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Hydrodynamic Flows in Electrowetting Sung Hee Ko, Horim Lee, and Kwan Hyoung Kang* Department of Mechanical Engineering, Pohang UniVersity of Science and Technology, San 31, Hyoja-dong, Pohang 790-784, South Korea ReceiVed August 9, 2007. In Final Form: October 15, 2007 Hydrodynamic flows are generated inside a droplet in electrowetting when an ac voltage is applied. To discover the characteristics and origin of the flows, we investigated the flow pattern for a sessile droplet for various needleelectrode positions, electrolyte concentrations, and applied electrical frequencies. Two distinct types of flows were observed under current experimental conditions. In the typical experimental condition, a quite fast flow appears in the low-frequency range of about 10 Hz to 15 kHz. A different type of flow is observed in the high-frequency range of about 35 to 256 kHz, but this frequency range depends significantly on the electrolyte concentration. Most typically, the flow directions are different for the two flows. A shape oscillation of a droplet was observed in the low-frequency range by a high-speed camera. The flow in the low-frequency range is insensitive to the conductivity of the solution and may be caused by the interfacial oscillation of the droplet. The flow at high frequency is very sensitive to the conductivity of the solution and electrode position, so the high-frequency flow is believed to be caused by some electrohydrodynamic effect.
1. Introduction The change of contact angle in electrowetting is basically induced by the electrical stress concentrated at the three-phase contact line (TCL).1,2 If an ac field is used instead of a dc field, interestingly, some distinctive features are observed. First, the contact-angle saturation occurs at a smaller contact angle and at a higher voltage.3,4 Second, edge instability takes place; i.e., tiny satellite droplets are disintegrated from the mother droplet.3,5,6 The edge instability occurs only in the ac case and especially at very low electrolyte concentrations.3,7 Third, the ac case has less contact-angle hysteresis, which may be why the ac field is preferred in some applications.8 Those phenomena observed in ac electrowetting have not yet been fully explained. We have been pursuing a reliable explanation for those intriguing phenomena. Recently, several groups have reported that hydrodynamic flows exist in electrowetting, which is not widely known yet.9-12 Ko et al.9 found hydrodynamic flows inside a sessile droplet with a needle electrode while they were investigating the effect of particle suspension on contact angle in ac electrowetting. Miraghaie et al.10 showed for a sessile droplet in electrowetting that mixing is significantly enhanced when ac signals are applied ranging from 30 to 300 Hz. They observed an oscillation of interface and concluded that the mixing enhancement might have resulted from the droplet oscillation. Hu et al.11 observed vortices * To whom correspondence should be addressed. Phone: +82-54-2792187. Fax: +82-54-279-3199. E-mail:
[email protected]. (1) Kang, K. H.; Kang, I. S.; Lee, C. M. Langmuir 2003, 19, 5407-5412. (2) Kang, K. H. Langmuir 2002, 18, 10318-10322. (3) Quilliet, C.; Berge, B. Curr. Opin. Colloid Interface Sci. 2001, 6, 34-39. (4) Blake, T. D.; Clarke, A.; Stattersfield, E. H. Langmuir 2000, 16, 29282935. (5) Vallet, M.; Berge, B.; Vovelle, L. Polymer 1996, 37, 2465-2470. (6) Vallet, M.; Vallade, M.; Berge, B. Eur. Phys. J. 1999, B11, 583-591. (7) Mugele, F.; Baret, J. C. J. Phys.: Condens. Matter 2005, 17, R705-R774. (8) Berge, B.; Peseux, J. Eur. Phys. J. 2000, E3, 159-163. (9) Ko, S. H.; Oh, J. M.; Kang, K. H. Fourth Natl. Congress Fluids Eng., Kyungju, Korea 2006, 379-382. (10) Miraghaie, R.; Sterling, J. D.; Nadim, A. NSTI-Nanotech 2006, 2006, 2, 610–613. (11) Hu, H.-C.; Lin, M.-Y.; Yu, C.-S.; Hu, Y.-C. 14th Int. Conf. Solid-State Sens., Actuators Microsyst. (Transducers’07), Lyon, France 2007, 1869-1872. (12) Baret, J.-C.; Decre´, M. M. J.; Mugele, F. Langmuir 2007, 23, 51735179.
and subsequent mixing enhancement for a liquid bridge formed between two planar insulator-covered electrodes. Mugele and co-workers12 induced a self-excited periodic oscillation of a sessile droplet in the frequency range of 20-100 Hz. They stated that a net transport of fluid is generated by the oscillation, which contributes to the mixing enhancement. The oscillation of droplet in Mugele et al. is not an inherent one; instead, it is induced by the repeated detaching and attaching of the droplet to the needle electrode. Flows in electrowetting have very important consequences. They can be beneficially utilized to enhance mixing of fluids9-12 and could be used as a countermeasure against the troublesome adsorption of DNAs and polymers13,14 in practical biochemical applications of electrowetting. Moreover, our preliminary experiment shows that the flow has a considerable effect on contact angle too. However, the details and origin of such hydrodynamic flows are still not understood very well. It is even unclear whether the flows are truly generated purely by the oscillation of the interface, or in combination with electrohydrodynamic effects. The present investigation is focused on characterizing the general features of the hydrodynamic flows to help determine the origin of the flows. For this, the sessile droplet with a needle electrode was studied; this is a rather simple and one of the most typical configurations in electrowetting. Specifically, the effects of electrode position, liquid conductivity, and frequency were investigated. Our experimental results reveal that two distinctive flow patterns exist, which are prevalent in low- and high-frequency regions, respectively. Observation with a high-speed camera showed a shape oscillation of a droplet in the low-frequency range. The oscillation of interface seems to be induced by the oscillatory electrical force acting on the TCL. A numerical analysis of electric field was also carried out to investigate any correlation between the electric field inside a droplet and the observed flows. The results of the present investigation provide useful information for determining the origin of the two types of flows. (13) Srinivasan, V.; Pamula, V.; Pollack, M.; Fair, R. B. IEEE Conf. Micro Electro Mech. Syst. (MEMS 2003), Kyoto, Japan 2003, 327-330. (14) Yoon, J.-Y.; Garrell, R. L. Anal. Chem. 2003, 75, 5097-5102.
10.1021/la702455t CCC: $40.75 © 2008 American Chemical Society Published on Web 01/05/2008
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Figure 1. Schematic diagram of experiment setup.
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Figure 2. Contact angle of a sessile droplet. The rectangular and the circular symbols correspond to the case of dc and f ) 10 kHz, respectively. The solid line represents the Lippmann-Young equation.
2. Experimental Section The conventional experimental setup for electrowetting was employed, as illustrated in Figure 1. The base material of the substrate was ITO-coated glass having a thickness of 0.7 mm. A Parylene-C layer of 5 µm thickness was deposited on the electrode surface as an insulating layer. On top of that, a Teflon AF1600 layer of about 100 nm thickness was spin-coated to make the surface hydrophobic. An aqueous NaCl droplet of 5 µL (the base radius of which is about 1 mm) was placed with a micropipette on the substrate. Most experiments were conducted at a NaCl concentration (c) of 10-3 M, which corresponds to an electrical conductivity of 1.3 × 10-2 S/m. The static contact angle of a water droplet on the coated surface was about 117° under standard atmospheric conditions. The contact angle of a droplet is measured by a goniometer (DSA 100, Kruss). The temperature and the relative humidity were kept in the range of 25 ( 0.5 °C and 45% ( 5%, respectively. An electrical signal was generated by a function generator (33220A, Agilent) and was amplified 100× by a voltage amplifier (A800, FLC Electronics). The frequency was varied from dc to 256 kHz, and the applied voltage was increased up to 200 V in rootmean-square (rms) value. All voltages in this paper are rms values. To visualize the flow in a cross section of a droplet, a sheet of laser beam was generated (see Figure 1). The laser beam generated by an Nd:Yag laser (LGL200, AIXIZ), which has the wavelength of 532 nm, was expanded by a beam expander and then focused on the center plane of the droplet by a cylindrical lens. The thickness of the laser sheet was on the order of 0.2 mm. The fluorescent polystyrene particles having a nominal diameter of 2 µm and density of 1.05 g/cm3 (Nile Red F8825, Molecular Probes) were used as tracer particles. A CCD camera (Infinity2-2M, Lumenera) having a 1280 × 1024 pixel array was used to capture the particle images. We attached a long distance zoom lens (7× precision zoom lens, Edmund) to the CCD camera. According to the specification of the zoom lens, the depth of focus of the zoom lens was about 1 mm. Actually, images were a little distorted by the lens effect of the droplets themselves,15 so the velocity is rather amplified in the center of the droplet.
3. Results and Discussion 3.1. General Flow Patterns. Most experiments were performed at an rms voltage (Vrms) of 80 V and NaCl concentration (c) of 10-3 M. Figure 2 shows the dependence of contact angle on the rms voltage for c ) 10-3 M. The contact angle is measured for the two cases of dc and f ) 10 kHz. The solid curve represents the Lippmann-Young equation,1-8 which is fitted to the dc case. Figure 2 shows that the voltage chosen here (80 V) corresponds to the classical regime where the cosine of the contact angle is a quadratic function of the voltage for which electrowetting is modeled. On the other hand, the contact angle tends to increase (15) Kang, K. H.; Lee, S. J.; Lee, C. M.; Kang, I. S. Meas. Sci. Technol. 2004, 15, 1104-1112.
Figure 3. Frequency dependence of flow pattern for Vrms ) 80 V and c ) 10-3 M. The exposure time is 120 ms for (a) and 200 ms for (b) and (c).
with an increase of frequency. It is confirmed that the contact angle for a frequency below 10 kHz is located between those two cases of dc and f ) 10 kHz. Figure 3 shows the flow patterns at frequencies of 1, 18, and 128 kHz. Supporting Information A and B contain movie clips that correspond to Figures 3a and 3c, respectively. When the frequency was on the order of 10 Hz, the droplet oscillated continuously with a large amplitude. As the frequency was
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Figure 4. Flow patterns for different horizontal positions of the needle electrode for Vrms ) 80 V and c ) 10-3 M. The exposure time is 120 ms for (a) and 200 ms for (b).
increased, the oscillation amplitude gradually decreased and the flow pattern shown in Figure 3a for f ) 1 kHz was established. Such a flow pattern persists up to about 15 kHz. Then, only negligible fluid motion is observed between about 15 and 35 kHz (see Figure 3b). If the frequency is increased further, the flow shown in Figure 3c for f ) 128 kHz, which is evidently different from that at low frequency, is observed. This frequency dependence of flow is commonly observed for different voltages and NaCl concentrations. For the sake of convenience, we call the two flow types shown at low- and high-frequency ranges the low-frequency flow (Figure 3a) and the high-frequency flow (Figure 3c), respectively. There appeared another vortical flow near the top of the droplet, immediately after application of electrical signal. Different from the low- and high-frequency flows mentioned above, this flow disappeared within 1 min. In the present investigation, we focused only on the two low- and high-frequency flows. As will be discussed shortly, the frequency range in which the two flow patterns appear depends on electrolyte concentration, i.e., the conductivity of solution. Figures 3a and 3c actually show all the features of the flows at low- and high-frequency ranges, respectively. Although it is not clearly shown for the low-frequency flow, (toroidal) vortex is commonly developed for the two types of flows. For the high-frequency flow, the two vortex centers are always located just beside the needle electrode, as shown in Figure 3c. All the droplet images shown in this work, such as that shown in Figure 3, are more or less distorted due to the lens effect of the droplet itself. In general, an image is enlarged in the center region of an imaginary sphere enclosing the droplet. The image is shrunk at the periphery of the droplet, so that a remarkable portion of the boundary region of a droplet is shrunk to a thin line.15 That is why the vortex center for the low-frequency flow is not clearly visible in Figure 3a. In Figure 3a, the flow looks almost axisymmetric; but, actually, the low-frequency flow is in fact quite unstable and shows a
somewhat unsteady flow pattern (see the Supporting Information A for the movie clip). When the voltage is increased from 80 to 120 V, the droplet itself vibrates unstably and even moves randomly on the substrate surface (see Supporting Information C for the movie clip). Our preliminary experiment shows that the contact angle is highly dependent on the flows. The meandering motion of a droplet is believed to be related to the unstable internal flow. The details on the effect of flows on contact angle will be discussed in a future publication. For the high-frequency flow, the two vortex centers are always located just beside the needle electrode, as shown in Figure 3c, and the flow shows a stable steady motion compared to the low-frequency flow (see Supporting Information B for the movie clip). What clearly distinguishes the flow is that the flow directions are different for the two flows. The flow is upward near the axis for the low-frequency flow and downward near the curved droplet surface, and just the reverse for the high-frequency flow. The flow speed is on the order of 1 mm/s for the two flows and is generally faster for the low-frequency flow. Interestingly, there is almost no flow in the intermediate frequency range of about 15-35 kHz. This suggests that the flow-generation mechanisms are different for the two types of flow. 3.2. Effect of Electrode Position. The flows were studied in terms of the effects of electrode position and electrolyte concentration. First, the effect of the position of needle electrode was considered. Immediately after the results in Figure 3 were obtained, the position of the needle electrode was changed slightly in the horizontal and vertical directions. Figure 4 shows the change of flow pattern for the case of horizontal movement (see Supporting Information D and E for movie clips). The change of flow pattern is more dramatic for the low-frequency flow. As shown in Figure 4a, the symmetric flow pattern is destroyed and the center of the vortex is moved to the opposite direction of the electrode. In contrast, the two vortex centers moved together with the needle electrode for the high-frequency flow (see Figure 4b). As mentioned earlier, the low-frequency flow is generally
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Figure 5. Flow patterns for different vertical positions of the needle electrode for Vrms ) 80 V and c ) 10-3 M. The exposure time is 120 ms for (a) and 200 ms for (b).
Figure 6. Flow patterns for different horizontal positions of the tip of the needle electrode at 128 kHz for Vrms ) 80 V and c ) 10-3 M. The exposure time is 200 ms.
somewhat unsteady. The change of the flow pattern in Figure 4a seems to be caused by an inherent unstable fluid structure of the low-frequency flow. Figure 5 shows the change of flow pattern when the needle electrode is moved in the vertical direction for the low- and high-frequency flows, respectively (see Supporting Information F and G for movie clips). For the low-frequency flow, there is no noticeable change in the flow pattern and flow speed. For the high-frequency flow, however, the vortex core moved vertically following the needle electrode. Figure 6 shows the change of flow pattern for the high-frequency flow when the needle electrode is inserted from the side of the droplet, rather than from the top. It shows that the high-frequency flow again is very sensitive to the position of the electrode. This different response of the two flows with respect to the position of needle electrode is, as will be discussed, concerned with the origin of the flows. 3.3. Effect of Conductivity. The electric field inside the droplet is a function of ac frequency. We consider here why the electric field becomes dependent on frequency, and see whether there is any correlation between the electric field and the flow pattern. The electrical current is in general composed of two contributions: the Ohmic current and the displacement current. For a time-periodic signal, the Ohmic current is proportional to σE while the displacement current is proportional to jωE, where σ and are the electrical conductivity and permittivity of solution and ω is the angular frequency. Here, j ) x-1 means that there is a phase difference of π/2 between the two currents. Since the
displacement current is proportional to the ac frequency, the Ohmic current dominates over the displacement current at very low frequencies, but this is reversed at an extremely high frequency. As a result, the droplet behaves more like a conductor at a very low frequency and like a perfect dielectric at an extremely high frequency.16,17 Actually, the Ohmic current is prevalent in our experimental conditions. Nevertheless, even in the lowfrequency range, the electric field can be frequency-dependent due to the RC-charging nature of the system.16,17 We numerically analyzed the ac electric field around a droplet with changing ac frequency (see ref 18 for details). Figures 7a-c show the distribution of electrical potential for the three frequencies of 15, 35, and 128 kHz at c ) 10-3 M. The densely packed potential contours show that the electric field is strong there. The electric field inside the droplet is almost zero up to f ) 15 kHz. This means that the period of the input signal is much smaller than the RC-charging time of the system. Accordingly, the low-frequency flow shown in Figure 3a may not be related to the electric-field distribution inside the droplet. As the frequency increases, the displacement current becomes dominant, and the electric field inside the droplet becomes stronger as shown in Figure 7c, the case of f ) 128 kHz. When the concentration is increased to c ) 10-2 M, the electric field inside (16) Jones, T. B.; Fowler, J. D.; Chang, Y. S.; Kim, C.-J. Langmuir 2003, 19, 7646-7651. (17) Jones, T. B.; Wang, K.-L.; Yao, D.-J. Langmuir 2004, 20, 2813-2818. (18) Hong, J. S.; Ko, S. H; Kang, K. H.; Kang, I. S. Microfluid. Nanofluid., in press.
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Figure 7. Numerical results for electric field inside a droplet.
the droplet almost completely vanishes up to about f ) 300 kHz (compare Figures 7c and 7d). Of course, this is because the RC-charging time of the system is decreased. The electric field can be controlled to a certain degree by changing the conductivity of the solution, i.e., the electrolyte concentration. Changing the conductivity, therefore, allows us to check whether the flows are dependent on the electric field. Figure 8 compares the flow patterns for NaCl concentrations of 10-3 and 1 M for Vrms ) 80 V. The low-frequency flow is almost independent of conductivity as expected (compare Figures 8a and 8b and Figures 8c and 8d). This fact together with the numerical result for electric field in the low-frequency range strongly suggests that the low-frequency flow is generated by some other means, rather than by the electric-field distribution inside the droplet. As will be explained shortly, the low-frequency flow is due to the oscillation of the droplet surface. The high-frequency flow, however, is significantly altered when the NaCl concentration is changed (compare Figures 8e and 8f). That is, at f ) 128 kHz, the strong flow shown for c ) 10-3 M is almost perfectly suppressed by increasing the NaCl concentration to 1 M. This is certainly because the internal electric field vanishes, and the droplet oscillation is absent. The increase of electrolyte concentration, as mentioned earlier, weakens the electric-field strength inside the droplet. This electric-field dependency implies that the high-frequency flow is somehow associated with the electric field inside the droplet. In addition, the flow pattern of the high-frequency flow changes dramatically when the position of the electrode is changed (see Figures 4 and 5). This also supports the belief that the high-frequency flow is significantly affected by the electric-field distribution. Figure 9 shows the frequency ranges in which the two types of flow appear when the electrolyte concentration changes from
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10-3 to 10-2 M. The voltage amplifier shows a linear response up to about 200 kHz. Therefore, in the present experiment, the change of electrolyte concentration was inevitably limited to c ) 10-2 M. As shown in Figure 9, the frequency range for the low-frequency flow is hardly affected by the change of electrolyte concentration. On the other hand, the incipient frequency for the high-frequency flow increases remarkably with an increase of electrolyte concentration. 3.4. Origin of Flows. Let us consider first the origin of the low-frequency flow. The surface of the droplet was blurred in the images made using a conventional CCD camera at about f ) 100 Hz. We supposed that there must be a certain oscillation of the droplet interface. Electrowetting, however, originates from the electrical stress acting on the edge of a droplet.1,2 Accordingly, an ac electric field must exist for a time-periodic force acting on the edge of the droplet that generates a subsequent oscillation of the droplet interface. We recorded the droplet oscillation by using a high-speed camera (1024 PCI, Photron) at a frame rate of 10000 fps. Figure 10 shows the instantaneous images of a droplet for frequencies of 100 Hz, 300 Hz, 1 kHz, and 8 kHz at Vrms ) 120 V. The shape oscillation of the droplet is clearly shown for the cases of 100 Hz, 300 Hz, and 1 kHz. The motion of the TCL would be dragged by the viscous friction at the substrate. If the inertia effect is considered together with the viscous friction, it is natural that the oscillation amplitude would decay with frequency as shown in Figure 10. The frequency of oscillation was exactly 2 times the applied frequency. This is because the electrical force acting on the TCL is proportional to the square of the voltage signal. The shape oscillation is barely detectable by using a series of images when f ) 8 kHz. Its amplitude is too small that the shape oscillation is almost invisible only with an individual image such as that shown in Figure 10d. We could not check if any oscillatory motion existed at greater frequencies due to the framerate limitation of the camera. We checked the effect of the electrode position on the wave pattern for the case of Figure 10c. Although it is not shown here, no significant change of wave pattern is observed. In Figure 11a, horizontal lines were formed (although they are not very clearly visible) across the droplet, which are marked by arrows. This sort of line is always observed for the low-frequency flow. The lines in Figure 11a may be caused by the deformation of the interface and the subsequent refraction of light. Figure 11b shows an instantaneous image of the droplet obtained by the high-speed camera for the identical condition of Figure 11a. The positions of the lines are consistent with the positions of the nodes and troughs of the surface (capillary) waves. It is well-known in fluid mechanics that an oscillatory motion of a solid wall can cause a steady fluid motion due to an effect of viscosity; this is called steady streaming.19 The steady fluid motion here means the time-averaged flow. The steady circulating fluid motion around an oscillating cylinder20,21 and a sphere22,23 are the most typical examples. Similar phenomena can be observed for a liquid-liquid or liquid-air interface in an oscillatory flow. For instance, the oscillation of a spherical droplet can generate a steady flow inside and outside a droplet24,25 and the same is (19) Batchelor, G. K. An Introduction to Fluid Dynamics; Cambridge University Press: Cambridge, 1967; p 358. (20) Bertelsen, A. J. Fluid Mech. 1974, 64, 589-597. (21) Van Dyke, M. An Album of Fluid Motion; The Parabolic Press: Stanford, CA, 1982; p 23. (22) Chang, E. J.; Maxey, M. R. J. Fluid Mech. 1994, 277, 347-379. (23) Mei, R. J. Fluid Mech. 1994, 270, 133-174. (24) Trinh, E.; Wang, T. G. J. Fluid Mech. 1982, 122, 315-338. (25) Trinh, E.; Zwern, A.; Wang, T. G. J. Fluid Mech. 1982, 115, 453-474.
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Figure 8. Effect of NaCl concentration for Vrms ) 80 V.
Figure 9. Effect of electrolyte concentration on the frequency range in which the two types of flow appear for Vrms ) 80 V.
true for a liquid bridge.26,27 The oscillation of a bubble due to acoustic excitation causes a steady flow pattern around a bubble submerged in a liquid.28,29 Considering that a steady flow occurs (26) Lee, C. P.; Anilkumar, A. V.; Wang, T. G. Phys. Fluids 1996, 8, 32343246. (27) Nicolas, J. A.; Rivas, D.; Vega, J. M. J. Fluid Mech. 1998, 354, 147-174. (28) Marmottant, P.; Hilgenfeldt, S. Nature 2003, 423, 153-156. (29) Chung, S. K.; Zhao, Y.; Yi, U.-C.; Cho, S. K. IEEE Conf. Micro Electro Mech. Syst., Kyoto, Japan; (MEMS 2007), Kobe, Japan 2007, 31-34.
inside an oscillating droplet, the low-frequency flow is certainly generated by the oscillation of the interface. Further investigation is necessary to determine the detailed mechanism of flow generation. Figure 12 summarizes all the experimental and numerical results obtained for c ) 10-3 M and Vrms ) 80 V. Only negligible flow was observed from about 15 to 35 kHz. Here, we call this state no-flow state. Oscillation was observed only up to 8 kHz due to the frame-rate limitation of the camera. The numerical results show that the internal electric field becomes significant only above 35 kHz. The frequency range for high-frequency flow more or less overlaps with the region where the internal electric field becomes strong. Between about 15 and 35 kHz, the electric-field strength is still not very strong, and moreover, the oscillation amplitude is supposed to become very small. Accordingly, between about 15 and 35 kHz, the low-frequency flow may become very weak, and the high-frequency flow will be at most just incipient as well. The direct cause of the high-frequency flow is still unknown, although it is certain that the flow is caused by some electrohydrodynamic effects. The ac electro-osmotic flow (or induced charge electro-osmosis)30-34 is one of the candidates for the (30) Squires, T. M.; Bazant, M. Z. J. Fluid Mech. 2004, 509, 217-252.
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Figure 10. Instantaneous images of oscillating droplets for Vrms ) 120 V and c ) 10-3 M.
Figure 12. Summary of results for c ) 10-3 M and Vrms ) 80 V.
observed that there appear vortices inside a droplet placed on the insulator-covered electrodes of Green et al. Nichols and Gardeniers34 developed a method to mix fluids by using spiralshaped (insulator-covered) electrodes patterned on a planar surface. The configuration of their mixing device is basically similar to that of Green et al. A numerical analysis for ac electroosmotic flow, which is based on the method of Green et al., is underway by our group.
4. Conclusion
Figure 11. Effect of interface deformation for Vrms ) 80 V, c ) 10-3 M, and f ) 500 Hz: (a) lines formed due to refraction of light; (b) pattern of surface waves.
cause of the flow. For example, Green et al.32 have shown that an electrohydrodynamic flow is generated when two electrodes are patterned on a planar surface side by side. Ishida et al.33 (31) Bazant, M. Z.; Squires, T. M. Phys. ReV. Lett. 2004, 92, 066010. (32) Green, N. G.; Ramos, A.; Gonza´lez, A.; Morgan, H.; Castellanos, A. Phys. ReV. E 2002, 66, 026305. (33) Ishida, Y.; Davoust, L.; Fouillet, Y. 5th Int. Electrowetting Meeting, Rochester, New York 2006, 18. (34) Nichols, K. P.; Gardeniers, J. G. E. 10th Int. Conf. Miniaturized Syst. Chem. Life Sci. (µTAS 2006), Tokyo, Japan 2006, 582-584.
We found two distinct types of hydrodynamic flows in ac electrowetting: the low-frequency flow and the high-frequency flow. According to our experiments, the low-frequency flow is insensitive to the conductivity of solution. An oscillatory motion of droplet surface is observed up to about 8 kHz; this motion is driven by the electrical force acting on the TCL. The lowfrequency flow is highly likely to be a kind of steady streaming phenomena caused by the oscillation of the interface. The flow pattern of the high-frequency flow is very sensitive to the position of electrode. The frequency range in which the high-frequency flow appears is clearly dependent on the conductivity of the solution. Moreover, the numerical result for the electric field shows that the electric field becomes strong inside the droplet at the point when the high-frequency flow appears. The high-frequency flow, therefore, is possibly a kind of electrohydrodynamic flow that is controlled by the electricfield distribution. The direct cause of the high-frequency flow is still unknown. Acknowledgment. This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by
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the Korea government (MOST) (R0A-2007-000-20098-0). The authors deeply appreciate the inspiring discussion with Dr. Jeong Min Oh of the Pohang University of Science and Technology. Supporting Information Available: Supporting Information A and B are movie clips of the low- and high-frequency flows which correspond to Figures 3a and 3c, respectively. Supporting Information C is a movie clip which demonstrates the meandering motion of a droplet
Langmuir, Vol. 24, No. 3, 2008 1101 for the low-frequency flow at a voltage of Vrms ) 120 V. Supporting Information D, E, F, and G are movie clips which show the effect of electrode positions; these correspond to Figures 4a, 4b, 5a, and 5b, respectively. The playing speed of all the movie clips is 1×. This material is available free of charge via the Internet at http:// pubs.acs.org. LA702455T
