISIONS, GUIDED TRANSPORT, AND DROPLET LOGIC Henrikki MERTANIEMI, Robin H.A. RAS Molecular Materials, Dept. of Applied Physics, Aalto University (formerly Helsinki University of Technology) 00076 Espoo, Finland E-mail: [email protected]

Superhydrophobicity enables transport of analytes or samples carried in liquid droplets, which is attractive in biochemical applications. Recently, we reported surprising observations of rebounding droplet-droplet collisions of droplets moving on superhydrophobic surfaces.[1] In another contribution, we presented superhydrophobic tracks for low-friction, guided transport of water droplets.[2] We demonstrated that in addition to gravity, droplets could be actuated in such tracks using an electric field. Utilizing superhydrophobic tracks, we demonstrated directed, rebounding collisions of water droplets, enabling the implementation of building blocks of computing using water droplets as bits of digital information.[1]

enough time for the gas between the two droplets to drain out, and the collision results in coalescence. Conversely, in region (II), the gas layer between the droplets remains sufficiently thick during the collision, and coalescence is prevented. In collisions with high enough velocity (III), liquid surfaces are forced to approach each other by the inertia of the colliding droplets, and coalescence occurs.

By definition, a surface is superhydrophobic if the contact angle between a water droplet and the surface at the solid-liquid-air interface is larger than 150°, and the contact angle hysteresis is small, i.e., droplets readily slide or roll off when the surface is tilted slightly. For obtaining a superhydrophobic surface, a surface with a suitable roughness is required. Additionally, a hydrophobic surface chemistry is typically needed. If these requirements are fulfilled, a water droplet applied to the surface can adopt the Cassie wetting state where air remains trapped in microscopic voids below the droplet. Collisions between water droplets classically lead to coalescence into larger droplets. However, we observed that when supported by a superhydrophobic surface, two colliding water droplets can rebound like billiard balls at all collision angles, given appropriate velocity. Droplet collisions are usually classified using two parameters: Weber number and impact parameter. The Weber number, We, is defined as We = 2Rρv²/γ, where R is the droplet radius, v the relative velocity of droplets, and ρ and γ density and surface tension of the liquid, respectively. In a collision of two similarly-sized water droplets discussed here, the Weber number is a dimensionless measure of kinetic energy. The impact parameter, B, is defined as B = χ/2R, where χ is the projection of the distance between droplet centers in the plane perpendicular to v. The impact parameter ranges from B = 0 for a head-on collision to B = 1 corresponding to a grazing collision. Outcomes of water droplet collisions on a superhydrophobic surface are illustrated in Fig.1. Colliding droplets will coalesce if the air gap between them is diminished to the dimension of molecular interaction. Thus, in a low- velocity collision (I), there is

Fig. 1. Top: a mid-angle droplet collision viewed from top and from side. A moving droplet (left) hits the droplet at rest, and the droplets rebound without coalescence. Bottom: experimentally determined regimes of rebound (bounce) and coalescence of water droplets colliding with each other on a superhydrophobic surface.

The complex shapes of the coalescence/bouncing regions in Fig. 1 open rich possibilities for tuning collision outcomes. Especially, the Weber number range from 2 to 5 allows controlling of rebounding and coalescence by adjusting the collision angle. For example, this control allows suppression or triggering of chemical reactions between reactants confined within the droplets. We demonstrated a collision-controlled chemical reaction using silver nanoclusters and the quenching of their fluorescence by reaction with cysteine. In the case of a rebounding collision, the chemicals did not mix, and no reaction occurred. However, when a collision resulted in coalescence, the chemicals mixed and a chemical reaction rapidly quenched the fluorescence of silver nanoclusters. For

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transport

of

water

droplets,

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superhydrophobic tracks were fabricated by milling shallow grooves into metal plates, or alternatively, laser cutting or etching through metal or silicon substrates, respectively. Subsequently rendering the surfaces superhydrophobic prevented water droplets from entirely entering a track, even when a track had no bottom. Water droplets were able to move in a superhydrophobic track when the substrate was tilted slightly, in this case, to an angle of about two degrees. Without tracks, a droplet would move in a straight trajectory, following the gravity gradient. However, in case of the superhydrophobic surface with tracks, the droplets travelled along the track, precisely guided by the track. A droplet could be guided through many subsequent curves, provided that it did not have too high a velocity. We also demonstrated two examples of single-droplet manipulations utilizing the superhydrophobic tracks. First, placing a superhydrophobic blade in the middle of a superhydrophobic track, a droplet could be split in two smaller droplets. Droplet splitting was observed if the droplet had a sufficiently high kinetic energy compared to its surface energy. Second, using a bottomless track with a varying width, droplets could be selected by size. A local widening permitted droplets larger than the track width to continue on the track but smaller droplets were not supported by the track and fell through the substrate. Since superhydrophobic tracks enable the control over the geometry of droplet collisions, we utilized such tracks to design superhydrophobic droplet logic components where droplets interact through collisions. The presence or absence of a droplet at a certain time and location on the substrate was considered to represent the logical value “1” or “0”, respectively. Fig. 2a presents the operation of one of the devices, the NOT/FANOUT gate. In the NOT/FANOUT device, a source (1) is connected to the top-left input. When there is no input from the synchronized signal channel A at the top-right, a signal in the middle output channel (Ā) at the bottom results. However, if there is an input droplet coming from channel A, droplets will collide in the crossing, and output is triggered both in the leftmost and rightmost output channels at the bottom. Thus, this droplet logic gate performs the logical NOT operation and additionally duplicates the input signal. A flip-flop is a device able to store a binary bit, i.e., to remember in which of the two states the device was last set up. In the device shown in Fig 2b, the memory bit is represented by a droplet sitting in one of the bistable positions in an infinity-symbol-shaped depression in the middle of the device. The incoming droplet will collide with the droplet in the bistable position, thereby triggering output in one of the two output channels depending on the initial position of the middle drop. After collision, the incoming droplet will land to the other position in the bistable depression. Thus, the incoming droplets trigger output alternating between the two outputs.

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Fig. 2. a) Operation of a NOT/FANOUT droplet logic gate. b) Operation of a toggle flip-flop device. The droplets have been colored via image editing for clarity.

In conclusion, rebounding water droplet collisions were surprisingly observed on superhydrophobic surfaces, and utilizing superhydrophobic tracks for guided droplet transport, we fabricated elementary logic devices. We foresee that the droplet logic concept presented here could find applications in devices that analyze chemical compounds carried inside droplets. Within the presented framework, programmable chemical reactions could be controlled using droplet logic. For complex devices, we find that the actuation of droplets using electric fields will be beneficial. References [1] Mertaniemi H., Forchheimer R., Ikkala O., Ras R.H.A., Rebounding Droplet-Droplet Collisions on Superhydrophobic Surfaces: from the Phenomenon to Droplet Logic, Advanced Materials, 24 (42), pp. 5738-5743, 2012. [2] Mertaniemi H., Jokinen V., Sainiemi L., Franssila S., Marmur A., Ikkala O., Ras R.H.A., Superhydrophobic Tracks for Low-Friction, Guided Transport of Water Droplets, Advanced Materials, 23 (26), pp. 2911-2914, 2011.

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DEACTIVATION OF MICROBUBBLE NUCLEATION SITES BY SOLVENT EXCHANGE Xuehua Zhang1,2*, Henri Lhuissier2, Oscar R. Enríquez 2, Chao Sun2 & Detlef Lohse2 1. Department of Chemical and Biomolecular Engineering, University of Melbourne, Parkville, VIC 3010, Australia 2. Department of Science and Technology, J.  M. Burgers Center for Fluid Dynamics and Mesa+, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands Email: [email protected] E-mail: [email protected]

The “inverse” of water droplets on surfaces in air is air bubbles on surfaces in water. Just as droplets, they come in various sizes. Presumably the most intriguing ones are surface nanobubbles, i.e., gaseous domains 1,2 of nanoscale thickness at solid-water interfaces. It is well known that the formation of these nanobubbles depends on the surface history. They are most easily 3-5 In this produced by a solvent exchange process. process, a hydrophobic substrate is in contact with a short-chain alcohol, such as ethanol, which is then replaced by water. Given that gases have a higher solubility in ethanol than in water, a local gas supersaturation can be created during the solvent 6-8 exchange, and nanobubbles form on the surface. Here we show that the same solvent exchange process fully suppresses the formation of microbubbles which normally form under heating of the solid-water interface towards boiling temperature. In our experiments, the freshly cleaved highly oriented pyrolytic graphite (HOPG) was exposed to water that was equilibrated with air at 4 °C. The temperature of the system was increased till microbubbles could be observed under the optical microscopy. Although the number density of the microbubbles varied with each cleavage of HOPG, typically 5 to 80 microbubbles 2 formed over an area of 2 mm at 85 °C, as shown in Figure 1A. On the same substrate, the solvent exchange process was performed by using ethanol and air-equilibrated water. When the temperature was then increased to 95 °C (for which one would expect even more bubbles than at 85 °C), only 0-1 microbubbles formed as shown in Figure 1B. To confirm that the solvent exchange did not alter the surface permanently, the substrate was exposed to air after the solvent exchange so that the nanobubbles were removed from the interface. The substrate was then heated up a second time in air-equilibrated water and many microbubbles formed again at the temperature of 85 °C as shown in Figure 1C. No more microbubbles formed with the further increase of temperature until the complete boiling of the water. The AFM images obtained at room temperature show the absence of nanobubbles on HOPG in water without the solvent exchange process and confirm the presence of nanobubbles with the solvent exchange process. This result demonstrates that nanobubbles do not facilitate the nucleation of microbubbles at elevated temperature. This may be due to the strong pinning on

the three-phase contact line of the nanobubbles. This pinning also plays a key role in the long lifetime of the 9-11 : It decreases the Laplace surface nanobubbles. pressure, by decreasing the bubble curvature, when the bubble volume decreases and therefore limits the dissolution of the bubble.

A

D

500 µm

B

C

E

F

500 µm

Fig. 1: Microbubbles nucleated on highly oriented pyrolytic graphite (HOPG) at elevated temperature. (A): Microbubbles formed on HOPG directly exposed o to water at 85 C; (B) After the solvent exchange, no o microbubbles formed on HOPG at 95 C; (C) Microbubbles formed again when HOPG was dried after the solvent exchange process and exposed to o water at 85 C. (D-F) AFM images of HOPG under the same conditions as (A-C), now at room temperature. The AFM image areas are 5 µm by 5 µm. The deactivation of microbubble nucleation by the solvent exchange process can be further demonstrated in Fig. 2. Here the substrate is decorated with 10 micropits (artificial crevices) that under standard conditions actively nucleate microbubbles in water at 75 °C. However, after the solvent exchange process, none of the micropits nucleates microbubbles, again even at higher temperatures of 90 °C. To discriminate whether (i) prewetting by the ethanol during the solvent exchange process or (ii) the depletion of the liquid from gas through the nanobubbles itself suppress the nucleation of

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microbubbles, we will perform the solvent exchange process by using degassed ethanol and degassed water, and then replaced the latter with air-equilibrated water. If then nanobubbles still do not form, we will have excluded above explanation (ii).We will report the outcome of these experiments in the Marseille conference.

(a)

75 °C

(b)

90 °C

Fig. 2: Optical images of micropits in water with and without the solvent exchange. (A) 10 microbubbles o formed on 10 micropits in water at 75 C without solvent exchange. (B) No microbubbles formed at the o micropits at 90 C after the solvent exchange process. Our present conclusion is that surface nanobubbles do not facilitate microbubble nucleation, possibly due to the contact line pinning of the surface nanobubbles which prevents their growth towards microbubbles under heating.

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References (1) Tyrrell, J. W. G.; Attard, P. Physical Review Letters 2001, 8717, 176104 (2) Ishida, N.; Inoue, T.; Miyahara, M.; Higashitani, K. Langmuir 2000, 16, 6377. (3) Lou, S. T.; Ouyang, Z. Q.; Zhang, Y.; Li, X. J.; Hu, J.; Li, M. Q.; Yang, F. J. Journal of Vacuum Science & Technology B 2000, 18, 2573. (4) Zhang, X. H.; Zhang, X. D.; Lou, S. T.; Zhang, Z. X.; Sun, J. L.; Hu, J. Langmuir 2004, 20, 3813. (5) Zhang, X. H.; Khan, A.; Ducker, W. A. Physical Review Letters 2007, 98, 136101. (6) Seddon, J. R. T.; Lohse, D. Journal of Physics-Condensed Matter 2011, 23, 133001. (7) Craig, V. S. J. Soft Matter 2011, 7, 40. (8) Hampton, M. A.; Nguyen, A. V. Advances in Colloid and Interface Science 2010, 154, 30. (9) Zhang, X. H.; Chan, D. Y. C.; Wang, D. Y.; Maeda, N. Langmuir 2013, 29, 1017. (10) Weijs, J. H.; Lohse, D. Physical Review Letters 2013, 110, 054051. (11) Liu, Y. W.; Zhang, X. R. The Journal of Chemical Physics 2013, 138, 6.

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OSCILLATION CHARACTERISTICS OF A DROPLET ON A VIBRATING SURFACE Young Sub SHIN, Hee Chang LIM School of Mechanical Engineering, Pusan National University Busan 609-735, South Korea E-mail: [email protected]

This study was aimed at understanding the mode characteristics of droplet and the condition of droplet detachment under a periodic forced vibration. Theoretical and experimental approaches were used to predict the resonance frequency of a droplet. High speed camera was used to capture a variety of the deformation characteristics of a droplet – the shape oscillation mode, the separated secondary droplet, the detachment. The comparison of theoretical and experimental results shows a less than 18% discrepancy in the predicted the resonance frequency, which seems to be reasonable. These discrepancies seem to have been caused by the effect of contact line friction, nonlinear wall adhesion, and the uncertainty of the experiment. Recently, the behaviors of sessile droplets at the resonance have received a significant interest. Studies on droplet with periodic forced vibration date back to the time of Lord Rayleigh.[1] Strani and Sabetta[2] numerically calculated the vibration of sessile droplets immersed in an outer fluid and in partial contact with a spherical bowl. Most of the previous studies described the behavior of droplet on surfaces which are under horizontal or vertical vibration.[2,3] and others which are on the electro wetting.[4] Recently heating, ventilation, and air conditioning (HVAC) systems, power plant condensers, and many chemical and material/manufacturing industries have been examining the characteristics of droplet dynamics. For example, in the case of evaporator and condenser cores inside home/commercial appliances, road vehicles, and factory facilities, sessile droplets on a humid surface can be easily converted into a dirty surface mould to block/reduce the rate of the heat transfer. In this case, it is important to search for ways to effectively remove the sessile droplets. In the present study, shape oscillation and mode characteristics were evaluated and the ways to effectively remove the droplet placed on the plate was found. Regarding the mode frequency, the experimental results were compared with theoretical calculations in each mode. The variation between theoretical and experimental study for the resonance frequency was observed to predict the behavior of droplet with respect to volume, contact angle, surface tension and density. Various shapes of droplet deformation for each mode frequency were observed detachment, separated secondary droplets, and waggling motion. In order to observe the precise movement of droplet oscillation, the outer shape was visualized by combining the use of a high-speed camera and backlight illumination. Before this experiment, we compared theoretical resonance frequencies with experimental resonance frequencies. In this study, theoretical equation is defined below.[5] 1)

where ρ, σ, R are respectively the surface tension, the density and the radius of the droplet. Comparison of theoretical and experimental frequencies is important to analyze to validate the actual resonance frequency. The variation occur in the theoretical frequency and experimental frequency from 8-15 due to the contact line friction between solid surface and liquid droplet and due to the adhesive forces which are not taken into account for theoretical calculations. The variations also occur due to the uncertainties in the experiment and due to the linear analysis of wall adhere not considered for calculations. From eq. 1 the resonance frequencies are 99.5Hz, 298.6 Hz, 545.2Hz and 832.8 Hz for mode 2, 4, 6 and 8 respectively. There was little difference with the experimental results. This might be due to uncertainties from contact line friction between the solid surface and liquid droplet and wall adhesive forces which cannot be taken into account in theoretical calculations. The differences between the theoretical and experimental results were less than 18% for the whole experiment; the experimental frequencies are 108Hz, 263Hz, 483Hz, and 707Hz step by step. Figure 1 shows the snapshot and superimposed images and waggling motion of droplet at a variety of frequencies. Fig. 1(a) shows the temporal oscillations of a droplet for four different modes; 108Hz for mode 2 oscillations, 263Hz for mode 4 oscillations, 483Hz for mode 6 oscillations and 797Hz for mode 8. In fig. 1(b), twenty consecutive snapshots are superimposed to visualize the overall deformation of the droplet boundary to clarify the shape oscillation of the droplet at four resonance frequencies and an input voltage of 10 mV. The overall patterns were quite similar to the electro-wetting oscillation of the Oh et al.[4] Interestingly, As shown in Fig. 1(c), when the mode frequency was increased from mode 2 to 4, a waggling motion of the droplet was observed at 184 Hz (i.e. intermediate frequency). During the vertical vibration, the droplet motion was not only in the vertical direction but also had a rapid shaking and wobbling motion. Therefore, it may contradict the conservative viewpoint, which holds that droplets always have a symmetric motion when they are placed in mechanical vibration. Figure 2 shows the shape oscillation at different input voltages and a certain resonance frequency. All figures superimpose twenty different snapshots at resonance frequencies of mode 2 and 4. For mode 2 (see Fig. 2(a)), pinning occurred at 2.2V, but unpinning occurred at 6.8 and 1.6V; this seems to be due to the weak adhesive forces between the droplet and contact surface of the substrate. Interestingly, secondary droplet formation (i.e. a detachment and a secondary ejection) occurred from the droplet at 16V, and periodic detachment. Detachment of the droplet occurred at 20.6V. As the voltage was increased, the droplet tended to overcome

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Fig 1.Temporal variation of a droplet deformation at 2.2V (a) with the changing mode frequency (i.e., 2, 4, 6 and 8), (b) with the superimposing 20 images (c) with the neighbor frequency (i.e., between modes 2 and 4). Fig 3. Temporal displacements of the vibrating plate against input mode frequencies and voltages

Fig 2. Shape pattern of droplet oscillation at various voltages for resonance frequencies of (a) 108 and (b) 263 Hz

the contact line friction and hysteresis of the contact angle.[6,7] In the case of mode 4, pinning of the droplet with the contact surface occurred at 2.2V, whereas unpinning occurred at 6.8 and 10.6V. However, these behaviors were unpredictable at 16 and 20.6V. In addition, no ejection of secondary droplets and detachments was observed. This is still in an unresolved state. Mode 2, which is one of the primary mode frequencies, had a periodic movement in the vertical direction along with detachment and secondary ejection from the main droplet. Temporal displacements of the vibrating plate against input mode frequencies and voltages are shown in Fig.3. In the figure, while the displacements are over 60µm, unpinning occurred, whereas over 100µm the secondary droplet and the detachment occurred in the contact line.

Acknowledgment This work was supported by Human Resources Development program (No. 20113020020010, 20114010203080) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry and Energy. In addition, this work was also supported by the Ministry of Education, Science and Technology (MEST) in 2011. References [1] Rayleigh L., The Theory of Sound, Macmillan, 1894. [2] Daniel S.,Sircar S., Gliem J., Chaudhury M. K., Ratcheting motion of liquid drops on gradient surfaces, Langmuir, 20, 4085-4098, 2004 [3] Daniel S., Chaudhury M. K., De Gennes P. G., Vibration-Actuated Drop Motion on Surfaces for Batch Microfluidic Processes, Langmuir, 21, 4240-4248, 2005 [4] Oh J. M., Ko S. H., Kang K. H., Shape Oscillation of a drop in ac electrowetting, Langmuir, 24, 8379-8386, 2008 [5] Lamb H., Hydrodynamics, Cambridge Univ. Press, 1932 [6] Daniel S., Chaudhury M. K., Rectified Motion of Liquid Drops on Gradient Surfaces Induced by Vibration, Langmuir, 18, 3404-3407, 2002 [7] Langley K. R., Sharp J. S., Microtextured surfaces with gradient wetting properties, Langmuir, 26, 18349-18356, 2010

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JANUS EMULSIONS STABILIZED BY PHOSPHOLIPIDS Ildyko KOVACHa, Joachim KOETZa, Stig E. FRIBERGb

a

Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476, Potsdam, Germany b Ugelstad Laboratory, NTNU, Trondheim, Norway E-mail: : [email protected]

Janus emulsions were formed by mixing olive oil (OO) and silicone oil of different molar mass (SiO1 and SiO2) with water (W) in presence of a non-ionic surfactant, e.g. the biocompatible surfactant Tween 80.[1] Nevertheless, direct measurements of the interfacial tension in Janus emulsions are rare, and the stability of Tween 80 stabilized emulsions is limited. Therefore, the aim of the research was to improve the stability of Janus droplets by adding biocompatible phospholipids. First experiments have already shown that the morphology, size and stability of Janus droplets formed depended on the type of surfactant used as well as the viscosity of the two oil components used. Figure 1 (micrograph 1) show completely engulfed Janus droplets in presence of Tween 80. Unfortunately the stability of the Janus droplets is limited. Video experiments have shown that Janus droplets coalescence when two olive-oil sides come in contact. This means the non-ionic surfactant Tween 80 is not able to stabilize Janus droplets for a longer time. When the viscosity of silicon oil is in the same order like the viscosity of olive oil, i.e. by using silicon oil SiO2 of higher molar mass, the droplet size is increased drastically, as to be seen in Figure 1 (micrograph 2). By adding phospholipids the droplet size can be decreased (micrograph 3), and the Janus droplets become more stable for a longer time. Interfacial tension measurements by using a spinning drop apparatus and a ring tensiometer clearly show that the addition of phosphatidylcholine (PC) leads to a decrease of the interfacial tension from 3 mN/m to 0.5 mN/m. Therefore, one can conclude that phosphatidylcholine, embedded in the mixed interfacial film between olive oil and water, stabilize the droplets due to an additional electrostatic effect. When phospholipids are used alone, i.e. in absence of Tween 80, also completely engulfed Janus droplets are formed, as to be seen in micrograph 4. Ring tensiometer experiments show that the interfacial tension between olive oil and water is decreased from 14.3 mN/m to 1.2 mN/m by adding PC. From these results one can conclude that phospholipids form an interfacial film between olive oil and water. Note that the viscosity of the silicon oil is of special relevance to form Janus emulsions in such systems. This means only by using silicon oil of lower molar mass (SiO1) double emulsions are formed.

Fig. 1: Completely engulfed Janus droplets. 1: SiO1/OO/W + Tween 80 2: SiO2/OO/W + Tween 80 3: SiO1/OO/W + Tween 80 + PC 4: SiO1/OO/W + PC

In general one can say, that smaller, more stable Janus droplets are formed, when the interfacial tension between oil and water becomes ≤1 mN/m. Such conditions are fulfilled when phospholipids are used in combination with non-ionic surfactant Tween 80. The morphology of the double droplets is predominantly controlled by the viscosity and interfacial tension between the liquid phases. By using different types of phospholipids, i.e. Asolectin and Lecithin instead of a more concentrated phosphatidylcholine (PC), the interfacial tension is decreased and different morphologies from partially to completely engulfed Janus droplets can be observed. Hereby, the solubility of phospholipids in the oil components and/or water is of special relevance, too. For example Asolectin can be dispersed in water or in olive oil without relevance on the interfacial tension between olive oil and water, which is constant at 1.2 mN/m. However, the results show that partially engulfed Janus droplets are formed when Asolectin or Lecithin are dispersed in water, and completely engulfed droplets are formed by adding PC to olive oil. References [1] Hasinovic, H., Friberg S.E., A one-step process to a Janus emulsion, J. Colloid Interface Sci., 354, pp. 424-426, 2010.

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PHYSICS OF SPIN CASTING DILUTE SOLUTIONS Stefan KARPITSCHKA, Constans WEBER, Hans RIEGLER Max-Planck-Institut fuer Kolloid- und Grenzflaechenforschung, Potsdam-Golm, Germany E-mail: [email protected]

248

z

early phase

late phase (evaporation dominated)

solvent evaporation (rate E)

height h

film

(spin-off dominated)

flow field

solute enrichment

r

spinning support angular frequency ! spin-off coefficient K " !2

Fig. 1: Schematics of spin-casting with processes dominating the early and late process stages.

htr = (E / 2K )1 3

(3)

∗ tSC = (2E 2 K )−1 3

(4)

htr is the “transition height” when evaporative and ∗ is the “reduced hydrodynamic thinning are equal. tSC process duration” (Eq. (5)). Integration of Eq. (2) yields the thinning behavior and the duration of the whole process (starting at h → ∞ , ending at h = 0 ): ∗ (5) tSC = (2π / 33 2 )(2E 2 K )−1 3 = (2π / 33 2 )⋅tSC 10 ttr !tsc 1

0.1

Reflectometry Fit of Eq. (5)

4

htr = 3.20 ± 0.01 µm tsc = 1.20 ± 0.01 s

2 0 0.0

0.001 0.0

Toluene, 3000 rpm, 20°C

6 h [µm]

0.01

only spinning

only evaporation 8

h!htr

An excess amount of liquid deposited on a spinning, planar, wettable substrate forms a thinning film of uniform thickness h(t) as the liquid flows outward (and is spun off) [1]. Evaporation of volatile film components adds to the film thinning (Fig. 1). The process of persistent deposition of nonvolatile components on a spinning support is called “Spin Casting" or “Spin-Coating". Coverage, structure, and other properties of the final deposit are strongly influenced by the processes occurring during film thinning. The nonvolatile components get continuously enriched, eventually exceeding saturation. The final deposit evolves from aggregation during film thinning in the presence of the solvent. We analyze the spin casting of dilute (ideal) binary mixtures of non-volatile solutes in volatile solvents [2]. The system-specific fundamental length and time scales of the process are introduced and an analytical description of the thinning of a volatile liquid film simultaneously subject to spinning and evaporation is presented for the first time. This reveals spin casting essentially as evaporative thinning of a hydrodynamically flattened film. The Sherwood number Sh is introduced as fundamental process parameter to distinguish between diffusion-dominated ( Sh < 1 ) or evaporation-dominated ( Sh > 1 ) internal film composition. Power laws link the process duration, final solute coverage and the spatio-temporal evolution of the internal film composition to the control parameters and the properties of the initial solution. The analysis is relevant for casting real solutions, in particular for the deposition of specifically structured (sub-)monolayers (“evaporation-induced self-assembly"). The quantitative validity of the analysis is verified experimentally. Because the analysis provides palpable physical insight into the influence of the different process parameters, improvements regarding real (non-ideal) conditions can be implemented easily. In addition to this theoretical analysis we finally discuss and analyze its relevance for real cases: 1.) A typical polymer solution and 2.) A nanoparticle solution for sub-monolayer deposition). Thus we can show that our analysis is in fact (quantitatively) relevant for real spin coating processes. The thinning of a Newtonian, volatile liquid film of thickness h on a rotating support is described by [3]: (1) dh / dt = −2Kh 3 − E 2 with spin-off coefficient, K = ω / (3υ ) , ω = rotational speed, υ = kinematic viscosity, and E = evaporation rate. The fundamental form of Eq. (1): (2) dξ / dτ = −ζ 3 −1 ∗ i.e., by is obtained by rescaling ξ = h / htr and τ = t / tSC the system inherent “natural" scales:

0.2

0.2

0.4

0.6

0.8

1.0

1.2 t [s]

0.4

0.6

0.8

1.0

t/ t sc

Fig. 2: Universal, spin cast thinning curve h / htr = f (t / tSC ) (dashed lines: thinning due to spinning and evaporation only). The Inset shows a measured thinning curve for toluene in physical units and its fit according to the theory.

Fig. 2 shows the universal, rescaled thinning curve h / htr = f (t / tSC ) . The inset shows the comparison between an experimentally obtained thinning curve (toluene) and the theory. The agreement is excellent. The transition time, ttr , at which htr is reached, is universal for spin cast processes described by Eq. (1): (6) ttr = ((2π − 3 log 4) / (4π ))⋅ tSC ≈ 0.309 ⋅ tSC The analysis also shows that in all cases the

Abstract #051

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This equation has been solved and analyzed. It turns out that the Sherwood number, Sh , is the fundamental parameter to characterize the spatio-temporal solvent/solute behavior. It parameterizes the ratio of evaporative to diffusive mass transport on the characteristic length scale of the system, htr : (8) Sh = Ehtr / D = E 4 3 (2K )−1 3 / D

5.0

1.5

Time

/

c c0

3.0 Sh = 4.00 Sh = 1.00 Sh = 0.25

1 4.

1.0 0.0

0.2

0.4

0.6

0.8

100 1.0

z/h

Fig. 3: Solute concentration profiles for three different Sherwood numbers Sh at different moments/heights h / htr .

Fig. 3 shows profiles of c during film thinning for Sh larger and smaller than 1 (i.e., convection dominating over diffusion and vice versa) and for film heights larger and smaller than htr , respectively. It reveals the competition between evaporative enrichment, spin-off, and diffusive dilution in both, spin-off and evaporation dominated regimes.

1.1

10 1.0

5 0.9

N#A!h" 0"#!c0 htrans "

c!z ! h ! htrans " # c0

20

0.8

0.1

1

c c0

Surface

2.0 1.0

Sh 10- 3 Sh 2 102

B

Sh Sh Sh

0.25 1.00 4.00

C

Sh Sh Sh

0.25 1.00 4.00

Substrate

1.00 cmax

0.10

hmax 0.1

0.5

1.0

5.0

10.0

h htr

10

Fig. 5 shows as function of h / htr : A) the total solute amount N per unit area A ( N / A = ∫ h0 cdz ); B) c / c0 at the surface respectively substrate/film interface; C) The difference between the surface and the substrate/film interface concentrations, Δc / c0 i.e., the relative enrichment. Both, h = htr and mark the transitions between distinctly different behavior. The occurrence of Δcmax / c0 (Fig. 5, Panel C) and its spatio-temporal properties as function of Sh can be described by power laws for Sh < 1 : (10) hpeak ≈ (D / K )1 4 ≈ 1.2htr Sh −1 4

t peak tSC ≈ 0.31E 2 3K −1 6 D −1 2 ≈ 0.35 Sh Δcmax c0 ≈ 0.46EK

−1 4

D

−3 4

≈ 0.55Sh

34

(11) (12)

References

2 0.01

Total Solute Amount

All these power laws can be rationalized and understood by analyzing the underlying processes.

1.2

1 0.001

2 1 20.0 10.0 5.0

Time

Fig. 5: For various Sherwood numbers Sh are shown as function of the reduced film thickness h / htr : A) Total solute amount N per unit area A (scaled by c0 htr ); B) Concentrations c at the surface respectively film/substrate interface (scaled by c0 ); C) Δc , the difference between the surface and the substrate/film interface concentrations, respectively (scaled by c0 ).

h/htr = 0.25

2.0

A

20 10 5

5.00 c c0

hydrodynamic film thinning dominates ≈ 30% of the total spin cast time (in the beginning). Evaporation dominates ≈ 70% of the total time (at the end, see dashed lines in Fig. 2). Spin casting processes aiming at obtaining a deposit means the liquid contains non-volatile solute. During spin casting this non-volatile solute enriches at the free surface (where the solvent evaporates) and migrates into the film via diffusion. The spatio-temporal evolution of the solute concentration c is described by (7) ∂t c = D∂ 2z c + Kz 2 (3h − z)∂ z c

N A c0 htr


100 Sh

Fig. 4: Normalized final solute coverage, N(h → 0) / (Ac0 htr ) and c / co at the film surface for h = htr as function of Sh .

[1] Emslie A. G., Bonner F. T., and L. G. Peck, J. Appl. Phys. 29, p 858, 1958. [2] The content of this abstract is submitted to Phys. Rev. Lett. The manuscript is currently in revision. [3] Meyerhofer D., J. Appl. Phys. 49, p 3993. 1978.

Fig. 4 shows c(z = h = htr ) / c0 , the concentration at the free surface for h = htr , and N(h → 0) / (Ac0 htr ) , the rescaled final coverage. For Sh < 1 this is: (9) Γ = N(h → 0) / A ≈ c0 htr ≈ 0.8c0 (K / E)−1 3 Abstract #051

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1 Int. Workshop onWetting and evaporation: droplets of pure and complexfluids th th Marseilles, France, June 17 to 20 , 2013

BREAKUP OF A THIN ELECTROLYTE FILM UNDER ELECTROSTATIC AND VAN DER WAALS FORCES Christiaan KETELAAR, Vladimir AJAEV Department of Mathematics, Southern Methodist University,Dallas, TX 75275, USA E-mail: [email protected]

Viscous flows in thin liquid layers have been studied since the days of Reynolds. Oron et al.[1] made an extensive review of dynamics of thin-film flows driven by various forces such as gravity, capillarity, thermocapillarity, and intermolecular forces with or without evaporation or condensation [2]. Film instabilities are important for a number of applications such as microfluidics, coating flows, and cooling on microscale and often lead to film rupture. Van der Waals interactions in thin liquid films were studied by Scheludko [3]. Ruckenstein and Jain [4] showed that such films are vulnerable to rupture through long-wave instability and obtained estimates for the rupture times. Williams and Davis [5] examined the nonlinear evolution equation for film thickness and indicated that nonlinearities can accelerate the rupture. An important aspect of studies of thin film instabilities is the procedure used to account for the influence of various forces on the film dynamics. For ultra-thin films (10-100) nm, intermolecular interaction is dominated by the van der Waals forces. If the thickness of the film is on the order of micrometers, electrostatic forces can be more significant than van der Waals interaction. Most of the previous studies have been focused on regimes where van der Waals forces are dominant [3,4], and for this reason the effect of the electrostatic component has not been fully understood. In our model, we are incorporating the effect of electrical charges present at the interfaces into both linear and nonlinear stability analyses of thin films. Moreover, we are also considering the effect of van der Waals forces to develop a model that is valid for a wide range of length scales (from nanometers to micrometers), and to validate the experimental observations showing that van der Waals forces are predominant for ultra-thin films but can be neglected as the film thickness increases. In our model, a thin liquid film of viscosity 𝜇 is a symmetric electrolyte with a screening length or Debye length denoted by 𝜆.

Fig.1: Sketch of a thin electrolyte film on a flat solid substrate The solid-liquid and liquid-gas interfaces are electrically 250

charged and the electrostatic potential (scaled by Ψ from eq. 3) of the electrolyte film satisfies the Debye ! Hückel equation where 𝜅 = is the film thickness ! scaled by the screening length. 𝜓!! = 𝜅𝜓 (1) If the capillary number is small 𝐶𝑎 ≪ 1 ,the Navier-Stokes equations simplify to a system of lubrication-type equations. At the solid wall, we use the no-slip and no-penetration conditions. At the liquid-gas interface, the shear stress is zero and the interfacial pressure jump condition incorporates the effect of van der Waals dispersion forces, 𝐴 𝑝 − 𝑝! = −ℎ!! + ! (2) ℎ where A is the scaled Hamaker constant that measures the relative strength of the van der Waals forces to the electrostatic forces, 𝐴=

𝐴∗ , 𝜀𝜅Ψ !

Ψ=

𝑒𝑧 , (3) 𝑘! 𝑇

where 𝜖 is the electrical permitivitty, 𝑘! Boltzmann’s constant, and 𝑇 is the temperature.

is

The small capillary number condition is equivalent to the lubrication long wave approach of Williams and Davis [5], where the thickness of the film is much smaller than the wave length of the film perturbations. With this assumption, we use the kinematic boundary condition to derive the film thickness evolution equation ℎ! + (ℎ! ℎ!!! +ℎ! Π! ℎ! )! = 0 . (4) The scaled electrostatic potential at the solid (𝜓! ), the scaled surface charge density at the liquid-gas interface (𝜎), and the van der Waals dispersion forces contribute to our model of disjoining pressure. Π=

1 𝜎 sinh 𝜅ℎ + 𝜓! cosh 𝜅ℎ 2

!

−

𝐴 . (5) ℎ!

The value of the dimensional Hamaker constant 𝐴∗ depends on properties of both solid and liquid interfaces and is typically on the order of 10!!" Joules. From the scaled Hamaker constant, van der Waals forces are predominant if the film thickness 𝑑 < 10!! 𝜆. In pure water, with a Debye length of 𝜆 = 10!! m, the van der Waals forces are predominant if the film thickness is of the order of 10 𝐴, which is consistent

Abstract #059

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1 Int. Workshop onWetting and evaporation: droplets of pure and complexfluids th th Marseilles, France, June 17 to 20 , 2013

with the experimental results. To analyze the stability of the film, we consider a small perturbation to the constant thickness solution ℎ = 1 + 𝜁(𝑥, 𝑡). The condition of instability for the wave number is 𝑘 ! < Π! . If the wave number is smaller than the magnitude of the derivative of the disjoining pressure, then any perturbations to the constant thickness solution will grow over time, which means that the film is unstable and will rupture. A linear stability diagram is useful to determine under which conditions the film will rupture (unstable perturbations). From the linear stability analysis, the stability branches are the boundaries between the stable region from the unstable regions and satisfy Π! = 0. 𝑟= Δ=

and the van der Waals forces are predominant. The film will rupture independently of the electric charge properties. In this case, there is a critical thickness where the film always ruptures and it is consistent with the experimental results of [3] and [4]. The linearization of the interface shape equation describes the initial stage of the instability development, but to predict significant departures from the uniform thickness solution we solve the nonlinear evolution equation numerically using the method of lines. The nonlinear numerical simulations of the film thickness evolution eq. 4 are shown in Figure 3 as snapshots for different times. We notice that the film is thinning in specific regions, resulting in the formation of droplets as dry spots appear between the film.

𝜎 1 = sinh 𝜅 − csch 𝜅 ± Δ (6) 𝜓! 2 sinh 𝜅 + csch 𝜅

!

−

4𝐴 cosh! 𝜅 csch 𝜅 𝜅𝜓!!

The stability branches show that the stability of the film is going to depend on the electrostatic properties (𝜓, 𝜎), the relative strength of the van der Waals forces (𝐴), and the scaled film thickness 𝜅. The diagram in figure 2, shows that we have three different regions. In the stable region, between the two unstable regions, any perturbation decays over time and the film returns to is constant thickness. In the unstable regions, the film can rupture resulting in a formation of dry spots or nonlinear effects can stabilize the film.

Fig. 3: Nonlinear interface evolutionfor𝐴 = 0.1, 𝜓! = 1, 𝜅 = 1.5, 𝜎 = −1. We considered the effects of electrostatic and van der Waals dispersion forces on the stability of thin electrolyte films. The linear stability results show a that there is a region where the film is unstable, however as the normalized Hamaker constant increases the two unstable regions coalesce via a saddle node bifurcation and the film ruptures in finite time. There is a critical film thickness were the van der Waals forces are predominant where the van der Waals forces are relatively strong (𝐴 ≈ 𝜅𝜓!! ) and the film ruptures into an array of droplets. References

Fig. 2: Linear stability diagram for𝐴 = 0.3, 𝜓! = 1. Another relevant fact about the linear stability diagram is that there is critical normalized Hamaker constant where the two stability branches coalesce. 𝐴! =

𝜅𝜓!! csch 𝜅 + sinh 𝜅 ! (7) 4 cosh! 𝜅 csch 𝜅

If 𝐴 > 𝐴! , the electrostatic potential is relatively weak

[1] Oron A., Davis S., Bankoff S.,Long-scale evolution of thinliquid films.,Rev. Mod. Phys, 69 (3), pp. 931-938, 1997. [2] Ajaev V.,Klentzman J., Gambarian-Roisman T., Stephan P., Fingering instability of partially wetting evaporating liquids,J Eng Math, 73 (1), pp. 1–8, 2011. [3] Scheludko, A., Thin liquid films.,Adv. Colloid Interface Sci., 1 (70), pp. 391-464, 1967. [4] Ruckenstein E.,Jain R., Spontaneous rupture of thin liquid films.,J. Chem. Soc. Faraday, 2 (70), pp. 132-147, 1974. [5] Williams M.,Davis S.,Nonlinear theory of film rupture, J. Colloid Interface Sci., 90 (1), pp. 220-228, 1982.

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WETTING AND EVAPORATION OF A SESSILE DROPLET UNDER AN EXTERNAL ELECTRIC FIELD

Valérie VANCAUWENBERGHE1, Paolo DI MARCO2, David BRUTIN1 1

2

Aix-Marseille University, UISTI UMR 7343, 13453 Marseille, France LoThAR, Department of Energy and Systems Engineering, University of Pisa, Pisa, Italy. E-mail: [email protected]

In the framework of two experiments, the effect of an electric field on the evaporation, the shape and the wetting of a sessile drop is being investigated. The ESA/CNES ARLES project intends to study evaporating drops of pure fluids and nano-fluids to enhance the heat transfer and to deal with the instabilities of the flow motion and flow instabilities occurring in the drop and at the drop interface. The ESA project intends to perform experiments in weightlessness with drop evaporations that have long evaporating time. The heat and mass transfer enhancement induced by the application of an electric field is a phenomenon that interests a wide range of industrial applications (electrospraying, cooling, heat exchange, etc.). In this scope, the boiling process in the presence of an electric field is a subject extensively investigated in the refrigerating and cooling areas [1, 2]. However, this intensification concerning the evaporation of sessile droplets is stills a subject poorly investigated and unknown. The enhancement of drop evaporation has been investigated by Takano [3-5]. In these studies, drops of ethanol and R113 are evaporated at substrate temperature exceeding the Leidenfrost temperature of the liquids under a maximum electric field respectively of 250V and 2000V using electrode configuration described on Fig. 2a). The maximum enhancement ratios of the heat transfer coefficient are 7.6 for ethanol and 2.8 for R113 at the highest applied voltage that illustrates the influence of the polarity of the liquids. The enhancement of the heat transfer due to the presence of an electric field can be useful on ground, to improve the evaporating rate as well as in weightlessness to replace the absence of the convective effect. Indeed, without the gravity effect, the heat transfer is normally only driven by the diffusion from the liquid-gas interface to the surrounded gas. Thus, the objective is to overcome the diffusion limitation on the evaporating rate by applying the external electric field. Moreover, in the scope of the nanoparticles deposition by evaporation which are limited on earth due to the presence of capillary convection and gravity (coffee ring effect), the use of the electric field would provide a tool to control the pattern formation. The applications are various on earth as well as in space in regards to the possibilities of the heat transfer enhancement such as, for instance, the cooling using droplet evaporation in space or the uniform deposition of nanoparticles that is required for almost all industrial application (coatings, printing, DNA mapping, etc.).

252

In order to have a better understanding of the enhancement mechanisms of the evaporation rate, the effect of the external electric field on the interfacial properties of the sessile drop should be predicted. The use of an electrostatic field on the shape of a drop is a well known phenomenon that induces the elongation of the drop along the direction of the field as shown on Fig.1. This effect, caused by the electric stress on the surface drop, has been widely theoretically investigated considering the solving of the Maxwell equation and Young-Laplace equation [6-10]. However, just a few authors have been interested by the effect on the contact angle and the interface of an electric field established outside the liquid drop (seen on Fig. 2b). Indeed, the Lippmann equation qualitatively predicts the decreasing of the contact angle in electrowetting process that schematized on Fig. 2a) [11-13]. This expression may not be considered to systems with dielectric multilayer, nonaqueous liquids and different electrolyte concentrations [14].

Fig. 1: Shape of ethanol droplet for different value of the electric field

Fig. 2: Schematic of the electrode configuration. a) The electric field is established inside the drop. The upper electrode is in contact with the droplet volume. b) The electric field is established outside the droplet.

Abstract #061

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As summarized in Table 1, Authors focused experiments on the change of contact angle for dielectric liquids, alcohols and water, under an external 3 3 electric field varying from 10 to 20·10 V/cm. The overall meaning of these results suggested an increase or a decrease of the contact angle with increasing magnitude of the electric field [8-10, 14, 15]. From these results, Bateni et al. [16] underlined some influencing factors such as the liquid polarity, the size of the liquid molecules and the no role of the direction of the electric field. They also suggested that the observed increase of the contact angles is due to a bulk effect rather than an interfacial effect. More investigations are required to interpret with caution the existing results including the influence of the liquid and the substrate properties (conductivity, permittivity, wettability, surface treatment, etc.). Substrate Θ0 Change PTFE 35 Increase Stainless 160 Decrease steel SS Roero [15] Water SS 68/10 Decrease Bateni [16] Alcohols PTFE 57-75 Increase Table 1 Summary of the effect of electric field E on the contact angle of drops Θ0. E varies from 0.1 to 2 MV/m. Author Di Marco Roux

Ref. Liquid [8] Ethanol [9,10] Water

For the future investigations, the enhancement of the evaporation of sessile droplets under a high external electric field (configuration of the Fig. 2b) will be studied. First, the effect of the electric field on the shape and contact angle of the pure liquid drop will be expanded. Indeed, preliminary experiments have already been performed in order to evaluate the electric force acting on the drop interfaced and to confront the experimental results with theoretical model (Fig. 1) [8]. The variation of the experimental parameters such as liquid polarity or nature of substrate will be explored. After this preliminary phase, the evaporation phenomenon under electric field will be investigated with and without gravity effect. Models to predict the enhancement of the evaporation rate will also be suggested. References [1] M.C. Zaghdoubi, M. Lallemand, Electric field effects on pool boiling, J. Enhanced Heat Transfer, Vol. 9, 187-208, 2002.

[2] P. Di Marco, W. Grassi, Saturated pool boiling enhancement by means of an electric field, J. Enhanced Heat Transfer, Vol. 1, 99-114, 1993. [3] K. Takano, I. Tanasawa, S. Nishio, Active enhancement of evaporation of a liquid drop on a hot solid surface using a static electric field, Int. J. Heat Mass Trans, Vol. 37, Suppl. 1, 65-71, 1994. [4] K. Takano, I. Tanasawa, Enhancement of evaporation of a droplet using EHD effect, JSME International Journal B, Vol. 38, 288-294 1995. [5] K. Takano, I. Tanasawa, S. Nishio, Enhancement of evaporation of a liquid droplet using EHD effect: Criteria for instability of gas-liquid interface under electric field, Journal of Enhanced Heat Transfer, Vol. 3, 73-81, 1996. [6] M.J. Miksis, Shape of a drop in an electric field, Phys. Fluids, Vol. 24, pp. 1967, 1981. [7] O.A. Basarin, F.K. Wohlhuter, Effect of nonlinear polarization on shapes and stability of pendant and sessile drops in an electric (magnetic) field, J. Fluid Mech., Vol. 244, pp. 1-16, 1992. [8] P. Di Marco, F. Pedretti, G. Saccone, Effect of an external th electric field on the shape of a dielectric sessile drop, 8 World Conference on Experimental Heat Teansfer, Fluid Mechanics, and Thermodynamics, June 16-20, 2013, Lisbon Portugal. [9] J.M. Roux, J.L. Achard, Forces and charges on a slightly deformed droplet in the DC field of a plate condenser, Journal of Electrostatics, Vol. 67, 789-798, 2009. [10] A. Glière, J.M. Roux, J.L. Achard, Lift-off of a conducting sessile drop in an electric field, Microfluid Nanofluid, Published online, 13 February 2013. [11] F. Mugele, J.-C. Baret, Electrowetting: from basics to applications, J. Phys.: Condens. Matter, Vol. 17, 705–774, 2005. [12] C. Quilliet, B. Berge, Electrowetting: a recent outbreak Current Opinion in Colloid & Interface Science, Vol. 6, 34–39, 2001. [13] R. Shamai, D. Andelman, B. Berge and R. Hayes, Water, electricity, and between... On electrowetting and its applications Soft Matter, Vol. 4, 38–45, 2007. [14] V. Peykov, A. Quinn, J. Ralston, Electrowetting : a model for contact-angle saturation, Colloid Polym. Sci., Vom. 278., 789-793, 2000. [15] C. Roero, Contact angle measurements of sessile drops deformed by a DC electric field, Contact Angle, Wettability and Adhesion, Vol. 4, 165-176, 2006. [16] A. Bateni, S. Laughton, H. Tavana, S.S. Susnar, A. Amirfazli, A.W. Neumann, Effect of electric fields on contact angle and surface tension of drops, J. Colloid and Interface Science, Vol. 283, 215-222, 2005.

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DIGITAL MICROFLUIDICS AND OPTOFLUIDICS ON FIBER NETWORKS Nicolas VANDEWALLE, Floriane WEYER, Anne HENROTIN, Marjorie LISMONT, Bernard JORIS*, Laurent DREESEN GRASP, Department of Physics B5a, University of Liege, B4000 Liege, Belgium. *CIP, Institute of Chemistry B6, University of Liege, B4000 Liege, Belgium. E-mail: [email protected]

Microfluidics is a domain of science, which aims to manipulate tiny fluid volumes from one picoliter to one microliter. This comes from an increasing demand from industry and science focussing on microsystems delivering and analyzing small liquid quantities. Many applications can be found in biotechnology, chemistry, microelectronics and optics.

droplets. A model based on the balance between capillary forces and gravity is proposed for describing such an effect.

In recent works [1,2], we studied the behavior of droplets moving along vertical treads due to gravity. We have shown that the motion of droplets can be stopped by horizontal fibers depending on the droplet volumes and the fiber diameter. In addition, such nodes are able to fragment the droplet into several parts. Microfluidic elementary operations can be therefore invented. Since the fiber-based microfluidic device is open, the evaporation of droplets, or the contamination of droplets by dust particles should be avoided as much as possible. In this work, we show that the encapsulation of droplets by a second liquid phase is possible on fibers. We study the shapes of compound droplets, as well as dynamical properties of such droplets along fibers. We focus our work on water-oil droplets. Moreover, we demonstrate that the fiber network can be exploited to probe the droplet content by optical means. This work opens new perspectives in both microfluidics and optofluidics. On a horizontal fiber, droplets adopt different shapes depending on their volume and wetting properties. Above a critical volume, the droplet is in a barrel shape around the fiber. Due to gravity, the center of the droplet is slightly placed below the fiber. When the volume increases, the droplet position changes below the fiber, before leaving it above some threshold. Figure 1 shows typical pictures of oil and water droplets placed on a horizontal fiber. Due their respective wetting properties, the shapes of the droplets are drastically different. The vertical position of the droplet center decreases as the volume increases. A scaling law is proposed for that behavior as a basis for the compound systems. Since the water surface tension is much higher than oil/air surface tension, water is encapsulated by oil. The compound object can be created along the fiber from a contact between a water and a oil droplet. Depending on the respective volumes of water and oil, the shape is modified. A model is proposed for describing such an effect. More importantly, compound droplets have different dynamical properties than pure systems. Indeed, oil is seen to enhance the motion of compound 254

Fig. 1: (top row) Droplets of silicone oil. Three volumes are illustrated : 0.5µl, 1.0 µl and 2.0 µl. (middle row) Droplets of colored water. Three volumes are represented : 0.5µl, 1.0 µl and 2.0 µl. (bottom row) Compound droplets (oil and water). Total volume is a constant (1µl). The respective water-oil volumes are 0.1-0.9 µl, 0.5-0.5 µl and 0.9-0.1 µl. The shape is modified by the volume fraction.

The intersection between two crossed optical fibers may be the basic unit of an original optofluidic biosensor. The first fiber can carry the probe molecules and the second one the target species, the interaction between both biological entities taking place at the fibers’ crossing. The use of optical fibers has a main interest: they can also carry and collect light. They can therefore allow the study of biological interactions using fluorescent labels. This new and versatile detection scheme is validated on a calcium indicator where ions detection is accomplished by using a dye, Oregon green Bapta-2 (Life Technologies), that has a recognition group as well as an entity exhibiting fluorescence. Oregon dye (probe molecules) and calcium solution (target molecules) are injected on the first and second fiber, respectively. These ones are also used to excite and collect the fluorescence. The fluorescence spectra of Oregon green Bapta-2 for different calcium ions’ concentration were recorded at an optical fiber junction. The results are reported on figure 2. As expected, the fluorescence signal strongly depends on Ca concentrations: it decreases when the Ca

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concentration increases. Using these curves, the Oregon green dissociation constant was deduced. 1 .0

O reg on's a bs orption 2+

[C a ]free = 0

0 .9

2+

[C a ]free = 0.038 µM 2+

[C a ]free = 0.1 µM 2+

[C a ]free = 0.225 µM

0 .7

2+

[C a ]free = 0.602 µM

0 .6

2+

[C a ]free = 1.73 µM 2+

[C a ]free = 7.37 µM

0 .5

F luore s c e nc e (a .u.) A bs orba nc e (a .u.)

0 .8

In this work, we studied the several shapes and configurations of compound droplets onto fibers. The understanding of droplet shapes and dynamics suggest that digital microfluidic operations can be imagined with compound droplets onto fibers. An original and versatile optofluidic biosensor, based on the crossing of two optical fibers, was also proposed. The new concept was validated on a calcium indicator.

0 .4 0 .3

References [1] Gilet T., Terwagne D., Vandewalle N., Digital microfluidics on a wire, Appl. Phys. Lett. 95, 014106 (2009). [2] Gilet T., Terwagne D., Vandewalle N., Droplets sliding on fibres, Eur. Phys. J. E 31, 253-262 (2010).

0 .2 0 .1 0 .0 350

400 450 500 550 600

650 700 750 800

850 900

W a ve le ng th (nm )

Fig. 2: (continuous colored curves) Fluorescence spectra of Oregon green for different calcium concentrations. (dashed grey curve) Absorption spectrum of Oregon green.

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EFFECT OF AN ELECTRICAL FIELD ON A LEIDENFROST DROPLET Geoffroy KIRSTETTER(1), Franck CELESTINI(1)

(1)

Laboratoire de Physique de la Matière Condensée, CNRS UMR 7336, Université de Nice Sophia-Antipolis, 06108 Nice, France Email: [email protected]

We investigate the effect of an electrical field applied on a Leidenfrost droplet. The increase of the voltage induces a decrease of the vapor layer thickness which sustains the droplet. Above a critical tension, the droplet comes into contact with the substrate and starts boiling. We present our experimental results and a simple model to describe this “Electro-Leidenfrost” effect.

droplet by analyzing the Newton’s rings obtained below the droplet (Figure 1). Thanks to these interference patterns, we measure with a micrometric precision the variation of the vapor layer height between the substrate and the droplet. We submit this system to an external tension, the more the tension increases, the more the mean vapor height decreases. We model this phenomenon with a Newtonian static approach. Like the electro-wetting effect, the “Electro-Leidenfrost” effect is proportional to the square of the applied voltage. At a critical tension, the vapor layer is suppressed and the droplet starts boiling (Figure 2). In the light of these results, the electrical field turns out to be an interesting tool to control the Leidenfrost effect.

Fig. 1: Interference patterns obtained below a Leidenfrost droplet of radius R = 1 mm for different external voltages: a) 0 V, b) 15 V, c) 25 V and d) 30 V.

The Leidenfrost effect was discovered by the physicist J.G. Leidenfrost in the XVIII century [1]. He put a water droplet on a sufficient hot spoon, and observed that the droplet levitates on its own vapor layer. The weak heat conduction of the vapor dramatically decreases the heat transfer between the water and the hot substrate. This phenomenon is a real problem in many domains, like nuclear reactor cooling. Over the twenty last years, this subject has motivated numerous studies and the effect is now globally understood [2] [3]. Nevertheless recent studies are still bringing into light unexpected behaviors. For example, Celestini & al. show that, below a critical size, the droplets spontaneously take off of the substrate [4]. We present an experimental study on the effect of an electrical field applied between a Leidenfrost droplet and a hot plate on which it is levitating. To examine the liquid/vapor interface, we use an interferential technique [5]. This experimental setup allows us to describe the vapor-liquid interface of the Leidenfrost 256

Fig. 2: A 40V tension is suddenly applied to a Leidenfrost droplet at t = 0s. The three successive pictures display the boiling crisis of the droplet due to the applied electrical field. References: [1] Leidenfrost J.G.(1756) De aquae communis nonullis qualitatibus tractatus. Duisbourg [2] Quéré D. (2012), Leidenfrost dynamics. Annual Review of Fluid Mechanics [3] Pomeau Y., Le Berre M ., Celestini F. & Frisch T. (2012), The Leidenfrost effect : From quasi-spherical droplets to puddles. C.R. Mécanique [4] Celestini F., Frisch T. & Pomeau Y. (2012), Take off of small Leidenfrost droplet. Phys. Rev. Let. [5] Celestini F. & Kirstetter G. (2012), Effect of an electrical field on a Leidenfrost droplet. Soft Matter

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NON-AXISYMMETRIC SHAPES, FISSION AND COALESCENCE OF SPINNING DIAMAGNETICALLY LEVITATED NEWTONIAN AND VISCOELASTIC DROPS Kyle A. Baldwin, Richard J. A. Hill School of Physics and Astronomy, University of Nottingham, NG7 2RD Email: [email protected]

We have developed a novel method for observing the behavior of spinning Newtonian and viscoelastic droplets from millimetric to centrimetric sizes, using magnetic levitation. The droplets, which are freely suspended and spherical at rest, are spun up using carefully directed air flow and filmed using high speed photography (960fps). Using this experimental setup we have studied the dynamics of spinning liquid droplets in three independent experiments, namely: the evolution of the droplet’s shape as a function of angular momentum, rate of angular acceleration and viscosity; the far-from-equilibrium structures at droplet fission/pinch-off due to the combination of capillary thinning and elongational viscosity; and the coalescence of two equally-sized droplets in a decaying orbit as a function of droplet viscosity, elasticity and surface tension. Equilibrium and far-from-equilibrium rotating droplet shapes: The study of the shapes of rotating liquid drops began in 1863 with the blind (yet insightful) Joseph Plateau [1], in which he used the rotation of centrimetric sized liquid drops suspended in an equally dense liquid as an analogy for the rotation of large astronomical bodies held together by self gravitation. Since then, Brown and Scriven [2] have expanded upon this with computational analysis of the equilibrium shapes that a Newtonian droplet can undergo during solid-body rotation, including the classical torus shape and 2, 3 or 4-lobed shapes, the angular velocity prior to droplet fission being dependent on surface tension and droplet size. The evolution of the 2-lobed shape family as a function of dimensionless angular velocity and momentum were subsequently confirmed experimentally in the Space shuttle work of Wang et. al. [3] and, later, in rotating diamagnetically levitated drops studied by Hill & Eaves [4]. In the latter experiments, 3-lobed equilibrium shapes were also observed, which are stabilized by surface travelling waves that propagate in the opposite direction to drop rotation. These travelling waves are the result of vorticity introduced by the electromagnetic technique used to spin the droplet. In addition to the analogies with rotating astronomical bodies, studying droplet shapes may shed light on the structures of splash-form tektites – pieces of spinning molten rock flung from the earth during volcanic eruptions and meteor impacts – that have been discovered in weird and wonderful shapes [5]. Indeed, tumbling molten metal experiments have shed some light on the equilibrium structures found [6]. We have developed an alternative method for laboratory production of tektite-like structures in the cooling of spinning, diamagnetically levitated droplets of molten paraffin wax (a substance sometimes used to model lava/magma flows [7]). Furthermore, molten

silica has been shown to have viscoelastic properties [8]. By studying spinning viscoelastic polymeric and colloidal drops, we hope to investigate the means by which some of the more elongated far-from-equilibrium shaped tektites form. This work has also provided insight into the effect of surface elasticity on the shape evolutions of such drops, compared to the equilibrium spinning shapes studied by Brown and Scriven. Inertially driven droplet pinch-off: When two plates connected by a liquid bridge are pulled apart, the connecting fluid progressively thins, maintains equilibrium, until a critical minimum radius is reached, at which point the bridge undergoes a Rayleigh-Plateau capillary instability resulting in pinch-off [9]. In Newtonian fluids, this droplet pinch-off results in the formation intermediary satellite droplets, with sizes depending most heavily on the viscosity ratio between the two fluids (droplet and air) and the separation speed of the two walls. In non-Newtonian fluids however, particularly polymer solutions, this pinch-off mechanism is drastically altered by both the elasticity of the surface of the bridge, and the elongational viscosity that is the result of quickly stretching the dissolved polymers out of their equilibrium configurations. This elongational viscosity, which is a function of the speed at which the walls are pulled apart compared to the relaxation speed of the dissolved polymer coils, dampens surface waves over the bridge inhibiting both pinch-off and satellite drop formation. Instead a filament forms which thins exponentially via capillary flow to a microfibre, at which point it either loses structural integrity and drifts away or snaps and is pulled back to one of the two large volumes of liquid. Similar pinch off mechanisms take place between a droplet and an ink-jet printer nozzle it has been ejected from, leading to great industrial demand for better understanding of pinch-off in order to remove satellite drop formation and increase printing precision. Here we examine an alternative novel method for observing pinch-off, compared to the established usual ink-jet/wall separation methods, by studying inertial break up of a spinning viscoelastic drop in a quasi-frictionless non-evaporating environment. What we find is a steady transition from single satellite formation (pure water) through to single or multiple beads on a string structure and then to long lasting thin filaments as concentration and molecular weight of the dissolved polymer (PEO) is increased. Interestingly, in highly entangled solutions, the total length of the thread structure during pinch off can reach more than an order of magnitude higher than the initial droplet radius, only here being limited to the size of the chamber (the magnet bore). Work is ongoing to investigate whether this inertially-driven pinch-off of non-Newtonian solutions offers a useful alternative

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method for probing the fluid properties, such as elongational viscosity.

Fig. 1. Inertially driven fission of 3 equally sized PEO droplets (Mw~8Mg/mol, (R0=0.62cm) concentration =0.0001, 0.001 and 0.01% by mass from top to bottom). Coalescence of liquid bodies in a decaying orbit: Studies of droplet coalescence under direct or grazing collisions can enhance our understanding of raindrop formation, various aerosol/spray technologies and combustion engines [10] [11]. Furthermore, the effect of droplet coalescence on the stability of emulsions (metastable dispersions of two immiscible fluids) is difficult to escape anyone’s notice: emulsion paints phase separate if left too long, but would have a much higher shelf life if the dispersed droplets were prevented from coalescing. While comprehensive studies of Newtonian droplet collisions exist [12], the understanding of how two viscoelastic drops of equal sizes transition from separate entities into one body is far from complete. Recent work on the stability of polymeric emulsions under shear have suggested that surface active polymers at the droplet-droplet interface can act to induce a steric repulsion force inhibiting coalescence [13] [14]. Those experiments however did not focus on single coalescence events but rather examined emulsion stability by measuring average drop radii with time. In this section we discuss the re-merger of two levitated drops that had previously undergone fission (spun up with air flow), and then been allowed to rotate around each other in a slowly decaying orbit (without air flow); the merger is studied for a range of surface tensions and viscoelasticities. Initial results comparing equally shear viscous drops of sucrose and polymer solution indicate that the effects of elasticity play very little role in coalescence once a liquid bridge is formed between the drops, but can delay the formation of this bridge, leading to longer merger times post-fission.

1% by mass from top to bottom) References [1] J. A. F. Plateau, “Experimental and theoretical researches on the figures of equilibrium of a liquid mass withdrawn from the action of gravity,” Annual report of the Board of the Regents of the Smithsonian Institution, pp. 259-302, 1863. [2] R. A. Brown and L. E. Scriven, "The shape and stability of rotating liquid drops," Proc. R. Soc. Lond. A, vol. 371, pp. 331-357, 1980. [3] T. G. Wang, A. V. Anilkumar, C. P. Lee and K. C. Lin, "Bifurcation of rotating liquid drops: results from USML-1 experiments in Space," J. Fluid. Mech., vol. 276, pp. 389-403, 1994. [4] R. J. A. Hill and L. Eaves, "Nonaxisymmetric shapes of a magnetically levitated and spinning water droplet," Phys. Rev. Lett., vol. 101, p. 234501, 2008. [5] J. S. Reinhart, "Impact effects and tektites," Geochemica et Cosmochemica Acta, vol. 14, pp. 287-290, 1958. [6] L. T. Elkins-Tanton, P. Aussiollous, J. Bico, D. Quére and J. W. M. Bush, "A laboratory model of splash form tektikes," Meteoritics & Planetary Science, vol. 38, pp. 1331-1340, 2003. [7] M. V. Stasiuk, C. Jaupart, R. Stephen and J. Sparks, "Influence of cooling on lava-flow dynamics," Geology Soc. America, vol. 21, pp. 335-338, 1993. [8] S. L. Webb and D. B. Dingwell, "The onset of non-Newtonian rheology of silicate melts," Phys. Chem. Minerals, vol. 17, pp. 125-132, 1990. [9] R. Sattler, S. Gier, J. Eggers and C. Wagner, "The final stages of capillary break up of polymer solutions," Phys. Fluids, vol. 24, p. 023101, 2012. [10] P. O'Rourke and F. V. Bracco, "Modeling of droplet interactions in thick sprays and a comparison with experiments," in Proceedings of the Institution of Mechanical Engineers, 1980. [11] G. M. Faeth, "Current status of droplet and liquid combustion," in Proc. Energy Combustion, 1977. [12] J. Qian and C. K. Law, "Regimes of coalescence and separation in droplet collision," J. Fluid. Mech, vol. 331, pp. 59-80, 1997. [13] S. Lyu, T. D. Jones, F. S. Bates and C. W. Macosko, "Role of block copolymers on suppression of droplet coalescence," Macromolecules, vol. 35, pp. 7845-7855, 2002. [14] D. Georgieva, V. Schmit, F. Leal-Calderon and D. Langevin, "On the possible role of surface elasticity in emulsion stability," Langmuir, vol. 25, no. 10, pp. 5565-5573, 2009.

Fig. 2. Coalescence of two colliding PEO droplets in a decaying orbit (Mw~8Mg/mol, concentration =0.1 and 258

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ELECTRIC FIELD INDUCED CONDUCTIVITY ENHANCEMENT DURING THE DRYING OF CONDUCTING POLYMER DISPERSION R.Piramuthu Raja Ashok, Susy Varughese Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai, India E-mail: [email protected]

Thiophene based conjugated polymer poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) PEDOT:PSS has been extensively used as an important layer in organic electronic devices such as organic light emitting diode, organic photovoltaics, field effect transistors, electronic memory chips and so on. The morphology of PEDOT:PSS has been extensively studied and many models have been proposed to correlate the microstructure with the transport properties at nanoscale level. The currently suggested model for the morphology of PEDOT:PSS consists of a polymer dispersion particle which has core-shell morphology. The core comprises of hydrophobic and highly conductive PEDOT while the shell comprises of the hydrophillic insulating PSS which results in a polyelectrolyte complex. The morphology of the conducting polymers undergoes changes during its course of film formation from their pristine state. Several investigations were made on different processing techniques for conducting polymers such as solvent casting; spin coating, dip coating, inkjet printing and the polymers form a solid film after the evaporation of solvent. Several groups have observed that the conductivity of PEDOT:PSS in water (0.1-1 Scm-1) can be enhanced by processing with glycerol, DMSO, sorbitol, diethylene glycol, etc., to above two orders of magnitude. The earlier studies attributed the enhancement of conductivity to the screening effects of the Columbic interaction between the positively charged PEDOT and the negatively charged PSS [1] or to a solvent induced conformational change in the dispersion [2]. More recent investigations have attributed the conductivity enhancement to the morphological changes and phase segregation process in PEDOT:PSS. Polar solvents are known to enhance the phase segregation in PEDOT:PSS. The phase segregated PEDOT:PSS results in two domains with highly conductive PEDOT chains surrounded by weakly ionic PSS chains. During processing, these phase segregated domains reorient themselves and undergo structural changes. The drying stage of the process plays a critical role in determining the morphology and physical properties of the final film. Experimental as well as theoretical [3] studies reported that a wide variety of controlled ordered structures can be formed using patterned top electrodes and non-uniform electric field. The conducting polymer dispersion of PEDOT:PSS is subjected to a similar electric field during the drying process, wherein the temperature effects are not considered. PEDOT:PSS (1.3 wt% dispersion in water) purchased from Sigma Aldrich, India, was used for the study. Secondary additives such as sorbitol, glycerol and dimethyl sulfoxide (DMSO) were added as 6 wt%

concentration in the polymer dispersion and stirred for 6 h and sonicated for 2 h. The resultant dispersion was then filtered through a 5 µm filter paper. A single drop (4 microliter) of the polymer dispersion dispensed from a micro-litre syringe was used for the wetting and drying experiments. The drying experiments were performed under ambient conditions (33°C; 69% RH). The drying of the drops was performed under natural drying conditions with an external DC electric field and without external field using a custom made field setup across the droplet. The electric field applied was in the range of 0 to 160 V/cm. The contact angles of conducting polymer droplets on different substrates were obtained using a Goniometer (GBX Digidrop Contact angle meter). The equilibrium contact angles were measured at 25±2 °C and 55±3 %RH. For each sample, the equilibrium contact angle was measured three times at different positions on the substrate and the average equilibrium contact angle is reported.

Morphology of the dried droplets were studied using Scanning Electron Microscope (SEM) (Hitachi S-4800) after gold sputtering of the dried droplets. The surface conductivity of the polymer dried droplets were determined using a four probe conductivity setup with Keithley 6221 current source and 2182A nanovoltmeter. Piranha treated glass and ITO coated glass were used as substrates for the wetting and drying experiments. The contact angles of PEDOT:PSS dispersions on glass and ITO coated glass are given in Table 1. The surface energy of glass and ITO coated glass were 110 mN/m, and 36 mN/m, respectively. As the surface tension of the dispersion remains constant for both the substrates, an ascending value in the contact angle was observed as the surface energy of the substrates decreases. It was also observed that on application of the electric field, the wetting of the polymer dispersion on both the substrate improves. We observed a steady decline in the contact angle of the polymer drop with increasing electric field and there exists a ‘saturation voltage’ above which the contact angle remained constant. On application of the electric field, the charged ions in the conducting polymer drop modify the energy balance in the solid-liquid interface thereby enabling the contact angle to decrease with increase in applied voltage. The contact angle for pristine PEDOT:PSS drop remained constant on increasing the voltage suggesting a strong solid-liquid interface. This behaviour seems to have both the influence of the electric field and natural drying phenomenon. In the case of natural drying, the contact line pinning i.e, the constant drop diameter exists due to the increased evaporative flux at the three phase contact line. The contact line pinning or constant drop diameter in the initial period of drying was observed in the case of

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drops dried without the application of electric field while the drop diameter continued to decrease till the saturation voltage when electric field was applied. We observed an increase in conductivity for dried drops of all PEDOT:PSS dispersions when an electric field was applied (Fig 1(c)). The surface conductivity of PEDOT:PSS + 6 wt% glycerol was higher (0.162 S/m) compared to others. In the case of pristine PEDOT:PSS a drastic increase in the conductivity was observed on applying electric field while the drop was drying. Morphology analysis of this drop using SEM showed crystallization (Fig 1(a)) which could be the reason for the increase in conductivity. When secondary additives were added and electric field was applied, conductivity was found to increase further, though there were no crystalline domains that could be observed. However, in the case of 6 wt% glycerol doped PEDOT:PSS, which showed the highest conductivity, clear pattern formations were observed (Fig 1(b)) in the morphology which needs further investigation. The following discussion based on the complex wetting behavior of polyelectrolyte complexes (PEC) is used as a supporting argument to arrive at a new hypothesis for the conductivity changes observed in PEDOT:PSS. The wetting behaviour of PEDOT:PSS doped with secondary additives such as glycerol and DMSO are similar on ITO coated glass (Table 1). However, the wetting behavior of sorbitol doped PEDOT:PSS dispersion is differen from others. In the case of sorbitol doped PEDOT:PSS, the observed decrease in contact angle and increase in wetting are more in comparison to glycerol and DMSO. Secondary additives are known to interfere in the Coulombic interactions between the PSS polyanion and the PEDOT polycation in polyelectrolyte complexes such as PEDOT:PSS. Polar solvents tend to have screening effect and thus the PEDOT and PSS domains phase separates out in water medium. In the present case all the additives are polar in nature. However, sorbitol is highly hygroscopic in comparison to glycerol and DMSO which may result in more interaction of sorbitol with the PSS domains. PSS domains may get trapped in the water that is present in the sorbitol resulting in a complex wetting behavior. The observed changes in contact angle also may be indicating the role of nano-sized domains of the PEDOT and PSS which preferentially wets a particular substrate depending on its polar or non-polar nature. The measured surface conductivity reflects the presence of the conducting, non-polar PEDOT domains being either in contact with the hydrophobic ITO surface or the polar PSS domains in contact with the glass surface resulting in observed changes in the conductivity. The electric field seem to be re-organising the charged PSS and PEDOT domains resulting in observed increase in conductivity.

260

Table. 1: Effect of secondary dopants and electric field on contact angles of PEDOT:PSS dispersions on glass and ITO coated glass 0 Contact Angle ( ) PEDOT:PSS Glass (at ITO (at 100 Dispersion Glass ITO 100 V/cm)

V/cm)

Pristine

35

90

15

38

+ Glycerol 6wt% + Sorbitol 6wt% + DMSO 6wt%

56 38 58

98 70 100

45 20 48

50 30 65

Fig. 1: SEM micrograph of dried PEDOT:PSS drop on ITO substrate electric field of 100 V/cm. (a) PristineCrystallization of domains and (b) with 6 wt% glycerol- pattern formation with shrinkage on the polymer surface. The effect of electric field (100 V/cm) on the conductivity of the dried polymer film on ITO substrate is shown in (c).

In this work, we explored the wetting behaviour of conducting PEDOT:PSS dispersion with different secondary additives on different surface energy substrates. An external electric field was applied during the drying of the polymer drop and the morphology of the dried drop were analysed. Interesting patterns, crystallization of the polymer and increase in conductivity of the dried film were observed. References [1] J. Y. Kim, J. H. Jung, D. E. Lee, and J. Joo, Enhancement of electrical conductivity by a change of solvents, Synthetic Metals, vol. 126, pp. 311-316, 2002. [2] J. Ouyang, C.Wei Chu, and F.Cchung Chen, Polymer Optoelectronic Devices with Poly (3, 4-Ethylenedioxythiophene) Anodes, Journal of Macromolecular Science, vol. 41, no. 12, pp. 1497-1511, 2004. [3]F. Mugele and J.Christophe Baret, Electrowetting: from basics to applications, Journal of Physics: Condensed Matter, vol. 705, p. R705-R774, 2005

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AIR LAYERS UNDER WATER ON THE WATER FERN SALVINIA EXPOSED TO PRESSURE FLUCTUATIONS Matthias J. MAYSER1,2, Wilhelm BARTHLOTT2

1

2

Microfluidics, University of Liege, Chemin des Chevreuils 1, 4000 Liege, Belgium Nees Institute for Biodiversity of Plants, University of Bonn, Venusbergweg 22, 53115 Bonn, Germany E-mail: [email protected]

Superhydrophobic technical surfaces are of high scientific and economic interest because of their remarkable properties. Highly efficient surfaces evolved in plants (e.g. Lotus) and animals [1, 2]. Whereas the superhydrophobic and self-cleaning abilities are well explored in biological as well as technical surfaces, little attention was given to their air-retaining properties under water. Only recently the immense potential of air-retaining surfaces e.g. for low friction fluid transport and drag reducing ship coatings has started to be explored. A major problem of superhydrophobic surfaces mimicking Lotus is the limited persistence of the air retained, especially under rough flow conditions [3]. However, a variety of floating or diving plant and animal species exist, which possess air-retaining surfaces optimized for durable water-repellency. Especially water ferns of the genus Salvinia have developed superhydrophobic surfaces, which is capable of maintaining air layers for month [4]. These surfaces are characterized by complex hairs. Depending on the species density, height, sculpture and other parameters of the hairs vary [5]. For the application of air layers on ship hulls the air film does not only have to persist over long periods of time under static conditions. It has also got to withstand the stresses of water pressure. There are two components leading to pressure on the ship hull. One factor is hydrostatic pressure. Due to the density of water the pressure increases by one bar for every 10m of depth. With a maximum loaded draft of current container ships of 12 meters [6] this results in a maximum hydrostatic pressure of 1.2 bar. The other factors to pressure on ship hulls result from the dynamic water forces during cruise. Combined with the hydrostatic pressure those add up to a total maximum pressure of about 2.5 bar [7]. However, the slamming forces, which occur in certain areas of the ship in high swell, can be much higher (up to 15 bar). But as those occur only for very short periods of time we will investigate only pressures well below the slamming forces in this study. To investigate the effect of pressure on air layers, a pressure cell was built of a PVC pipe crossing (TÜV rated to 10 bar) with 10 cm inner diameter, all four ends bolted with 2 cm thick disc by eight M8 screws and is placed upright with a 45° angle of all tubes. Both upper ends were covered with PVC discs; one gets removed for sample change, the other sports a connector for pressurization. Both lower ends were closed by acrylic glass discs. One of those gave access for illumination while the other served the purpose of sample

observation by a camera. The cell gets pressurized through a pressure reducer by helium, which has the lowest solubility of all gases in water [8]. For safety reasons a relief valve limited the pressure to 6 bar. Fresh leafs of four Salvinia species with different hair structures (n=10) get clamped on a custom designed holder and placed in the center of the pressure cell, which is filled to just above the crossing with water. The leafs were being observed by a digital camera (Canon D550, Canon Inc., Tokyo, Japan) equipped with a macro lens (Canon 60mm, Canon Inc., Tokyo, Japan) and mounted directly in front of the viewing glass of the pressure cell. It was connected to a computer and remote controlled with EOS remote capturing software to prevent camera shake. Pressure was slowly increased in 0.2 bar steps. An image was shot before the pressure was applied and for each step to be analyzed for air coverage on the leaf. Additionally videos of pressurization were taken to examine the progress of air suppression. After 6 bar were reached the pressure was slowly released and a further image was taken at 0 bar for comparison with the initial air layer. The images were examined on the pressure at which water penetrated in between the hairs for the first time, the pressure at which no air layer was visible as well as the degree of restoration of the air layer after the pressure was released.

Fig. 1: A) Pressure at which water penetrated between the

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hairs of different Salvinia species, B) Pressure at which no air is visible between the trichomes of different Salvinia species, (n=10)

Taking the pressure at which water penetrates in between trichomes as a benchmark, three species are quite equal with two scenarios sticking out. While S. minima and S. oblongifolia range slightly below 0.3 bar, S. molesta and S. cucullata display a significant difference (Fig. 1a). For S. molesta the lower resistance against pressure can be explained by the longest hairs and the lowest trichome density of all the species. A slight bending of the leaf can lead to a rather big gap between two adjacent hairs. This gap provides a weak point in the resistance against water penetrating the air layer. S. cucullata with its large reservoir of air held by the leaf shape instead of the hairs encounters the situation of air pressing against the tips of the hair only after the air has been sufficiently compressed for its volume to just fill the space between the hairs. S. oblongifolia is the only species that is not capable of retaining at least a minimal amount of air in between the trichomes at the pressures experienced on a ship hull (2.5 bar) [7]. Fig. 1b shows clearly that its ability to maintain air is significantly lower compared to the other species. Because of its small air volume per surface area the air gets compressed enough to just cover the surfaces as a thin layer held up by the wax crystals at approximately 1.2 bar. This air layer also collapses partially as the pressure reaches 3 bar. The experiments also revealed that surfaces with a higher hair density (like S. oblongifolia and S. cucullata) experience a more uniform depression of the air layer while the lower densities of the other species led to local failures which could then spread horizontally through the hairs.

Fig. 2: Percentage of air layer regeneration on different Salvinia species after lowering the pressure from 6 bar to ambient pressure (n=10)

The regeneration of the air layers works obviously best, if the surface has not been wetted during the pressure cycle (Fig. 2). Thus a high volume per surface area is beneficial for the restoration. S. oblongifolia has the lowest hair structures and accordingly the lowest volume per surface area. This leads to water wetting 262

even the nano structure of the wax crystals (at least partially) and the surface being wetted in the Wenzel-state. This gets apparent by a more intense green color of the leaf surface at pressurizations to 3 bar and above. A reformation of a Cassie-Baxter-state after depressurisation is thereby prevented [9]. The high volumes of S. cucullata and S. molesta prevent a full Wenzel-state even if compressed by 6 bar overpressure. So the regeneration rate is much better. Additionally the air trapped in the baskets of the egg beater hairs act like a magnet to the air water interface. As soon as the interface rises enough to touch this air bubble, the interface immediately jumps to the tip of the hairs. The smaller air water interface between the hair tip is energetically favorable to the sum of the interfaces of the air bubble in the basket and the interface between the basket. Concluding the pressurization experiments revealed that three of the four examined Salvinia species are capable of maintaining air layers at the pressures relevant for application on ship hulls. High air volumes per surface area are advantageous to retain at least a partial Cassie-Baxter-state under pressure, which also helps the restoration of the air layer after depressurization. Closed loop structures like the baskets at the top of the egg beater hairs also help setting the air layer back to its original level at the tip of the hairs by trapping air bubbles in them. References [1] Barthlott W, Neinhuis C. Purity of the sacred lotus, or escape from contamination in biological surfaces. Planta. 1997;202:1–8. [2] Koch K, Barthlott W. Superhydrophobic and superhydrophilic plant surfaces: an inspiration for biomimetic materials. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2009;367(1893):1487–1509. [3] Balasubramanian AK, Miller AC, Rediniotis OK. Microstructured hydrophobic skin for hydrodynamic drag reduction. AIAA Journal. 2004;42(2):411–414. [4] Barthlott W, Schimmel T, Wiersch S, Koch K, Brede M, Barczewski M, et al. The Salvinia Paradox: Superhydrophobic Surfaces with Hydrophilic Pins for Air Retention Under Water. Advanced Materials. 2010;22(21):2325–2328. [5] Barthlott W, Wiersch S, Colic Z, Koch K. Classification of trichome types within species of the water fern Salvinia, and ontogeny of the egg-beater trichomes. Botany. 2009;87(9):830–836. [6] Germanischer-Lloyd. Bauvorschriften & Richtlinien. Germanischer Lloyd, Hamburg; 2011. [7] Kaeding P. Belastung des Schiffbodens nach GL. ThyssenKrupp Marine Systems; 2009. [8] Greenwood A Norman N ; Earnshaw. Chemistry of the Elements. 2nd ed. Butterworth-Heinemann, Oxford; 1997. ISBN 0750633654. [9] Quéré D, Lafuma A, Bico J. Slippy and sticky microtextured solids. Nanotechnology. 2003;14:1109–1112.

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KINETIC ENERGY DISSIPATION ON SUPERHYDROPHOBIC SURFACES REVEALED BY A MAGNETIC DROPLET OSCILLATOR Jaakko V. I. TIMONEN, Mika LATIKKA, Olli IKKALA, Robin H. A. RAS Department of Applied Physics, Aalto University School of Science, P.O.B. 15100, FI-00076 Aalto, Finland E-mail: [email protected]

Extremely water-repellent, i.e. superhydrophobic, surfaces have experienced an enormous boost of 1 Artificial interest during the last decade. superhydrophobic coatings have been used for self-cleaning, anti-fogging and anti-icing surfaces, non-wetting textiles, drag reduction and storing and 2,3 Many of these attractive displaying information. features are based on the greatly increased droplet mobility on these surfaces. This is a property of the Cassie-Baxter state, where the droplet is partly resting on air trapped within the nano- and microscale surface roughness. Air pockets allow liquid to flow along the apparent liquid-solid interface (so called macroscopic viscous slip), which reduces drag and enhances flow 4 speed. Despite the promising characteristics, kinetics of droplets on these surfaces are poorly understood and even methods for surface quality and wetting characterization are insufficient. For example one of the most used wetting investigation method, optical contact angle goniometry, suffers from optical errors when very 5 water-repellent surfaces are studied. Measurements are also generally performed with static or quasi-static droplets, and thus obtained results may not be valid for moving droplets due to time-dependent wetting 6 effects. We have developed a new method for measuring kinetic energy dissipation in droplets moving on superhydrophobic surfaces, based on oscillation of a water-like magnetic droplet on a surface in external magnetic field. The position of the droplet during either free decay or forced oscillations is observed as a function of time, and dissipative parameters are computed from the data. Contrary to conventional techniques, this method is capable of separately determining dissipation due to contact angle hysteresis (CAH) force and viscous force (at a precision of ~10 nanonewtons) directly from the moving droplet. Average contact angle of the moving droplet and contact angle hysteresis can also be extracted from the results. In addition, forces acting on the droplet are easily tunable by adjusting the magnetic field strength or geometry, making versatile investigations possible. We created magnetically controllable droplets by adding a small amount (0.2% v/v) of superparamagnetic iron oxide nanoparticles to water. Because of the low particle concentration, the density, viscosity and surface tension of the fluid deviated no more than 4% from those of pure water. Thus the obtained results represent behavior of a water droplet. Magnetic properties of the fluid were measured with a SQUID magnetometer.

Free decay measurements were performed with 5 µ l 7 magnetic droplets on a fluorinated Cu/Ag test surface with a cylindrical permanent magnet underneath (fig. 1a). The parabolic magnetic field produces a Hookean restoring force -kx on the droplet when it is displaced from the equilibrium position at the magnet axis. Released droplet is brought to a harmonic oscillatory motion dampened by dissipative forces (fig. 1b). These forces and the magnetic spring constant k were obtained by fitting the recorded position of the droplet center x as a function of time t with the solution for the general harmonic oscillator (fig. 1c):

m

d2 x = −kx + Fη ± Fµ dt 2

(1)

dx is the dt is the CAH force and β is the

where m is the droplet mass, Fη = −2β viscous force, Fµ

viscous dissipation coefficient. Identical measurements repeated on a single spot on the substrate illustrate the high precision of the method (fig. 1c inset). Dissipation rates due to Fµ and Fη are shown in fig. 1d. Droplet shape is strongly dependent on the normal force mgE (fig. 1b), which is a sum of gravity and downward magnetic force. By varying the magnetic field, we measured the dissipative forces Fµ and Fη as a function of mgE (fig. 2a,b). Contact line length l and apparent contact area A were calculated using Young-Laplace equation for each mgE. Average CA and CAH were then determined by fitting measured Fµ as a function of l with approximate equation for Fµ :

Fµ =

Δθ ⎞ Δθ ⎞⎤ l ⎡ ⎛ ⎛ γ ⎢cos⎜θ − ⎟ − cos⎜θ + ⎟⎥ 2 ⎣ ⎝ 2 ⎠ 2 ⎠⎦ ⎝

8

(2)

where γ is the surface tension. Average CA of θ = 176.5 ± 2° and CAH of Δθ = 5 ± 1° were obtained.

Fη was found to be nearly linearly proportional to A (fig. 2b). This suggests that the viscous dissipation does not propagate far from the liquid-solid contact area, probably because the droplet oscillates back and forth and never reaches steady-state motion. Measured values for k were in good agreement with the predicted values calculated from droplet and field properties.

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Fig. 2: a) CAH force Fµ versus normal force gE and contact line length l, and the best linear fit through origin. b) Viscous dissipation coefficient β versus gE and apparent contact area A, and the best linear fit through origin. c) Schematic figure of the experimental setup for the externally driven oscillations. d) Droplet amplitude a versus magnetic field frequency f, showing a resonance peak near 4.7 Hz. Dashed line indicates the amplitude of the driving magnet (0.9 mm).

Fig. 1: a) A photograph of the experimental setup showing a superhydrophobic (SH) test surface placed above a cylindrical NdFeB magnet and a 5 µl magnetic droplet in its equilibrium position. b) Force diagram of the moving droplet, showing velocity v, CAH force Fµ , viscous force Fη , magnetic restoring force -kx, adjustable normal force mgE and advancing and receding contact angles θ A and θ R . c) Position of the droplet center x versus time t for ten measurements on one spot on the surface and the extracted parameters. Close-up (inset) shows that data points from different measurements are very close to each other, illustrating good repeatability. d) The dissipation rate of the total energy and its division into two components due to CAH and viscosity.

The method is not limited to free decay oscillations, but also forced resonant measurements can be performed with an oscillating magnetic field created by a magnet in horizontal sinusoidal motion (fig. 2c). By measuring the droplet amplitude as a function of field frequency, a distinct resonance peak can be found. Dissipative parameters can be obtained by fitting the data with a numerically calculated theoretical prediction (fig. 2d). In conclusion, observing magnetically induced oscillations of water-like magnetic droplets allows high precision measurements of energy dissipation on superhydrophobic surfaces. With the presented method it is possible to separately quantify dissipation due to 264

contact angle hysteresis and viscous losses as a function of tunable normal force. With its versatility, simplicity and compatibility with existing optical goniometers, it holds promise of becoming a widely for investigation of dynamic used method superhydrophobicity and surface characterization. References [1] Roach P., Shirtcliffe N. J., Newton M. I., Progess in superhydrophobic surface development, Soft Matter, 4 (2), pp. 224-240, 2008. [2] Guo Z., Liu W., Su B.-L., Superhydrophobic surfaces: From natural to biomimetic to functional, Journal of Colloid and Interface Science, 353 (2), pp. 335-355, 2011. [3] Verho T. et al., Reversible switching between superhydrophobic states on a hierarchically structured surface, Proceedings of the National Academy of Sciences, 109 (26), pp. 10210-10213, 2012. [4] Bocquet L., Lauga E., A smooth future?, Nature Materials, 10 (5), pp. 334-337, 2011. [5] Srinivasan S., McKinley G. H., Cohen R. E., Assessing the Accuracy of Contact Angle Measurements for Sessile Drops on Liquid-Repellent Surfaces, Langmuir, 27 (22), pp. 13582-13589, 2011. [6] Tadmor R. et al., Drop Retention Force as a Function of Resting Time, Langmuir, 24 (17), pp. 9370-9374, 2008. [7] Larmour I. A., Bell S. E. J., Saunders G. C., Remarkably Simple Fabrication of Superhydrophobic Surfaces Using Electroless Galvanic Deposition, Angewandte Chemie International Edition, 46 (10), pp. 1710-1712, 2007. [8] Quéré D., Non-sticking drops, Reports on Progress in Physics, 68 (11), pp. 2495-2532, 2005.

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PLASMA SURFACE MODIFICATION OF POLYETHERETHERKETONE (PEEK) Diana RYMUSZKA, Konrad TERPIŁOWSKI, Lucyna HOŁYSZ Dept. of Physical Chemistry - Interfacial Phenomena Faculty of Chemistry Maria Skłodowska- Curie University in Lublin, Poland E-mail: [email protected]

treated by air plasma for 25 seconds, 1 minute and 3 minutes. The contact angles (advancing and receding) were measured for water, formamide and diiodomethane using sessile droplet method. After the plasma surface modification contact angles have a much lower value compared to that of the original surface. The lowest values of the contact angle were observed for plates treated by plasma for 3 minutes. The reduced water contact angle was observed from 107° to less than 35° with only 25 s plasma treatment. The influence of plasma treatment time on the PEEK surface properties were studied as well [Fig. 1]. It was found that the effect of the plasma is not permanent. 120 W

A .

θA 100

W

θR

θ [°]

80 60 40 20 0 0

20

40

60

80 100 120 140 160 180 200

t [sec]

80

B .

F

70

θA

60

θR

F

50 40

θ [°]

Solid surface properties play a crucial role in many processes in nature, everyday life, agriculture and industry. One of important properties is wettability, which depends on the hydrophilic-hydrophobic nature of the surface. While in some processes, poor wettability is important for hydrophobic surfaces, in others, good wettability is important for hydrophilic surfaces. The processes in which surface wettability is required are corrosion protection, bonding, chemical plant protection, irrigation, soil washing and washing processes, pharmaceutical and cosmetic industry and many others. Hydrophilic-hydrophobic properties of the solids can be modified in several different ways of which plasma surface treatment has become very popular recently [1]. Plasma technique is quick, clean and ecological. Furthermore, it allows obtaining various materials with different surface properties from the initial polymer. Usually, the surface free energy of the modified by plasma surface significantly increases. However, the appropriate plasma choice, its duration and temperature allow to increase the hydrophobicity as well. Materials which are the subject of this type of research are often polymers due to their susceptibility to plasma surface modification and potential application, such as: polypropylene (PP), polyethylene (PE), polymethyl methacrylate (PMMA), polyetheretherketone (PEEK), polyethylene terephthalate (PET), poly(tetrafluoroethylene) (PTFE), polydimethylsiloxane (PDMS) polyvinylidene fluoride (PVDF) and polysulfone (PS) whose surfaces can be modified by using argon, helium, oxygen, nitrogen, air or less carbon dioxide plasma [2,3].

30 20 10

The aim of the study was to determine the wettability and surface energy properties of PEEK before and after activation by air plasma. PEEK plates were

0 0

20

40

60

80 100 120 140 160 180 200

t [sec]

100 D

C .

θA

D

80

θR

60

θ [°]

The purpose of the plasma polymer modification is: production of specific functional groups which can interact specifically with other groups, surface nature and morphology changes, elimination of impurities, formation of cross-linking or improvement of chemical inertness [4]. From a medical point of view very important polymer is polyetheretherketone (PEEK), which is used as implants for the cervical, thoracic and lumbar spine because of its good mechanical properties, low density and good chemical resistance. However, its relatively low adhesion to bone tissue has limited its more common application. Unfortunately, it has a relatively low mechanical strength compared to metallic materials, which often limits its use. Therefore, the aim is to modify PEEK by spreading a titanium layer and changing the nature of the surface interactions, such as by plasma modification, in order to improve its biocompatibility [5].

40

20

0 0

20

40

60

80 100 120 140 160 180 200

t [sec]

Fig.1. Water (W) (A), formamide (F) (B) and diiodomethane (D) (C) advancing (θA) and receding (θR) contact angle measured on PEEK plates modified by air plasma for different time (25 seconds, 1 minutes and 3 minutes).

Then the surface free energy and components of the surface free energy were calculated using the values of

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the measured contact angles and applying the acid-base approach proposed by van Oss, Good and Chaudhury as well that based on the contact angle hysteresis (Chibowski approach) [6-8]. The values of the acid-base dispersion and polar interactions allowed the estimation of the hydrophilic-hydrophobic modified PEEK surface changes before and after the plasma activation. Furthermore, the chemical changes on the polyetheretherketone surface are also reflected in their spectroscopic spectra – after the plasma surface treatment new functional groups appear [Fig.2]. 2,2

t= 0

2,0 1,8 1,6

Absorbance, A

A .

1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0

500 1000 1500 2000 2500 3000 3500 4000 4500

Wavenumber, ν [cm-1]

References [1] Jung H., Gweon B., Kim D.B., Choe W., Plasma Process. Polym., 8, 535–541, 2011. [2] Barankin M.D., Gonzalez II E., Habib S.B., Gao L., Guschl P.C., Hicks R.F., Langmuir, 25, 2495–2500, 2009. [3] Luthon F., Cl´ement F., Conference Proceeding: Int. Conf. on Automation, Quality & Testing, Robotics, AQTR'06, Cluj-Napoca Romania, 1–6, 2006. [4] Bryjak M., Janecki T., Gancarz I., Smolińska K., Wykłady Monograficzne i Specjalistyczne, Toruń, 64–79, 2009. [5] Cheol-Min Han, Eun-Jung Lee, Hyoun-Ee Kim, Young-Hag Koh, Keung N. Kim, Yoon Ha, Sung-Uk Kuh, The electron beam deposition of titanium on polyetheretherketone (PEEK)and the resulting enhanced biological properties, Biomaterials, 31, 3465–3470, 2010. [6] Chibowski E., Perea-Carpio R., Ontiveros-Ortega A., J. Adhesion Sci Technol., 16, 1367–1404, 2002. [7] E. Chibowski, Adv. Colloid Interface Sci., 113, 121–131, 2003. [8] van Oss C. J., Good R. J., Chaudhury M. K., Langmuir, 4, 884–891, 1988.

2,2

B .

t=25 seconds

2,0 1,8

Absorbance, A

1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 -0,2 0

500 1000 1500 2000 2500 3000 3500 4000


2,2

C .

t=1 minute

2,0 1,8

Absorbance, A

1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 -0,2 0

500 1000 1500 2000 2500 3000 3500 4000


2,2

D .

t=3 minutes

2,0 1,8

Absorbance, A

1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 -0,2 0

500 1000 1500 2000 2500 3000 3500 4000


Fig.2 IR spectra of polyetheretherketone (PEEK) pure (A) and treated by air plasma and treated by air plasma for 25 seconds (B), 1 minute (C) and 3 minutes (D).

The studies show that after plasma treatment wettability, surface free energy and topography are changed, which results from an increase in polar, more hydrophilic nature of the surface. However, the effect of the plasma is not permanent and disappear over time.

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RESONANT OSCILLATIONS OF PENDANT HEMISPHERICAL LIQUID DROPLET AS A MEANS TO EXAMINE TRANSIENT PROCESSES IN THE LIQUID-AIR INTERFACE Nikolay Zografov, Nikolay Tankovsky University of Sofia, Faculty of Physics, 5 James Bourchier Blvd., Sofia-1164, Bulgaria E-mail: [email protected]

In a recent work [1] we have shown that pendant spherical droplets can easily be driven into oscillations by a dielectric force acting upon the interface. The pressure difference p at the surface of a droplet in electric field E, can be evaluated by the formula:

3 ε −1 p = ε0E2 2 ε +2

(1)

It can be seen that the electric field can be used as a driving force for achieving resonant oscillations not only for charged liquid drops, but also for insulating liquids, when ε>1. The frequency of the n-th resonant mode for a perfect sphere, calculated by Rayleigh, is the following:

f n2 = n(n − 1)(n + 2)

σ 4π 2 ρR 3

(2)

The lowest possible mode for n=2 is called the Rayleigh frequency. In the gravitational field of the Earth the droplet should be supported by a surface from below (sessile drop) or from above (pendant drop). The real supported drop differs from an ideal free sphere because of the disturbance introduced by the supporting surface and the disturbance introduced by the gravitational force. M. Perez et al [2] have proposed the following empirical formula for the resonant frequency of a sessile drop:

f 0 ( R) =

3 Re 2σ ( ) 2 R p ρπ 2 R 3

r R

(3)

Here Re and Rp are the radiuses at the equator and at the pole of the gravitationally distorted sphere, ρ is the density of the liquid and σ is the surface tension. The first factor in the right hand side of (3) is a correction for the gravitational shape distortion of the droplet, the second factor is the Rayleigh frequency and the third factor takes into account the boundary conditions at the supporting area. A characteristic factor describing the influence of the boundary conditions is the ratio (r/R)≤1. The radius of the circular region, where the drop is in touch with the supporting surface is r, and the radius of the droplet is R. One can avoid the non-spherical gravitational deformations of the droplet by choosing small enough radius, providing smaller than unity Bond 2 number B=ρgR /σ. However, one can not avoid the influence of the supporting element. Hence, we shall ignore the shape correction term and we can use the following proportionality relation:

f 0 ( R) ≈

σ r x ( ) ρR 3 R

(4)

x

The multiplier (r/R) is a correction term taking into account the boundary conditions at the supporting area. In [2] the power x has been evaluated to be equal to one for a sessile drop, whereas in the present work the value of x for pendant droplets is a free parameter, defined experimentally for different conditions. Evidently, the value of x is a measure for the influence of the boundary conditions upon the experimental value of the resonant frequency. We have shown that the value of x for spherical droplet depends on the type of the liquid, which makes impossible to calibrate the measurements. This difficulty can be overcome by using a hemispherical pendant droplet, for which the equivalence r=R is valid, x making the ratio (r/R) equal to unity for any x. Thus, the correction term for the boundary conditions in (4) is eliminated. Moreover, it is much easier to build a perfect hemispherical than a perfect spherical droplet. The oscillations of hemispherical droplets have been studied mainly theoretically [3], but to the best of our knowledge, no efforts for practical implementations have been made. In the present work we examine the resonant frequency of pendant, hemispherical supported droplets and its application to evaluate the surface tension in real time. The experimental set-up is shown schematically in fig.1. The droplet is formed with the help of a syringe 1, whereas the syringe piston is driven by a micrometric screw. To build a hemispherical droplet a Teflon cylinder has been used with the needle along its axis. One of the electrodes is the syringe needle 2 and the second electrode is an aluminum plate 3 below the needle. The droplet is illuminated by a lamp 4 and observed by a videocamera 5 connected to a computer 6, whereas the image contours are analyzed by a software program allowing a precise measurement of the droplet radius R and height H. The droplet is also illuminated by a He-Ne laser 7 and the oscillation amplitudes are detected by a photodiode 8, followed by a digital oscilloscope 9. The electrical signal from the oscilloscope, proportional to the oscillation amplitude, is fed to the computer for saving and analysis. The driving ac voltage is generated by a generator 10 and fed to an amplifier 11. A dc voltage is applied additionally to the amplifier by a bias voltage source 12.

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Fig. 1. Еxperimental set-up

We have assessed the error in defining the surface tension from the resonant frequency of a hemispherical pendant drop to be less then 2%. In this way we can use a hemispherical droplet of deionized water as a sensor of impurities or gas pressure, perturbing the interface water-air from the gas phase. The same approach can be used for perturbations from the liquid side i.e. influence of adsorbed surfactants, biopolymers or ions in the liquid. The influence of the gas pressure can be deduced by the Laplace law, showing that an increase of gas pressure decreases surface tension when the drop radius is kept constant: Рdrop - Pgas= 2σ /R

(5)

The adsorbed gas molecules or particles disturb the intermolecular interactions and also decrease the surface tension. Thus the total decrease of surface tension is due to the sum of the influence of gas pressure and of adsorption: ∆σ = ∆σvap + ∆σads

(6)

We have registered the normalized change of surface tension of water hemispherical droplet in time when gas is introduced in a closed transparent container by evaporation. The obtained dynamical processes ∆σ(t) are shown in fig.2 for three different volumes of the evaporated acetone 5µl, 10µl and 20µl.

268

Fig. 2: Dynamics of the influence of acetone vapors on the normalized surface tension of water hemispherical droplet.

Acetone is volatile and well miscible with water. The evaporation starts at t=0 and when the volatile liquid drop is evaporated a saturation of ∆σ occurs. Then the vapors are pumped out in moments denoted by arrows and fresh air is let in. A sharp increment of ∆σ to a new higher level is observed, defined by adsorption alone. Further slow changes can be attributed to acetone molecules leaving the interface by absorption in the liquid bulk or by evaporation back in the air. Analogous curves are obtained and discussed for chloroform, which is volatile but immiscible in water and for cigarette smoke, where gas pressure is missing and only deep level of continuous and stable adsorption is observed. References [1] Tankovsky N., Zografov N., Oscillations of a hanging liquid drop, driven by interfacial dielectric force, Z. Phys. Chem. 225, pp. 405-411, 2011. [2] Perez M. et al, Oscillation of liquid drops under gravity: Influence of shape on the resonant frequency, Europhys. Lett., 47(2), pp. 189-195,1999. [3] Lyubimov D.et al, Non-axisymmetric oscillations of a hemispherical drop, Fluuid Dynamics, 32(6), pp 851-862, 2004.

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ULTRASONIC STUDY OF BLOOD EVAPORATION Didier LAUX, Jean-Yves FERRANDIS, Fanny FAURE Université Montpellier II. IES. UMR CNRS 5214. 34095 MONTPELLIER E-mail: [email protected]

The main goal of this work is to analyze the mechanical behavior of a blood droplet during evaporation. Indeed, regarding the work of D.Brutin and co-workers [1], during blood evaporation a sol-gel transition occurs and can be identified on curves representing the evolution of mass versus time. It has been demonstrated that at the end of evaporation the crack pattern is depending of blood composition. It can be thought that this pattern is also determined by the viscoelastic properties of blood during its evaporation. In order to evaluate the viscoelastic behavior (shear moduli G’ and G’’) of a blood droplet we have used shear ultrasonic reflectometry. As describded in [2], it is essentially based on the measurement of the complex reflection coefficient at an interface between an elastic solid and a viscoelastic material. This means that, when an ultrasonic wave is reflected on such an interface, its amplitude decreases and the wave undergoes a phase shift. Experimentally, an ultrasonic transducer, made of a piezoelectric crystal and a delay line (DL) in silica or glass for instance, is used. As the ultrasonic attenuation is small in the delay line, multiple reflections are possible leading to the existence of many echoes. Then, the complex reflection coefficient, j R* = ro e , is calculated with the following relationships, where : Ai is the amplitude of the echo n° i , in the case of the interface (DL) /air, Bi , the amplitude for the interface (DL) / material, dti the time shift between these two echoes and f the operating frequency. Φ

USB / GPIB interface. All softwares were home made with Labview. After we took blood sample, a droplet of precise volume was put on the delay line. During evaporation we also recorder the mass with a Ohaus Explorer precision balance connected to the computer. For all the experiments realized the evolution of ro(t) was very characteristic and obtained with a good accuracy. At the beginning of the experiment, when the mass decreases very rapidly, ro does not evolve because blood behaves as a “light liquid” with small viscosity. For the high frequency used, ultrasonic waves cannot propagate into such a material. Then, when the evaporation is quite finished, the sol-gel transition occurs and blood droplet is like a visco-elastic material with higher G’ and G’’. For the ultrasonic signal it appears like a harder material and the waves can go from the delay line to the droplet under study. At the end of the process, it seems that when cracks appear under the droplet, ultrasonic signals cannot propagate and so, ro increases again. The following graph represents versus time the evolution of m and ro. Following the method proposed in [1] we have reported τD (dessication time) and τF =1.25 τD (gelation time) evaluated from the curve m(t).

1

⎛ B ⎞ i ro = ⎜⎜ i ⎟⎟ ⎝ A i ⎠ ⎛ Δt ⎞ Φ = −2πf ⎜ i ⎟ ⎝ i ⎠

(1) (2)

With R*, G* = G’ + j G’’ is calculated with (3) and (4) where ρ is the density of the studied material, ρDL the density of the delay line and VDL the shear ultrasonic velocity in the delay line.

G' = (ρ DL VDL )2

(r02 − 1) 2 − 4r02 sin 2 Φ ρ(2r0 cos Φ + 1 + r02 ) 2 2

G' ' = −4(ρDL VDL )

(r02 − 1)r0 sin Φ ρ(2r0 cos Φ + 1 + r02 ) 2

(3) Fig 1. Mass and Reflection coefficient versus time

(4)

For blood evaporation investigation, we used a 20 MHz Panametrics shear ultrasonic transducer excited with an Olympus pulse generator. All the signals were displayed on a Lecroy Wave Runner 334 and transmitted to a personal computer for analysis via an

For mechanical analysis, it was more difficult to assess Φ because the time shift is very small. That is the reason why in this communication we will only analyzed the evolution of ro(t). As Φ is very small and can be considered equal to zero, it is not possible to give a reliable value of G’’. On the other hand G’ can be expressed as :

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G' = (ρDL VDL )2

(r02 − 1) 2 ρ(1 + 2ro + r02 ) 2

The density ρ of blood during evaporation has been estimated with the knowledge of initial volume and mass versus time. G’ is represented in figure 2. Between

τF and τD

G’ is increasing a lot. Such an element is not surprising during a sol-gel transition.

Regarding these first results concerning ultrasonic investigation of blood droplets seems that such an approach could be because it is very complementary with analysis.

high frequency evaporation, it very interesting optical or m(t)

Indeed, when m(t) evolves a lot, ultrasonic parameters are not evolving. On the contrary, ultrasonic parameters are evolving a lot when the mass is constant at the end of the evaporation. Furthermore having the viscoelastic moduli gives a quantitative result which is certainly related to blood composition and could be useful for crack pattern interpretation at the end of the experiment. Works are now going on in order to improve the experimental bench to obtain G’’ with a good accuracy. The measurement of both G’ and G’’ will lead to a more precise estimation of the gelation time defined as G’=G’’. References [1] B. Sobac, D. Brutin. Structural and evaporative evolutions in desiccating sessile drops of blood. Physica l Review E, 84, 011603 (2011). [2] V.Cereser Camara, D.Laux. “High frequency shear ultrasonic properties of Water / Sorbitol solutions.” Ultrasonics. 50 (2010) 6-8.

Fig 2. Evolution of G’ versus time during evaporation

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