Height-resolved velocity measurement of the boundary flow during ...

Exp Fluids (2015) 56:76 DOI 10.1007/s00348-015-1944-4

RESEARCH ARTICLE

Height‑resolved velocity measurement of the boundary flow during liquid impact on dry and wetted solid substrates Philipp Erhard Frommhold1 · Robert Mettin1 · Claus‑Dieter Ohl2 

Received: 3 December 2014 / Revised: 13 March 2015 / Accepted: 14 March 2015 / Published online: 27 March 2015 © Springer-Verlag Berlin Heidelberg 2015

Abstract  The impact of a droplet onto a dry or wet surface leads to a rapid formation of a shear flow at the boundary. We present a novel method to experimentally resolve this flow in time at different heights above the solid. The radial flow field close to the substrate is reconstructed by evaluation of streak images of fluorescent tracer particles in the liquid. By using a microscope objective with a narrow depth of field, it is possible to scan through the flow in thin horizontal layers of 5 μm thickness. We focus on the flow close (≤40 μm) to the boundary during the impact of elongated drops with diameters of 0.3–0.4 mm and speeds in the range of 2–3 m s−1. The spatial resolution is obtained from several individual events of the repeatable impact process and varying the focal plane. Fluorescent streaks formed by the suspended particles are recorded with highspeed photography at up to 20,000 frames per second. The impact of water and of ethanol is investigated both on dry glass and on glass covered with a thin film of the same liquid. Results are given as spatio-temporal maps of radial flow velocity at different heights, and the maximum shear stress at the substrate is evaluated. The implications of the results are discussed with respect to cleaning applications. * Philipp Erhard Frommhold [email protected]‑goettingen.de Robert Mettin [email protected]‑goettingen.de Claus‑Dieter Ohl [email protected] 1

Christian Doppler Laboratory for Cavitation and Micro‑Erosion, Drittes Physikalisches Institut, Georg-August-University Göttingen, Göttingen, Germany

2

Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore





1 Introduction Worthington (1908) was the first one who captured and studied in-depth the astonishing details, complexity and aesthetic beauty of the impact of liquid drops using high-speed photography. More than a century later, drop impact is still an active research area, due to the often quite complicated flow phenomena, but also the importance in a wide range of processes and applications. Examples comprise rain noise (Pumphrey et al. 1989), erosion of material by high impact pressures and shock wave formation (Dear and Field 1988; Kennedy and Field 2000; Haller et al. 2002, 2003a, b), spray-cooling (Srikar et al. 2009), deposition of liquid on surfaces (van Dam and Clerc 2004) such as painting or printing, and many others. Many important aspects of drop impact have been investigated in the past decades, often with the help of the ever advancing techniques of high-speed photography and computational fluid dynamics. Topics include the impact morphology, such as droplet deformation and spreading (Rioboo et al. 2002; Roisman et al. 2002; Clanet et al. 2004; Roisman et al. 2009; Visser et al. 2012, 2015), fingering (Mehdizadeh et al. 2004; Thoroddsen and Sakakibara 1998), splashing (Yarin and Weiss 1995; Cossali et al. 1997; Xu et al. 2005; Mandre et al. 2009; Mani et al. 2010; Pan et al. 2010; Driscoll and Nagel 2011; Thoroddsen et al. 2011), or rebounds which are reviewed in (Rein 1993) and (Yarin 2006), sideways jetting (Weiss and Yarin 1999; Haller et al. 2002), impact onto a liquid film (Berberović et al. 2009; van Hinsberg et al. 2010; Thoraval et al. 2013) or the formation and evolution of a gas film between the impacting droplet and a solid target (de Ruiter et al. 2012; van der Veen et al. 2012).

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To illustrate that still a better understanding of the mechanisms and parameters of drop impact is desirable, we briefly motivate our experimental research. The repeated impact of drops from a fine spray is used for the cleaning of delicate solid surfaces, for example in the semiconductor industries (Kanno et al. 1997; Okorn-Schmidt et al. 2014). These sprays utilize droplets ranging from a few microns up to slightly more than 100 μm in diameter and impacting at velocities of 1–100 m s−1 or more (Watanabe et al. 2009; Frommhold et al. 2014). At impact, high-pressure regions are formed due to stagnation-point pressure and the water-hammer pressure (Joukowsky 1900), while strong shear stress is created by the spreading droplet front. For semiconductor cleaning, transient pressure peaks appear unfavourable as they may lead to structural damage of the surfaces, but a fast boundary layer flow seems useful. At sufficient shear strength, this flow may support the removal of surface attached particulate contamination (Andreas et al. 2009; Xu et al. 2009; Okorn-Schmidt et al. 2014). Such applications need a deeper knowledge of the flow field to optimize the cleaning while reducing the damage to fragile structures on the substrates. As the dimensions of integrated circuits become smaller and smaller, the size of contaminating particles to be removed shrinks accordingly. To affect these smaller particles attached to the substrate, higher shear stresses in the boundary layer flow are needed, but too high impact pressures should be avoided at the same time to stay away from damage (Kanno et al. 1997). For the task of optimizing boundary layer shear from spray drop impact, experimental measurements of flow velocities and shear at the substrate for small fast drops in the indicated spray regime are needed. From experiments, only little is known about the actual velocity field within the bulk flow during drop impact (Smith and Bertola 2011; Castrejón et al. 2011; Erkan and Okamoto 2014). Our study tries to contribute to the understanding of how exactly the vertically impacting liquid on a flat solid spreads sideways from the stagnation point, and to quantify the shear stresses at the substrate. An advanced experimental measurement technique provides sufficient resolution in space and time to investigate drops of about 0.3–0.4 mm head diameter and 2–3 m s−1 velocity. Due to technical details of the preparation method of the drops, partly elongated (though highly reproducible) drop shapes appeared at impact. Therefore, we sometimes use the notion of “liquid impact” instead of “drop impact”. The latter typically refers to quite spherical shapes. Still, in the first part of the impact flow, the scenario is identical to the exactly spherical drop case, whereas in the later phase the stretched drop shape leads to extended liquid inflow during spreading. After impact and spreading, the inflow stops because of the finite drop volume, and a receding flow of the liquid is observed due to surface tension. The

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highest shear stresses at the substrate are expected during spreading, and this period is therefore in the focus of our investigation. A detailed presentation of the experimental method and set-up is given in Sect. 2. In Sect. 3, we present the measured velocity fields of the four impact cases of dry and wet (thin liquid film) substrate, and for water and ethanol. Shear stresses at the substrate surface are derived from the velocities. A discussion of the results and of implications for cleaning methods employing drops or sprays follows in Sect. 4.

2 Experiment The experimental challenge consists in studying the flow field close to the solid boundary at sufficient temporal and spatial resolution [see, e.g. Lindken et al. (2009)]. Our approach is commonly termed particle streak photography (e.g. Dimotakis et al. 1981). Streak images of transported fluorescent tracer particles in the drop (and the liquid film, if present) are recorded from the bottom through a glass slide, upon which the droplet impacts from above. The fluorescent particles deliver high contrast without specular reflections from gas-liquid interfaces. Sufficient magnification is achieved by an inverted microscope, where a large numerical aperture (NA) objective reduces the depth of focus [350 μm) build up slightly retarded. In the liquid layer directly at the substrate, there is no motion of particles detectable at all. Above that layer, the radial fluid velocity increases over time. As a further difference to the water case, a kind of two-step velocity

3.4 Ethanol impact onto ethanol film on glass For the wet impact of ethanol, we prepared a drop with front diameter Dhead ≈ 0.3 mm and velocity U = 2.7 m s−1 hitting onto a layer from a predeposited 20 µl droplet. Due to the smaller contact angle of ethanol,

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Fig. 11  Ethanol impact onto ethanol film on glass. Right Velocity profiles for seven altitudes above the substrate. Left High-speed recording at 20 kfps for illustration of the drop morphology at the instants of the velocity profiles. In (a), the white scale bar is 200 μm and the white rectangle indicates the data range of the right column. The inset in (a) depicts the lower droplet interface shape just before the impact. The real times t with respect to the impact are indicated in each picture (non-dimensional times t ∗ are given in brackets). A down falling satellite droplet appears in the top of (d). Red squares label the first measurement plane, referred to as z = 0 µm, where particles may be in contact with the substrate, and therefore, the measured velocity might deviate from the actual speed of the liquid

profile builds up with a faster radial spreading at larger heights, floating on top of a moderate velocity layer (up to 20 μm). This structure remains until approximately 0.5 ms (t ∗ = 4.50) after impact. Then, the faster spreading decays to similar outward velocities as the lower layers which remain almost unchanged. Around 0.8 ms (t ∗ = 7.20) a slow and mostly laminar receding flow occurs, which is not shown in the figures.

In contrast to the impact onto the water film, the observed maximum velocities are almost one order of magnitude larger for ethanol (although there was no detectable motion in the first layer, which might be caused by particle adhesion to the substrate). Apart from the slightly higher impact velocity, this can be explained by the fact that the film thickness was about three times lower in the case of ethanol impact (due to the smaller contact angle, see

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Exp Fluids (2015) 56:76

Fig. 12  Ethanol impact onto ethanol film on glass. Evolution of the colour-scale-coded radial velocity magnitude v in dependence of time t and non-dimensional time t ∗ versus radial distance from centre of impact r. Four horizontal layers are presented (height above solid is indicated). Note the different colour-scale bars in each plane

Fig. 3). Hence, the film liquid mass between impact region and solid is less, and the inertia dominated impact transfers more momentum to the radial flow close to the substrate. The maximum spreading velocity is observed for alcohol at z = 30 µm (the uppermost measurement plane) and around t = 0.3 ms (t ∗ = 2.70). For water, these values are z = 20 µm and t = 0.6 ms (t ∗ = 4.36). This shows a significant retardation of the maximum velocity, possibly also due to the thicker water film. 3.5 Evaluation of the maximum occurring wall shear stress The shear stress at the solid substrate is defined by τ = η · ∂ur /∂z(z=0) with the dynamic viscosity η of the liquid. It can be approximated, under assumption of the no-slip boundary condition at the solid, by the finite difference quotient τ ≈ η · ur (z)/z with ur (z) being the observed radial velocity at small height z. Therefore, spatio-temporal maps of the shear stress at the substrate can be immediately obtained from the velocity maps of the lowest liquid layers, i.e. Figs. 6, 8, 10 and 12a, b. For the first layer (directly at the substrate), a z of 2.05 µm is assumed, and for the second layer the indicated height of observation of 5 or 10 µm (only for water impact onto water film). The maximum shear stresses τmax occurring over the whole impact have been calculated accordingly from the maximum captured radial velocities ur, max within the first two layers. The values are given in Table 1. As stated before, the measurements of the velocities (especially close to the substrate

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and for larger vertical velocity components), as well as the derived wall shear stresses, have to be considered as lower estimates.

4 Discussion The main motivation for the spatio-temporal resolved flow measurements is the quantification of shear stresses at a solid substrate during liquid impact. The results show, for the four cases investigated, that the maximum stresses occur on a ring around the impact centre at radial distances slightly larger than the drop front radius. For the impact onto a dry substrate, the instant of maximum shear almost directly follows the passing of the spreading liquid front and occurs with the according time delay in relation to the moment of impact (here about 0.2–0.3 ms). These findings essentially agree with reports in the literature for millimetre-sized drops (Smith and Bertola 2011; Erkan and Okamoto 2014). For impact onto a liquid film, the velocity field at the substrate builds up much faster and also at larger radial distances, as the impact pressure is mediated with the speed of sound and no liquid has to spread first. Still, a delay (0.2–0.6 ms) is observed until the maximum shear stress is reached. However, the maximum is less pronounced, and the velocity field at the substrate appears more uniform than in the dry impact cases. In any case, the absolute values of the shear maxima for impact on liquid film are significantly lower than for the dry case: We observed a decrease

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Exp Fluids (2015) 56:76 Table 1  Maximum wall shear stress τmax for the four cases: water impact onto dry glass (w. d.), ethanol impact onto dry glass (e. d.), water impact onto water film on glass (w. f.), and ethanol impact U in m/s

Dhead in μm

Re

We

Oh

onto ethanol film on glass (e. f.). For the shear stress values of the first layer, a flow height of z = 2.05 µm above the substrate has been assumed

First layer τmax in

Second layer

N/m2

r in μm

t ∗ (t

in ms)

w. d. e. d. w. f.

1.9 2.5 2.4

360 300 330

684 545 792

18 68 26

0.006 0.015 0.006

224 203 29

225 175 75

1.56 (0.3) 1.67 (0.2) 5.81 (0.8)

e. f.

2.7

300

589

80

0.015

–

–

–

τmax in N/m2

r in μm

t ∗ (t in ms)

342 114 17

175 275 75

1.56 (0.3) 2.50 (0.3) 5.09 (0.7)

81

325

3.60 (0.4)

This corresponds to the mean of minimum distance of particle centre (z = 1.6 µm) and maximum height within focal depth when focused on the z = 0 µm plane (i.e. z = 2.50 µm). The derived numbers have to be treated as lower bounds, since contact interactions between particles and substrate cannot be excluded. The second layer corresponds to a z = 5 µm and only for w. f. to z = 10 µm)

by a factor of ≈8–10 for water and of ≈2–3 for ethanol, depending on the chosen measurement layer (directly at the substrate or first measurement plane in the bulk at 5 μm or 5 μm height). Surely, one expects a dependence of the occurring shear maxima on the film thickness h. An evaluation of our data with respect to this dependence is difficult, as it is very sparse with only two realized values of h (1 mm for water and 0.3 mm for ethanol). Additionally, the drop impact parameters have not been exactly the same. More data would be needed for a sound statement. A comparison of impact of water with impact of ethanol on dry glass shows the following: Both liquids spread with a characteristic advancing front or lobe directly at the substrate. An indentation of the spreading front occurs accordingly above, at about 10–15 μm height. Due to the larger contact angle, the liquid front of the water appears convex with respect to the substrate, whereas the alcohol has a concave front. The maximum shear stresses exerted by the water drop impact are slightly higher than for ethanol. Finally, some remarks on cleaning with droplet impact can be made. As expected within the scope of the experiments, faster impacts lead to higher shear stresses at the substrate. The maximum shear occurs in a ring around the centre; therefore, multiple impacts might be necessary to sufficiently clean an area. As a consequence, this would lead to a liquid film on the substrate, which can damp the flow by orders of magnitude, depending on its thickness. However, this film can be favourable for other reasons (e.g. attenuation of high transient pressures or shocks). To control film thickness, a continuous spinning of the substrate might be employed. Also low surface tension fluids such as ethanol support thinner films, as seen in the experiments.

5 Conclusion We have demonstrated the feasibility of spatio-temporally resolved radial velocity measurements in

impacting drops of approximately 2–3 m s −1 speed and with about 350 μm front diameter. A variant of μ-PTV has been employed where streaks of fluorescent tracer particles are evaluated in the narrow focal plane of a microscope. Vertical resolution of 5 µm and high-speed recordings up to 20 kfps allowed for the measurement of velocity gradients and thus shear stresses at a flat glass substrate over the impact and spreading period of the drops. Water and ethanol drops were investigated for dry and wetted target, and we could measure maximum wall shear stresses of order 100–230 N m −2 during the dry impact processes, as well as their locations on rings around the impact point. A liquid film of dimensionless height h/Dhead ≈ 3 (water) has reduced the maximum shear stress about one order of magnitude, while a film of h/Dhead ≈ 1 (ethanol) reduced the maximum wall shear only by a factor of two to three. Our work can be seen as an extension of previous flowfield measurements done by Smith and Bertola (2011), Castrejón et al. (2011) and very recently by Erkan and Okamoto (2014) where the velocities were averaged over the vertical position (i.e. height). By our method, the spreading flow of impacting drops can be evaluated in more detail and in particular the shear stress at the substrate is accessible. Such measurements of shear flow near the boundary are crucial for applications such as surface modifications or cleaning by controlled drop impact. The scaling of shear stresses with impact and liquid parameters has to be investigated in the future, as our data are too sparse. Other future work should address the effect of film thickness heights. Acknowledgments  We would like to thank W. Lauterborn for valuable comments regarding the manuscript. The financial support by the Austrian Federal Ministry of Economy, Family and Youth and the Austrian National Foundation for Research, Technology and Development is gratefully acknowledged as is the support from Lam Research AG. Special thanks go to Chan Chon U for inspiring discussions.

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Appendix For estimation of the depth of field δz we used equation (4) from Meinhart et al. (1999)

δz =

ne n + 2 NA M NA

with index of refraction n = 1, fluorescence wavelength  = 612 nm, numerical aperture NA = 0.725, smallest resolvable distance of the image detector e = 20 µm, and magnification M = 20. This results in a value of 2.4 µm for the depth of field.

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