Backward flow in a surface tension driven

IOP PUBLISHING

JOURNAL OF MICROMECHANICS AND MICROENGINEERING

doi:10.1088/0960-1317/18/8/087002

J. Micromech. Microeng. 18 (2008) 087002 (5pp)

NOTE

Backward flow in a surface tension driven micropump Jongil Ju1,4 , Joong Yull Park1,4 , Kyung Chun Kim2, Hyundong Kim2, Erwin Berthier3, David J Beebe3 and Sang-Hoon Lee1 1

Department of Biomedical Engineering, College of Health Science, Korea University, Jeongneung-dong, Seongbuk-gu, Seoul 136-703, Republic of Korea 2 Department of Mechanical Engineering, Pusan National University, Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of Korea 3 Department of Biomedical Engineering, University of Wisconsin—Madison, Madison, WI 53706, USA E-mail: [email protected]

Received 10 April 2008, in final form 10 June 2008 Published 4 July 2008 Online at stacks.iop.org/JMM/18/087002 Abstract A surface tension driven micropump harnessing the pressure difference generated by drops of different curvature radii proves to be a simple and attractive passive method to drive fluid flow in microdevices. Here we observed the appearance of backward flow when the initial sizes of the droplets at the inlet and outlet ports are similar. To explain this phenomenon several hypotheses have been investigated. Consideration of the inertia of the fluid in the channel revealed that it alone is insufficient to explain the observed backward flow. We discovered that rotational flow inside the outlet droplet could be a source of inertia, explaining the generation of the backward flow. In addition, we have experimentally determined that the ratio of the volumes of the initial outlet drop and inlet drop correlates with the occurrence of the backward flow. M Multimedia enhancements and supplementary data are available from stacks.iop.org/JMM/18/087002 (Some figures in this article are in colour only in the electronic version)

a surface tension driven micropump is a simple and versatile passive pumping technique. The method utilizes the difference in pressure generated by the difference in curvature between a smaller drop placed at the inlet of a microchannel and a larger droplet placed at the outlet of the channel (figure 1). The flow rate can be controlled by changing the volume of droplets placed at the inlet and outlet ports [9, 10]. A phenomenon causing spontaneous reversal of the direction of the flow, or backward flow, at the end of the pumping process has been occasionally observed in our experiments and has not been reported elsewhere. This phenomenon can prevent or reduce the reliable and controllable operation of a surface tension driven micropump. In this note we investigated the backward flow through experimental and mathematical analysis, and propose ranges

1. Introduction The handling of very small amounts of fluid is of importance for high throughput screening, point-of-care diagnostics, biosensing, chemical synthesis and cellular research [1–4]. Many silicon or polymer based micro pumps and valves have been developed for this purpose [5]. However, the most common drawbacks shared by these approaches are the need for peripheral devices and external energy sources as well as excessive dead volume in the connection networks. To minimize such limitations, passive micropumping methods have been developed harnessing physical and chemical properties of fluids such as evaporation [6, 7], permeation [8], surface tension [9, 10] and osmosis [11]. Among them, 4

These two authors contributed equally to this work.

0960-1317/08/087002+05$30.00

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J. Micromech. Microeng. 18 (2008) 087002

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Figure 1. (a) Schematic of a surface tension driven micropump. θ is the contact angle, H is the height of droplet, r is the radius of droplet and a is the drop contact radius. The difference in pressure generated by the surface tension of each droplet is the source of driving force. Geometrical notions for the droplet are provided in the inset. (b) The flow direction is determined by the radius balance of the droplets basically; the bold arrows in the figures denote the flow direction. When ri < ro, the forward flow pumping is established (inset A). However, ri can become greater ro due to the inertial force of the flow causing the backward flow phenomenon (inset B). A similar effect can occur again and the flow switched back to forward motion (inset C).

on the inlet and outlet droplet volumes for operating the micropump to avoid backward flow.

2. Modeling study and experimental observation 2.1. Mathematical modeling The surface tension driven micropump (figure 1(a)) is modeled using the Young–Laplace relationship linking the curvature of the fluid interface and the pressure generated to determine the pressure drop between input and output drops [9, 10]. Thus we write 
1 1 Pstatic = Pi − Po = 2γ (1) − ri ro where Pstatic is the pressure drop between the inlet and outlet, Pi between the inlet and surrounding air, Po between the outlet and surrounding air, γ is the surface tension coefficient, and ri and ro are the radii of the inlet and outlet droplets, respectively. However, this model neglects dynamic effects. We observed that a backward flow phenomenon sometimes occurred at the end of the pumping process (figure 2 and the movie clip of backward flow recorded by particle image velocimetry (PIV) available at stacks.iop.org/JMM/18/087002) when the initial size of the inlet droplet is similar to that of the outlet droplet. Therefore, we hypothesized that the mechanism of backward flow occurred in three phases (figure 1(b)). Initially, the radius of the input drop is smaller than the output drop (ri < ro) and the direction of flow is forward (from inlet to outlet), causing

Figure 2. Experimental data (error bar: standard deviation (SD)) were gained from micro PIV (n = 3). The volume of the inlet-drop is 20 µL and that of the outlet-drop is 40 µL for this test. A backward flow phenomenon occurs between times t = 50 s and 150 s. The predicted flow rate using the two-droplet model is plotted with and without contributions of inertia in the channel (solid line and dashed line, respectively).

the volume of the inlet drop to decrease. Theoretically, the flow stops when ri becomes identical to ro as the pressure difference is cancelled (equation (1)). If inertial forces are exerted, the forward flow may continue and ri becomes bigger than ro. Secondly, the inertial effects will dampen, resulting in 2

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a new imbalance of pressures, with the outlet pressure being higher than the inlet, generating a backward flow. Finally, a similar effect can occur again and the flow switched back to forward motion. Eventually, all flow will cease as inertial forces disappear and the pressures are balanced. In this assumption, the key point is determining the source of the inertial force, usually neglected in microchannels, causing the system to flow pass the pressure balance. Thus, we have investigated, through an analytical study, the importance of the inertial force generated by the fluid in the microchannel and whether it is sufficient to cause the effect observed. A mathematical analysis of the operation of a surface tension driven pump was first proposed by Berthier and Beebe [10]. However, the model neglects variation in the pressure at the outlet drop; thus it does not accurately describe cases where the volume of the output drop varies significantly— for example, when the initial volumes of the two droplets at the inlet and outlet ports have a similar size. We established a two-droplet model including the inertial force of flow in the microchannel (see the supplementary data available at stacks.iop.org/JMM/18/087002 for detailed derivation of the two-droplet model, including the height of the drops and velocity of the flow): 
ρL dQ 1 1 + 2 (2) − P = Pstatic + Pch = 2γ ri ro A dt where Pstatic is the static pressure drop mentioned before, Pch is the pressure drop linked to inertia in the channel, ρ is the density, L is the length of the channel, A is the crosssectional area of the channel and Q is the flow rate in the channel.

Figure 3. (a) Observation of the rotational flow in the outlet drop using a goniometer. Each picture was taken at 1 s intervals, approximately. The scale bar is 500 µm. (b) We found that there is rather stable flow in the inlet droplet and rotating flow in the outlet droplet. The rotational fluid exerts non-negligible inertial force that could induce flow to continue to pass the static pressure balance (ri > ro).

2.2. Experimental observation using micro PIV fluid in the microchannel is not responsible for the observed effect. In fact, quantitative analysis revealed that Pch is three orders of magnitude smaller than Pstatic when compared with the static pressure drop for t > 80 s in figure 2. The discrepancy between the modeling profiles and the experimental results was due to a practical reason that a simultaneous and centered placement of two droplets at inlet and outlet ports was not practically achieved in the experiments. In addition, non-ideal features, such as surface roughness, evaporation effect, nonideal channel geometry and microparticles’ interaction should be considered as additional causes of the discrepancy.

The microchips having dimensions of 0.2 (width) × 0.4 (height) × 15 (length) mm were fabricated using poly(dimethylsiloxane) (PDMS) (Sylgard 184 silicone, Dow Corning, USA). For the operation of the pumping system, the microchannel was filled with DI (deionized) water by using a micropipette. Then a droplet of DI water was placed on the outlet port, and the working fluid was dropped on the inlet port; the fluid was slowly introduced in the microchannel driven by surface tension force. The average velocity of the flow in the microchannel was recorded using micro-PIV which consisted of a 10 bit high speed CCD camera (pco.1200hs, PCO AG, Germany) and a microscope (BX51, Olympus, Japan). A mixture of DI water and fluorescent particles (diameter: 1 µm; Molecular Probes Inc., USA) was used as the working fluid for the micro PIV. Based on the low diffusivity (5 × 10−10 m2 s−1) [12] of the fluorescent particles, we assumed, in this study, that microparticle motion and its effects on the flow are negligible. The time resolution of the PIV was 1 ms, and the measurements were carried out at 0.5 s intervals. The calculated velocity profile of the flow in the channel including or excluding inertia shows a similar pattern to experimental measures using PIV (figure 2). However, the backward flow occurring in the experiment was not predicted in the model. This indicates that the inertial force of the

2.3. Inertia of rotational flow in a droplet Observation of the output droplet using a goniometer revealed another possible source of inertia. The fluid entering the output droplet during the flow creates a rotational motion which can store inertia (figures 3(a) and (b)) and cause an increase of pressure according to the Navier–Stokes equation. Note that the flow in the inlet droplet is relatively stable (figure 3(b)). This suggests adding a term to equation (2) to account for the pressure variation due to the rotational flow in the outlet drop: P = Pstatic + Pch + Pdrop

(3)

where Pdrop represents the force generated by the inertial force of rotating flow in the droplet. An analytical solution 3

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Figure 5. The data points when the backward flow was observed were collected (dots: mean value ± SD; dashed line: linear fit). For prevention of backward flow, the volume ratio of the two droplets should be in the light gray area.

conditions (30, 50 and 70% at a room temperature of 20 ◦ C). Constant humidity and temperature was achieved using a controlled environment acrylic box. A 20 µL droplet was used at the inlet port and a 30 µL droplet at the outlet port. Neglecting experimental aberrations principally due to inaccurate placement of the droplets or fabrication issues, backward flow was observed in all three humidity conditions with the same intensity. This result allowed us to rule out evaporation as a source for the backward flow as the intensity of the flow should increase for lower humidities if it was related to evaporation. Additionally, we evaluated the radius change of droplets; two droplets (20 and 40 µL) were placed on a flat surface for 2 min in low relative humidity (20%) (figure 4(a)). The radius changes were very small (2%), thus implying that the evaporation effect is negligible in our system (figure 4(b)).

Figure 4. (a) Droplets (20 and 40 µL) were placed on a flat surface for 2 min. (b) The original radius of a droplet reduced in 2% by evaporation because of low relative humidity (about 20%); the inset shows the evaluation method of the evaporation rate.

for this term proves difficult to write as it involves strongly nonlinear behavior of fluids. To evaluate the soundness of this hypothesis, a numerical two-dimensional simulation of the flow field in a droplet was conducted using CFD-ACE+Ver. 2006 (CFD Research Corporation, USA). An axisymmetric geometry was constructed; the total grid cell number was about 3000. A droplet of radius 2 mm (about 10 µL) is placed on a surface containing a 300 µm radius port with a contact angle of 90◦ . The surface tension of a water droplet in the air (0.0725 N m−1) was considered in the simulation. Flow of liquid through the port into the drop is added with a velocity of 1 mm s−1, similar to what is observed experimentally. As a result, rotational flow was observed even in a droplet presenting a low Reynolds number (Re is of the order of 0.01–0.1; the velocity is 0.1–1 mm s−1; the characteristic length is 2 mm) (see figure S1 in the supplementary data available at stacks.iop.org/JMM/18/087002). This confirmed the existence of rotational flow in droplets with radii down to order of 1 mm. Evaporation has been used to generate flow from the output drop to the inlet port after the pressure balance is reached [7, 13]. Evaporation was therefore considered as another possible source of the backward flow. A series of experiments to test the effect of evaporation on the setup were conducted at three different relative humidity

2.4. Prevention of backward flow We discovered that backward flow does not occur for all input/output droplet conditions. A series of experiments were conducted to map the values of R (R = Vout/Vin, ratio of initial output over input droplet volumes) for which a backward flow exists. For three different volumes of the inlet drop (10, 15 and 20 µL), a range of volumes for the outlet drop was chosen to screen values of R varying from 2.0 to 3.5 in steps of 0.1. In the 48 cases explored, backward flow was observed for values of R less than 2.3 to 2.6 but never for values of R above 3 (figure 5). Therefore, for sensitive applications, it is recommended to operate the surface tension micropump with inlet droplets at least three times smaller in volume than the output droplet, in order to prevent backward flow generation. A possible case where backward flow can be problematic occurs when wanting to create slow flows using this passive pumping technique. To obtain a slower flow rate in the channel, the surface tension pressure drop (equation (1)) should be as small as possible, which means that the radii of the drops and also their volumes should be similar. A smaller volume ratio implies the generation of backflow. The guidelines proposed 4

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here enable stable and reproducible operation for slow flow applications using this surface tension driven pumping system.

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3. Summary and conclusion In this note, a spontaneous reversal of the flow direction, or backward flow, in a surface tension driven micropump system was observed and reported. By ruling out different inertia in the channel and evaporation, rotational flow occurring in the outlet drop is hypothesized as a possible cause of the backward flow. Numerical two-dimensional simulation and experimental observation support this hypothesis. Finally, the ratio of the volumes of the inlet drop and outlet drop was identified as a parameter that correlated with the appearance of the backward flow, and it was found that for values of this parameter above 3 no backward flow occurred. Further study is required to fully understand the source of the backward flow, but our observations and modeling suggest that rotational flows in the output drop may contribute to this phenomenon. These results also suggest that other parameters, such as the output drop radius or volume, may be more closely linked to the backward flow and thus should be studied further. That is, rotational inertia effects are likely to be larger at the larger volumes used in this study as compared to the smaller volumes typically used with passive pumping. Still the results presented here provide useful guidelines to avoid backward flow, and suggest that rotational flows are of interest.

Acknowledgment This study was supported by a grant from the Korea Health 21 R&D Project, Ministry of Health & Welfare, Republic of Korea (0405-ER01-0304-0001).

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