Article pubs.acs.org/Langmuir
Ultralow Voltage Irreversible Electrowetting Dynamics of an Aqueous Drop on a Stainless Steel Surface Yanna Liu,†,‡ Yu-En Liang,∥ Yu-Jane Sheng,*,∥ and Heng-Kwong Tsao*,‡,§ †
Faculty of Chemical Engineering, Kunming University of Science and Technology, Kunming 650500, China Department of Chemical and Materials Engineering and §Department of Physics, National Central University, Jhongli, Taiwan 320, ROC ∥ Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 106, R.O.C ‡
ABSTRACT: The electrowetting dynamics of a water drop on a stainless steel surface in air is investigated under ultralow voltages. The spreading behavior can be classified into three regimes. The drop expands slowly in regime I, but the spreading accelerates quite rapidly in regime II. The spreading becomes insignificant in regime III. The experimental results are compared to the equilibrium shapes acquired by Surface Evolver simulations. The good agreement between them indicates that the slow electrowetting dynamics can be considered to be a quasi-equilibrium process. The influences of the electric field and drop size on the spreading dynamics are examined. The variation of both the contact angle and base diameter with time in regimes II and III can be well described by the exponential change with a characteristic time, which grows with the drop volume but is inversely proportional to the electric field. A simple model based on the electromechnical mechanism is proposed to explain the spreading dynamics. The exponential change is attributed to ion migration from the bulk of the drop to the contact line. The experimental results agree well with the prediction of our simple theory.
I. INTRODUCTION The effect of an electric field on the wettability of liquids on solid surfaces, so-called electrowetting, has drawn great attention since the first description of electrocapillarity by Lippmann.1 By applying a voltage between a droplet and an electrode, the contact angle and base diameter of the drop on a conductive surface can be changed.2,3 Furthermore, the deformation and displacement of the liquid interface can be controlled by manipulating the electric field. Along with the work of electrocapillarity, the electrowetting system involves aqueous electrolytes in direct contact with a mercury electrode. The applications are often hindered by the electrolytic decomposition of water. By introducing a thin dielectric layer between the electrode and the conductive droplet, known as electrowetting on dielectric (EWOD), applications based on electrowetting have developed rapidly and successfully in the areas of liquid lenses,4,5 electronic displays,6,7 laboratory-on-achip systems,8−10 and mixing in microfluidic channels.11,12 Previous studies focused mainly on the static electrowetting, especially the explanation of the reduction of the contact angle driven by an electric field. On the basis of the Lippmann equation (Gibbs’ interfacial thermodynamics), the change in the contact angle of a sessile drop can be described by the Lippmann−Young law. The solid−liquid interfacial tension is effectively lowered by the formation of the field-induced surface charge density. In EWOD, the electrostatic energy is stored in a thin dielectric layer which insulates the liquid from the electrode and resembles the solid−liquid interface.13−15 For practical applications, the dynamic electrowetting is of interest © 2015 American Chemical Society
as well. To improve the performance of electrowetting, a good understanding of the spreading dynamics of a drop driven by an electric field is essential. The molecular kinetic theory has been proposed to explain the motion of the contact line.16,17 When the electric work is small compared to the thermal energy, the spreading velocity is proportional to the product of the surface tension and the difference in the cosines of the apparent contact angle and the intrinsic contact angle. Also, it is inversely proportional to the friction coefficient associated with the contact line. The typical response time associated with EWOD is less than 1 s.18 To slow down the electrowetting dynamics for experimental observation, the addition of glycerol to a drop of aqueous electrolyte solution is employed to increase the viscosity.19−21 It is found that there exists a critical viscosity at which the spreading pattern changes from an under- to overdamped response. Moreover, the friction coefficient is rarely affected by the drop size and applied voltage.22 The use of EWOD allows a significant contact angle variation of about 30−100° but requires a high voltage of about 20−300 V.23 The high voltage leads to a short duration of the spreading dynamics typically of several tens or hundreds of milliseconds.24,25 This consequence hinders the experimental study of the electrowetting dynamics. To reduce the applied voltage, the thickness of the insulating film has to be decreased. However, there exists a limitation of the film thickness without Received: October 27, 2014 Revised: February 26, 2015 Published: March 2, 2015 3840
DOI: 10.1021/acs.langmuir.5b00411 Langmuir 2015, 31, 3840−3846
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obtained and compared with our experimental results, including the height and base diameter of the drop.
weakening its blocking effect associated with the liquid electrolysis and breakdown of the dielectrics. As a result, a conductive electrode such as metal is directly used to lower the applied voltage significantly and lengthen the time scale of the electrowetting process. In this article, the spreading dynamics of a droplet on the stainless steel surface with an ultralow applied voltage in air is explored. Surface Evolver simulations are performed to demonstrate that slow electrowetting dynamics can be taken as a quasi-equilibrium process. The effects of the electric field and drop size on the spreading dynamics are examined. A simple model is also developed to interpret the mechanism of ultralow electrowetting.
III. RESULTS AND DISCUSSION A. Dynamics of an Electrowetting Drop. The typical dynamics associated with electrowetting on a conductive surface is shown in Figure 2a for a 5 μL water drop containing
II. EXPERIMENTAL SECTION A. Materials and Experimental Method. The experimental setup used in this study is shown in Figure 1. Stainless steel slices with
Figure 1. Electrowetting system for an aqueous droplet spreading on a stainless steel substrate under electrical actuation. a thickness of 1 mm purchased from KWO-YI (Taiwan) were used as substrates and cleaned with alcohol and deionized water before use. The surface roughness of the steel slice is determined by a surface profilometer (Veeco DEKTAK 150) and is about 40.2 nm. A water droplet containing NaCl (10 mM) was deposited from a micropipet on the substrate and surrounded by air. The typical size of the drop is 5 μL. The viscosity and surface tension of the liquid drop for electrowetting are similar to those of pure water, about η = 0.95 mPa·s and γ = 72.0 dyn/cm, respectively. The electrical conductivity is 0.12 S/m. The advancing water contact angle is about 85°. A stainless steel needle of 0.125 mm diameter was inserted into the droplet from the top, as illustrated in Figure 1. The voltage applied between the substrate and the needle was produced by a function generator (LPS305B-TC, BK Precision, Taiwan) with dc electrical signals. The voltage ranges from 0.80 to 1.75 V. In our electrowetting experiments, the electrical potential is always kept constant during the process. The actuation time for applying a constant electrical potential U is about 100 s. Note that the electrowetting phenomenon cannot be observed if the stainless steel surface is not cleaned before use. The dynamic contact angle measurements were performed at room temperature under the open-air condition with a relative humidity of 45−50% by a CA goniometer, drop shape analysis system (DSA10-MK2, Krüss, Germany). B. Surface Evolver Simulation. To examine the difference between the experimental observation of the dynamic process and the equilibrium shape (without fluid flow), numerical simulations by the public domain finite element Surface Evolver (SE) package were conducted.26,27 The fundamental idea of SE is to minimize the free energy of the system subject to the constraint of constant volume. The drop surface is modeled as unions of triangles with vertices, and it is evolving down the energy gradient until a configuration with minimum energy is acquired. For a given snapshot of the spreading dynamics in our experiments, the dynamic contact angles on both the substrate (θ) and needle (θ′) can be determined. On the basis of θ and θ′, SE can be performed for a specified drop volume. The equilibrium shape is then
Figure 2. (a) Snapshots of the drop with a volume of 5 μL during the electrowetting process under a voltage of 1.5 V. Left column: side view. Right column: top view. (b) Variation of the contact angle (θ) and base diameter (d) of the spreading drop with a volume of 5 μL under a voltage of 1.5 V.
10 mM NaCl on stainless steel under a voltage of 1.5 V. The electrowetting process takes about 1 min, and there is no hydrolysis during the spreading period. The initial contact angle and base diameter of the drop are about 85° and 2.94 mm, respectively. After the electrical voltage is applied, the drop spreads gradually to the final state with a contact angle of about 30° and a wetting diameter of 4.65 mm. Because of the conservation of the drop volume, the height of the drop declines from 1.36 to 0.82 mm. Different from the electrowetting behavior on Teflon surfaces with weak contact angle hysteresis,28 the spread drop does not retract after the electrowetting process is complete. In fact, when the voltage is turned off at any stage, the expanding contact line stops and does not withdraw. Note that the irreversibility associated with EWOD has been reported29−31 and is attributed to surface roughness, trapped charge, or contact angle hysteresis. The presence of the steel needle disturbs the drop shape significantly so that the spherical cap cannot be maintained. The contact angle associated with the needle is actually altered from the 85° advancing contact angle to the 30° receding 3841
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Langmuir contact angle. These results are consistent with those observed on a steel substrate. Note that the contact angle of the steel surface in the presence of the needle is the same as that with the removal of the needle. The variations of the contact angle and base diameter of the spreading drop are illustrated in Figure 2b. The spreading response is overdamped. The transient behavior can be classified into three regimes. Right after the electrical voltage is applied, the drop spreads slowly in the first 5 s. It is identified as regime I. However, in the next 35 s, the spreading accelerates quite rapidly. The contact angle decreases sharply, but the base diameter grows rapidly. This is defined as regime II. After t = 40 s, the spreading behavior becomes insignificant. It seems that both the contact angle and base diameter approach plateaus gradually. Such a slow change is characterized as regime III. Note that the final contact angle is about 30°, which is consistent with the receding contact angle of the steel substrate determined by the deflation method. B. Slow Electrowetting Dynamics as a Quasi-Equilibrium Process. As demonstrated in the influence of fluid viscosity and the underdamped spreading response in the dynamics of EWOD,22 the hydrodynamics inside a drop may play an essential role. However, as the spreading dynamics is much slower than the relaxation of fluid motion, the electrowetting dynamics can be considered to be a quasiequilibrium process. In this work, the electrowetting process is slow because of ultralow voltage. As a result, each stage of electrowetting is close to thermodynamic equilibrium and can be characterized by static contact angles. As the voltage is turned off at any stage, the time-varying contact angle halts instantly and remains unchanged. That is, the relaxation of fluid motion inside the drop is fast, and thus the equilibrium state is reached quickly. This assumption of quasi-equilibrium can be further examined by the comparison between the dynamic observation and equilibrium simulation of Surface Evolver (SE). Figure 3a shows some images of the transient shape of the spreading drop and the corresponding SE simulation results, which are obtained by knowing the apparent contact angles on the substrate (θ) and on the needle (θ′) at a fixed drop volume. It is evident that the shape profile of the spreading drop can be well depicted by equilibrium simulations in which hydrodynamics is absent and only the hydrostatic pressure is involved in the Young−Laplace equation. The quantitative comparison is further made in Figure 3b, where the variations of both the base diameter and drop height with the apparent contact angle on the substrate (θ) are shown. Good agreement between the experimental and simulation outcomes indicates that the overdamped electrowetting dynamics in this work can be described by a quasi-equilibrium process. The quasi-state equilibrium evolution can be linked to the Tomotika time, which characterizes the time taken by a distorted interface to regain its equilibrium shape by the action of surface tension. It is estimated as τcapillary = ηR/γ = 3.9 × 10−5 s. Here R is the characteristic dimension of the surface and is represented by the drop size. Because the Tomotika time is small compared to the actuation time (about 1 min), the quasi-equilibrium assumption made in our analysis for electrowetting dynamics is justified. Note that the equilibrium SE simulation will fail to capture the transient shape of the drop with an underdamped spreading response if the dynamic pressure associated with fluid motion is significant.
Figure 3. (a) Comparison of the drop profiles between the experimental results and SE simulation outcomes for the volume of 5 μL and voltage of 1.5 V. Left column: experiment. Right column: simulation. (b) Comparison of the evolution of the geometric characteristic of the drop (contact angle (θ), base diameter (d), and height (h)) between the experimental results (symbols) and SE simulation outcomes (lines) for a volume of 5 μL and a voltage of 1.5 V.
C. Simple Model of Ultralow Electrowetting. In the electrowetting dynamics, the spreading behavior including the reduction of apparent contact angle and the growth of the base diameter is mainly driven by the electric field in the vicinity of the triple contact line according to the electromechanical theory.32 The droplet shape adjacent to the triple contact line is similar to the geometry of a wedge and therefore the electric fields and charges are concentrated close to the liquid−gas interface near the contact line. Because the electrostatic pressure on the liquid−gas interface is limited to a very small region, the electric force can be regarded as a point pulling force acting on the contact line outwardly. As a result, the shape of the droplet is still dominated by the hydrostatic pressure as shown in the previous section. According to our experimental results, it seems that the dynamic process can be classified into the stage prior to the exponential change and the stage associated with exponential change. When the voltage is applied, charges are accumulated on the metal side of the solid−liquid interface almost instantly. In the earlier stage, the electrostatic pressure is built up by the electric field and the charges in the neighborhood of the triple contact line. Because the local charge density is still small in the beginning, the changes in contact angle and base diameter are slow. As the time of voltage application proceeds, however, the electric field inside the drop drives counterions in the bulk to migrate toward the metal electrode and the liquid−gas interface 3842
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Langmuir near the contact line. That is, the local charge density grows with time and thereby the electrical pulling force is increased accordingly. In a later stage, the increment of the local charges near the contact line can be estimated by the loss of counterions in the bulk. Assume that the bulk counterion concentration and bulk volume are c(t) and Vl, respectively. The loss of counterions is caused by the electrical migration of counterions out of the bulk region. The migration velocity v is proportional to the electric field E, v = ME. Here, M denotes the electric mobility. The balance equation of the counterion in the bulk is then given by
Vl
dc = −vc dt
(1) Figure 4. Variation of cos θ − cos θ0 with U2 for a drop of 5 μL. In the inset, the variation of contact angle (θ) and base diameter (d) with drop volume (by the deflation method) is depicted to determine the receding contact angle.
The solution is simply ⎛ t⎞ c(t ) = c0 exp⎜ − ⎟ ⎝ τ⎠
(2)
where τ = Vl/v is inversely proportional to E and c0 depicts the concentration at the beginning of the second stage. To a first approximation, c 0 can be considered to be the bulk concentration, about 10 mM, because the number of ions driven to the contact line is still small in the first stage. The increment of the local charge density near the contact line σ(t) can be estimated from the sum of the initial charge density σ0 and the loss of ions in the bulk. Consequently, one has σ(t ) ≈ σ0 +
1 A
∫V [c0 − c(t )] dVl l
drop.34 In this work, the saturation angle is about θsat ≈ 30°, which is somehow the same as the receding contact angle (θr) determined from the deflation method35 as shown in the inset of Figure 4. Note that the needle size is small compared to the drop size and therefore the contact angle measurement is not disturbed by the needle. It is postulated that once the saturation voltage is reached, most of the ions are accumulated in the electric double layer near the electrodes at equilibrium. Because the charge carriers are absent in the bulk of the drop, the electric resistance reaches its maximum.34 In addition to affecting the equilibrium contact angle of electrowetting, the magnitude of the applied voltage also influence its dynamic process. As revealed by our simple theory, the spreading rate in terms of the relaxation time τ declines with increasing E. To explore the effects of the applied voltage on the spreading dynamics, the variations of the contact angle and base diameter of the drops were measured for U ranging from 0.8 to 1.75 V. Evidently, drops with high voltage arrived at the equilibrium condition faster than those with lower voltage. The earlier stage identified as regime I, as illustrated in Figure 2b, can be clearly shown through the semilogarithmic plot in Figure 5. During the first few seconds of electrowetting, the contact angle descends slowly from the advancing contact angle of 85° as shown in Figure 5a whereas the base diameter ascends gradually from 2.94 mm as depicted in Figure 5b. The period of regime I is decreased as the applied voltage is increased. Because the electrical pulling force is proportional to the electric field, it is anticipated that the movement of the contact line becomes faster for larger voltage. In the later stage identified as regime II, both the contact angle and base diameter experience a trend in exponential decay and reach their equilibrium state in regime III. The relaxation time τ can be determined from regime II of the dynamic process and varies from about 10 to 20 s. It is found that the relaxation time declines with increasing applied voltage. The variation of τ obtained from the contact angle with U is shown in Figure 5c while the plot of τ acquired from the base diameter against U is depicted in the inset. A linear relationship between τ and U is evidently seen. For both the data of the contact angle and base diameter, their slopes are consistent and have a value of −1. In accord with our simple theory, τ is inversely proportional to U because E is proportional to U. The good agreement between the theory and experimental results reveals that the main resistance to the spreading dynamics
(3)
where A is the area near the contact line region. By using eq 2, σ(t) can be expressed by ⎡ ⎛ t ⎞⎤ σ(t ) = σ0 + α⎢1 − exp⎜ − ⎟⎥ ⎝ τ ⎠⎦ ⎣
(4)
where α ≈ c0Vl/A is a positive constant. Because the electrical pulling force grows proportionally to σ(t), the base diameter is expected to increase accordingly. This simple model indicates that in the electrowetting dynamics process there exists a regime associated with exponential change due to ion migration. In addition to the base diameter, the contact angle can be approximately described by the exponential variation under the constraint of constant volume. The relaxation time τ represents the characteristic time scale of electrowetting and can be reduced by increasing the electric field. D. Effects of Electric Field. In the thermodynamic explanation of electrowetting based on the Lipmann−Young equation, the equilibrium contact angle is increased from cos θ0 to cos θ by CU2/2γ. Here, C represents the capacitance of the liquid/substrate interface, γ is the surface tension, and U is the applied voltage. In general, C comes mainly from the capacitance of the dielectric layer separating the bottom from the liquid. This result indicates that the increment of U leads to the decrease in θ. As demonstrated in Figure 4, cos θ − cos θ0 is proportional to U2 at low voltages. However, when the applied voltage is large enough (∼1.25 V), a saturation in the contact angle occurs. The contact angle saturation is generally observed in electrowetting. Although many explanations of contact angle saturation have been proposed, it is not yet clearly understood. Some explanations of contact angle saturation are plausible on steel surfaces under ultralow voltages, including the zero effective solid−liquid interfacial tension33 and increment of the electric resistance of the liquid 3843
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Figure 5. (a) Temporal evolution of the contact angle (θ) of the spreading drop under the applied voltage ranging from 0.8 to 1.75 V. (b) Temporal evolution of the base diameter (d) of the spreading drop under the applied voltage ranging from 0.8 to 1.75 V. (c) Variation of the characteristic times (τ) determined from contact angle measurements under the applied voltage ranging from 0.8 to 1.75 V. In the inset, the characteristic times (τ) are determined from base diameter measurements.
Figure 6. (a) Temporal evolution of the contact angle of the spreading drop with different volume ranging from 3 to 12 μL. Symbols: experimental results. Line: simulation outcomes with exponential decay. (b) Temporal evolution of the base diameter of the spreading drop with different volume ranging from 3 to 12 μL. Symbols: experimental results. Line: simulation outcomes with exponential decay. (c) Variation of the characteristic times (τ) determined from contact angle measurements with different volumes ranging from 3 to 12 μL. In the inset, the characteristic times (τ) are determined from base diameter measurements.
originates from the electrical migration of ions, and the increment in electric field enhances the migration velocity in regime II. E. Effects of Drop Size. It has been reported that the drop size can affect the spreading dynamics.22 Our simple model also reveals that the relaxation time can be altered by the drop volume associated with electrical migration resistance. To investigate the effects of the drop size on the electrowetting dynamics of drops, the variations of the contact angle and base diameter with time are measured. As designated in Figure 6 with an applied voltage of 1.25 V, the differences between the final value and the initial value, including contact angle Δθ = θ0 − θf and base diameter Δd = df − d0, are insensitive to the drop volume, ranging from 3 to 12 μL. That is, θf and df are
essentially determined by the applied voltage. However, the spreading dynamics does vary substantially with the drop size. It is evident that the drops with smaller volumes reach the final state faster than those with larger volumes. The influence of the drop size on the spreading dynamics is different in different regimes. As shown in the semilogarithmic plots of Figure 6a,b, the period of regime I grows as the drop volume is increased. Under the same voltage, the larger drop volume leads to a weaker electrical field in the drop, which results in a smaller electrical pulling force. The exponential changes in regime II are also identified in the variations of the contact angle and base diameter for different drop sizes. The 3844
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Langmuir relaxation time τ gained from the contact angle is depicted in Figure 6c whereas that attained from the base diameter is illustrated in the inset. Evidently, the relaxation time rises with increasing drop volume. Moreover, a linear relationship between τ and Vl is observed. This result is consistent with our simple theory and indicates that a larger liquid volume yields a greater resistance to ion migration.
(2) Frumkin, A.; Gorodetskaya, A.; Kabanov, B.; Nekrasov, N. Electrocapillary phenomena and the wetting of metals by electrolytic solutions. I. Phys. Z. Sowjetunion 1932, 1, 255−284. (3) Chen, L.; Bonaccurso, E. Electrowetting - From statics to dynamics. Adv. Colloid Interface Sci. 2014, 210, 2−12. (4) Hendriks, B. H. W.; Kuiper, S.; Van, A. M. A. J.; Renders, C. A.; Tukker, T. W. Electrowetting-Based Variable-Focus Lens for Miniature Systems. Opt. Rev. 2005, 12, 255−259. (5) Kuiper, S.; Hendriks, B. H. W. Variable-focus liquid lens for miniature cameras. Appl. Phys. Lett. 2004, 85, 1128−1130. (6) Shamai, R.; Andelman, D.; Berge, B.; Hayes, R. Water, electricity, and between...On electrowetting and its applications. Soft Matter 2008, 4, 38−45. (7) Hayes, R. A.; Feenstra, B. J. Video-speed electronic paper based on electrowetting. Nature 2003, 425, 383−385. (8) Fair, R. B. Digital microfluidics: is a true lab-on-a-chip possible? Microfluid. Nanofluid. 2007, 3, 245−281. (9) Miller, E. M.; Wheeler, A. R. Digital bioanalysis. Anal. Bioanal. Chem. 2009, 393, 419−426. (10) Cho, S. K.; Moon, H. J. Electrowetting on Dielectric (EWOD): New Tool for Bio/Micro Fluids Handling. Biochip J. 2008, 2, 79−96. (11) Mugele, F.; Baret, J.-C. Electrowetting: from basics to applications. J. Phys: Condens. Matter 2005, 17, R705−R714. (12) Cho, S. K.; Moon, H. J.; Kim, C. J. Creating, Transporting, Cutting, and Merging Liquid Droplets by Electrowetting-Based Actuation for Digital Microfluidic Circuits. J. Microelectromech. Syst. 2003, 12, 70−80. (13) Berge, B. Électrocapillarité et mouillage de films isolants par l’eau. CRAS 317 Série II 1993, 317, 157. (14) Peykov, V.; Quinn, A.; Ralston, J. Electrowetting: a model forcontact-angle saturation. Colloid Polym. Sci. 2000, 278, 789−93. (15) Quilliet, C.; Berge, B. Electrowetting: a recent outbreak. Curr. Opin. Colloid Interface Sci. 2001, 6, 34−39. (16) Blake, T. D.; Haynes, J. M. Kinetics of Liquid/Liquid Displacement. J. Colloid Interface Sci. 1969, 30, 421−423. (17) Blake, T. D.; Clarke, A.; Stattersfield, E. H. An Investigation of Electrostatic Assist in Dynamic Wetting. Langmuir 2000, 16, 2928− 2935. (18) Berge, B.; Peseux, J. Variable focal lens controlled by an external voltage: An application of electrowetting. Eur. Phys. J. E 2000, 3, 159− 163. (19) Decamps, C.; De Coninck, J. Dynamics of Spontaneous Spreading under Electrowetting Conditions. Langmuir 2000, 16, 10150−10153. (20) Bavière, R.; Boutet, J.; Fouillet, Y. Dynamics of droplet transportinduced by electrowetting actuation. Microfluid. Nanofluid. 2007, 4, 287−294. (21) Roques-Carmes, T.; Hayes, R. A.; Feenstra, B. J.; Schlangen, L. J. M. Liquid behavior inside a reflective display pixel based on electrowetting. J. Appl. Phys. 2004, 95, 4389−4396. (22) Hong, J.; Kim, Y. K.; Kang, K. H.; Oh, J. M.; Kang, I. S. Effects of Drop Size and Viscosity on Spreading Dynamics in DC Electrowetting. Langmuir 2013, 29, 9118−9125. (23) Kornyshev, A. A.; Kucernak, A. R.; Marinescu, M.; Monroe, C. W.; Sleightholme, A. E. S.; Urbakh, M. Ultra-Low-Voltage Electrowetting. J. Phys. Chem. C 2010, 114, 14885−14890. (24) Chen, L. Q.; Li, C. L.; van der Vegt, N. F. A.; Auernhammer, G. K.; Bonaccurso, E. Initial Electrospreading of Aqueous Electrolyte Drops. Phys. Rev. Lett. 2013, 110, 026103. (25) Annapragada, S. R.; Dash, S.; Garimella, S. V.; Murthy, J. Y. Dynamics of Droplet Motion under Electrowetting Actuation. Langmuir 2011, 27, 8198−8204. (26) Chou, T.-H.; Hong, S.-J.; Sheng, Y.-J.; Tsao, H.-K. Wetting Behavior of a Drop Atop Holes. J. Phys. Chem. B 2010, 114, 7509− 7515. (27) Wang, Z. J.; Chang, C.-C.; Hong, S.-J.; Sheng, Y.-J.; Tsao, H.-K. Capillary Rise in a Microchannel of Arbitrary Shape and Wettability:Hysteresis Loop. Langmuir 2012, 28, 16917−16926.
IV. CONCLUSIONS The spreading dynamics of a water droplet on stainless steel under ultralow voltage is investigated. It takes about 1 min to reach the equilibrium state, and no hydrolysis occurs. Once the applied voltage is switched off during the electrowetting process, the spread is halted and the drop does not retract. The spreading dynamics can be divided into three regimes: regime I, slow spreading; regime II, rapid growth of the base diameter; regime III, slowly reaching the plateau. The electrowetting dynamics can be explained by the electromechanical mechanism. In the beginning, the local density of ions near the contact line is small. The weak electrical pull leads to slow changes in the contact angle and base diameter. As time proceeds, ions migrate from the bulk to electrodes. As a result of the accumulation of charges in the vicinity of the contact line, the electrical pulling force is increased and gives rise to the rapid decay of the contact angle and the rapid growth of the base diameter. SE simulations are performed to compare the dynamic observation with the equilibrium shape. The agreement between the experimental results and simulation outcomes indicates that the overdamped electrowetting dynamics can be considered to be a quasi-equilibrium process. The effects of both electric field and drop size on the spreading dynamics are explored. It is found that the variation of both the contact angle and base diameter with time in regimes II and III can be well described by the exponential change with a characteristic time (τ) for the specified electric field and drop size. A simple model is proposed to depict such electrowetting dynamics. The charge accumulation near the contact line can be followed by the loss of ion concentration in the bulk of the drop. According to the exponential decay of the bulk density, the characteristic time grows with the drop volume but is inversely proportional to the electric field. The experimental results agree well with the prediction of our simple theory. When the applied voltage is high enough, the charge carriers are eventually absent in the bulk of the drop and the electric resistance reaches its maximum. Contact angle saturation is therefore observed.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail: [email protected]. *E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research work is supported by the Ministry of Science and Technology of Taiwan.
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REFERENCES
(1) Lippmann, G. Relations entre les phénoménes électriques etcapillaires. Ann. Chim. Phys. 1875, 5, 494−549. 3845
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Ultralow Voltage Irreversible Electrowetting Dynamics of an Aqueous Drop on a Stainless Steel Surface Yanna Liu,†,‡ Yu-En Liang,∥ Yu-Jane Sheng,*,∥ and Heng-Kwong Tsao*,‡,§ †
Faculty of Chemical Engineering, Kunming University of Science and Technology, Kunming 650500, China Department of Chemical and Materials Engineering and §Department of Physics, National Central University, Jhongli, Taiwan 320, ROC ∥ Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 106, R.O.C ‡
ABSTRACT: The electrowetting dynamics of a water drop on a stainless steel surface in air is investigated under ultralow voltages. The spreading behavior can be classified into three regimes. The drop expands slowly in regime I, but the spreading accelerates quite rapidly in regime II. The spreading becomes insignificant in regime III. The experimental results are compared to the equilibrium shapes acquired by Surface Evolver simulations. The good agreement between them indicates that the slow electrowetting dynamics can be considered to be a quasi-equilibrium process. The influences of the electric field and drop size on the spreading dynamics are examined. The variation of both the contact angle and base diameter with time in regimes II and III can be well described by the exponential change with a characteristic time, which grows with the drop volume but is inversely proportional to the electric field. A simple model based on the electromechnical mechanism is proposed to explain the spreading dynamics. The exponential change is attributed to ion migration from the bulk of the drop to the contact line. The experimental results agree well with the prediction of our simple theory.
I. INTRODUCTION The effect of an electric field on the wettability of liquids on solid surfaces, so-called electrowetting, has drawn great attention since the first description of electrocapillarity by Lippmann.1 By applying a voltage between a droplet and an electrode, the contact angle and base diameter of the drop on a conductive surface can be changed.2,3 Furthermore, the deformation and displacement of the liquid interface can be controlled by manipulating the electric field. Along with the work of electrocapillarity, the electrowetting system involves aqueous electrolytes in direct contact with a mercury electrode. The applications are often hindered by the electrolytic decomposition of water. By introducing a thin dielectric layer between the electrode and the conductive droplet, known as electrowetting on dielectric (EWOD), applications based on electrowetting have developed rapidly and successfully in the areas of liquid lenses,4,5 electronic displays,6,7 laboratory-on-achip systems,8−10 and mixing in microfluidic channels.11,12 Previous studies focused mainly on the static electrowetting, especially the explanation of the reduction of the contact angle driven by an electric field. On the basis of the Lippmann equation (Gibbs’ interfacial thermodynamics), the change in the contact angle of a sessile drop can be described by the Lippmann−Young law. The solid−liquid interfacial tension is effectively lowered by the formation of the field-induced surface charge density. In EWOD, the electrostatic energy is stored in a thin dielectric layer which insulates the liquid from the electrode and resembles the solid−liquid interface.13−15 For practical applications, the dynamic electrowetting is of interest © 2015 American Chemical Society
as well. To improve the performance of electrowetting, a good understanding of the spreading dynamics of a drop driven by an electric field is essential. The molecular kinetic theory has been proposed to explain the motion of the contact line.16,17 When the electric work is small compared to the thermal energy, the spreading velocity is proportional to the product of the surface tension and the difference in the cosines of the apparent contact angle and the intrinsic contact angle. Also, it is inversely proportional to the friction coefficient associated with the contact line. The typical response time associated with EWOD is less than 1 s.18 To slow down the electrowetting dynamics for experimental observation, the addition of glycerol to a drop of aqueous electrolyte solution is employed to increase the viscosity.19−21 It is found that there exists a critical viscosity at which the spreading pattern changes from an under- to overdamped response. Moreover, the friction coefficient is rarely affected by the drop size and applied voltage.22 The use of EWOD allows a significant contact angle variation of about 30−100° but requires a high voltage of about 20−300 V.23 The high voltage leads to a short duration of the spreading dynamics typically of several tens or hundreds of milliseconds.24,25 This consequence hinders the experimental study of the electrowetting dynamics. To reduce the applied voltage, the thickness of the insulating film has to be decreased. However, there exists a limitation of the film thickness without Received: October 27, 2014 Revised: February 26, 2015 Published: March 2, 2015 3840
DOI: 10.1021/acs.langmuir.5b00411 Langmuir 2015, 31, 3840−3846
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obtained and compared with our experimental results, including the height and base diameter of the drop.
weakening its blocking effect associated with the liquid electrolysis and breakdown of the dielectrics. As a result, a conductive electrode such as metal is directly used to lower the applied voltage significantly and lengthen the time scale of the electrowetting process. In this article, the spreading dynamics of a droplet on the stainless steel surface with an ultralow applied voltage in air is explored. Surface Evolver simulations are performed to demonstrate that slow electrowetting dynamics can be taken as a quasi-equilibrium process. The effects of the electric field and drop size on the spreading dynamics are examined. A simple model is also developed to interpret the mechanism of ultralow electrowetting.
III. RESULTS AND DISCUSSION A. Dynamics of an Electrowetting Drop. The typical dynamics associated with electrowetting on a conductive surface is shown in Figure 2a for a 5 μL water drop containing
II. EXPERIMENTAL SECTION A. Materials and Experimental Method. The experimental setup used in this study is shown in Figure 1. Stainless steel slices with
Figure 1. Electrowetting system for an aqueous droplet spreading on a stainless steel substrate under electrical actuation. a thickness of 1 mm purchased from KWO-YI (Taiwan) were used as substrates and cleaned with alcohol and deionized water before use. The surface roughness of the steel slice is determined by a surface profilometer (Veeco DEKTAK 150) and is about 40.2 nm. A water droplet containing NaCl (10 mM) was deposited from a micropipet on the substrate and surrounded by air. The typical size of the drop is 5 μL. The viscosity and surface tension of the liquid drop for electrowetting are similar to those of pure water, about η = 0.95 mPa·s and γ = 72.0 dyn/cm, respectively. The electrical conductivity is 0.12 S/m. The advancing water contact angle is about 85°. A stainless steel needle of 0.125 mm diameter was inserted into the droplet from the top, as illustrated in Figure 1. The voltage applied between the substrate and the needle was produced by a function generator (LPS305B-TC, BK Precision, Taiwan) with dc electrical signals. The voltage ranges from 0.80 to 1.75 V. In our electrowetting experiments, the electrical potential is always kept constant during the process. The actuation time for applying a constant electrical potential U is about 100 s. Note that the electrowetting phenomenon cannot be observed if the stainless steel surface is not cleaned before use. The dynamic contact angle measurements were performed at room temperature under the open-air condition with a relative humidity of 45−50% by a CA goniometer, drop shape analysis system (DSA10-MK2, Krüss, Germany). B. Surface Evolver Simulation. To examine the difference between the experimental observation of the dynamic process and the equilibrium shape (without fluid flow), numerical simulations by the public domain finite element Surface Evolver (SE) package were conducted.26,27 The fundamental idea of SE is to minimize the free energy of the system subject to the constraint of constant volume. The drop surface is modeled as unions of triangles with vertices, and it is evolving down the energy gradient until a configuration with minimum energy is acquired. For a given snapshot of the spreading dynamics in our experiments, the dynamic contact angles on both the substrate (θ) and needle (θ′) can be determined. On the basis of θ and θ′, SE can be performed for a specified drop volume. The equilibrium shape is then
Figure 2. (a) Snapshots of the drop with a volume of 5 μL during the electrowetting process under a voltage of 1.5 V. Left column: side view. Right column: top view. (b) Variation of the contact angle (θ) and base diameter (d) of the spreading drop with a volume of 5 μL under a voltage of 1.5 V.
10 mM NaCl on stainless steel under a voltage of 1.5 V. The electrowetting process takes about 1 min, and there is no hydrolysis during the spreading period. The initial contact angle and base diameter of the drop are about 85° and 2.94 mm, respectively. After the electrical voltage is applied, the drop spreads gradually to the final state with a contact angle of about 30° and a wetting diameter of 4.65 mm. Because of the conservation of the drop volume, the height of the drop declines from 1.36 to 0.82 mm. Different from the electrowetting behavior on Teflon surfaces with weak contact angle hysteresis,28 the spread drop does not retract after the electrowetting process is complete. In fact, when the voltage is turned off at any stage, the expanding contact line stops and does not withdraw. Note that the irreversibility associated with EWOD has been reported29−31 and is attributed to surface roughness, trapped charge, or contact angle hysteresis. The presence of the steel needle disturbs the drop shape significantly so that the spherical cap cannot be maintained. The contact angle associated with the needle is actually altered from the 85° advancing contact angle to the 30° receding 3841
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Langmuir contact angle. These results are consistent with those observed on a steel substrate. Note that the contact angle of the steel surface in the presence of the needle is the same as that with the removal of the needle. The variations of the contact angle and base diameter of the spreading drop are illustrated in Figure 2b. The spreading response is overdamped. The transient behavior can be classified into three regimes. Right after the electrical voltage is applied, the drop spreads slowly in the first 5 s. It is identified as regime I. However, in the next 35 s, the spreading accelerates quite rapidly. The contact angle decreases sharply, but the base diameter grows rapidly. This is defined as regime II. After t = 40 s, the spreading behavior becomes insignificant. It seems that both the contact angle and base diameter approach plateaus gradually. Such a slow change is characterized as regime III. Note that the final contact angle is about 30°, which is consistent with the receding contact angle of the steel substrate determined by the deflation method. B. Slow Electrowetting Dynamics as a Quasi-Equilibrium Process. As demonstrated in the influence of fluid viscosity and the underdamped spreading response in the dynamics of EWOD,22 the hydrodynamics inside a drop may play an essential role. However, as the spreading dynamics is much slower than the relaxation of fluid motion, the electrowetting dynamics can be considered to be a quasiequilibrium process. In this work, the electrowetting process is slow because of ultralow voltage. As a result, each stage of electrowetting is close to thermodynamic equilibrium and can be characterized by static contact angles. As the voltage is turned off at any stage, the time-varying contact angle halts instantly and remains unchanged. That is, the relaxation of fluid motion inside the drop is fast, and thus the equilibrium state is reached quickly. This assumption of quasi-equilibrium can be further examined by the comparison between the dynamic observation and equilibrium simulation of Surface Evolver (SE). Figure 3a shows some images of the transient shape of the spreading drop and the corresponding SE simulation results, which are obtained by knowing the apparent contact angles on the substrate (θ) and on the needle (θ′) at a fixed drop volume. It is evident that the shape profile of the spreading drop can be well depicted by equilibrium simulations in which hydrodynamics is absent and only the hydrostatic pressure is involved in the Young−Laplace equation. The quantitative comparison is further made in Figure 3b, where the variations of both the base diameter and drop height with the apparent contact angle on the substrate (θ) are shown. Good agreement between the experimental and simulation outcomes indicates that the overdamped electrowetting dynamics in this work can be described by a quasi-equilibrium process. The quasi-state equilibrium evolution can be linked to the Tomotika time, which characterizes the time taken by a distorted interface to regain its equilibrium shape by the action of surface tension. It is estimated as τcapillary = ηR/γ = 3.9 × 10−5 s. Here R is the characteristic dimension of the surface and is represented by the drop size. Because the Tomotika time is small compared to the actuation time (about 1 min), the quasi-equilibrium assumption made in our analysis for electrowetting dynamics is justified. Note that the equilibrium SE simulation will fail to capture the transient shape of the drop with an underdamped spreading response if the dynamic pressure associated with fluid motion is significant.
Figure 3. (a) Comparison of the drop profiles between the experimental results and SE simulation outcomes for the volume of 5 μL and voltage of 1.5 V. Left column: experiment. Right column: simulation. (b) Comparison of the evolution of the geometric characteristic of the drop (contact angle (θ), base diameter (d), and height (h)) between the experimental results (symbols) and SE simulation outcomes (lines) for a volume of 5 μL and a voltage of 1.5 V.
C. Simple Model of Ultralow Electrowetting. In the electrowetting dynamics, the spreading behavior including the reduction of apparent contact angle and the growth of the base diameter is mainly driven by the electric field in the vicinity of the triple contact line according to the electromechanical theory.32 The droplet shape adjacent to the triple contact line is similar to the geometry of a wedge and therefore the electric fields and charges are concentrated close to the liquid−gas interface near the contact line. Because the electrostatic pressure on the liquid−gas interface is limited to a very small region, the electric force can be regarded as a point pulling force acting on the contact line outwardly. As a result, the shape of the droplet is still dominated by the hydrostatic pressure as shown in the previous section. According to our experimental results, it seems that the dynamic process can be classified into the stage prior to the exponential change and the stage associated with exponential change. When the voltage is applied, charges are accumulated on the metal side of the solid−liquid interface almost instantly. In the earlier stage, the electrostatic pressure is built up by the electric field and the charges in the neighborhood of the triple contact line. Because the local charge density is still small in the beginning, the changes in contact angle and base diameter are slow. As the time of voltage application proceeds, however, the electric field inside the drop drives counterions in the bulk to migrate toward the metal electrode and the liquid−gas interface 3842
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Langmuir near the contact line. That is, the local charge density grows with time and thereby the electrical pulling force is increased accordingly. In a later stage, the increment of the local charges near the contact line can be estimated by the loss of counterions in the bulk. Assume that the bulk counterion concentration and bulk volume are c(t) and Vl, respectively. The loss of counterions is caused by the electrical migration of counterions out of the bulk region. The migration velocity v is proportional to the electric field E, v = ME. Here, M denotes the electric mobility. The balance equation of the counterion in the bulk is then given by
Vl
dc = −vc dt
(1) Figure 4. Variation of cos θ − cos θ0 with U2 for a drop of 5 μL. In the inset, the variation of contact angle (θ) and base diameter (d) with drop volume (by the deflation method) is depicted to determine the receding contact angle.
The solution is simply ⎛ t⎞ c(t ) = c0 exp⎜ − ⎟ ⎝ τ⎠
(2)
where τ = Vl/v is inversely proportional to E and c0 depicts the concentration at the beginning of the second stage. To a first approximation, c 0 can be considered to be the bulk concentration, about 10 mM, because the number of ions driven to the contact line is still small in the first stage. The increment of the local charge density near the contact line σ(t) can be estimated from the sum of the initial charge density σ0 and the loss of ions in the bulk. Consequently, one has σ(t ) ≈ σ0 +
1 A
∫V [c0 − c(t )] dVl l
drop.34 In this work, the saturation angle is about θsat ≈ 30°, which is somehow the same as the receding contact angle (θr) determined from the deflation method35 as shown in the inset of Figure 4. Note that the needle size is small compared to the drop size and therefore the contact angle measurement is not disturbed by the needle. It is postulated that once the saturation voltage is reached, most of the ions are accumulated in the electric double layer near the electrodes at equilibrium. Because the charge carriers are absent in the bulk of the drop, the electric resistance reaches its maximum.34 In addition to affecting the equilibrium contact angle of electrowetting, the magnitude of the applied voltage also influence its dynamic process. As revealed by our simple theory, the spreading rate in terms of the relaxation time τ declines with increasing E. To explore the effects of the applied voltage on the spreading dynamics, the variations of the contact angle and base diameter of the drops were measured for U ranging from 0.8 to 1.75 V. Evidently, drops with high voltage arrived at the equilibrium condition faster than those with lower voltage. The earlier stage identified as regime I, as illustrated in Figure 2b, can be clearly shown through the semilogarithmic plot in Figure 5. During the first few seconds of electrowetting, the contact angle descends slowly from the advancing contact angle of 85° as shown in Figure 5a whereas the base diameter ascends gradually from 2.94 mm as depicted in Figure 5b. The period of regime I is decreased as the applied voltage is increased. Because the electrical pulling force is proportional to the electric field, it is anticipated that the movement of the contact line becomes faster for larger voltage. In the later stage identified as regime II, both the contact angle and base diameter experience a trend in exponential decay and reach their equilibrium state in regime III. The relaxation time τ can be determined from regime II of the dynamic process and varies from about 10 to 20 s. It is found that the relaxation time declines with increasing applied voltage. The variation of τ obtained from the contact angle with U is shown in Figure 5c while the plot of τ acquired from the base diameter against U is depicted in the inset. A linear relationship between τ and U is evidently seen. For both the data of the contact angle and base diameter, their slopes are consistent and have a value of −1. In accord with our simple theory, τ is inversely proportional to U because E is proportional to U. The good agreement between the theory and experimental results reveals that the main resistance to the spreading dynamics
(3)
where A is the area near the contact line region. By using eq 2, σ(t) can be expressed by ⎡ ⎛ t ⎞⎤ σ(t ) = σ0 + α⎢1 − exp⎜ − ⎟⎥ ⎝ τ ⎠⎦ ⎣
(4)
where α ≈ c0Vl/A is a positive constant. Because the electrical pulling force grows proportionally to σ(t), the base diameter is expected to increase accordingly. This simple model indicates that in the electrowetting dynamics process there exists a regime associated with exponential change due to ion migration. In addition to the base diameter, the contact angle can be approximately described by the exponential variation under the constraint of constant volume. The relaxation time τ represents the characteristic time scale of electrowetting and can be reduced by increasing the electric field. D. Effects of Electric Field. In the thermodynamic explanation of electrowetting based on the Lipmann−Young equation, the equilibrium contact angle is increased from cos θ0 to cos θ by CU2/2γ. Here, C represents the capacitance of the liquid/substrate interface, γ is the surface tension, and U is the applied voltage. In general, C comes mainly from the capacitance of the dielectric layer separating the bottom from the liquid. This result indicates that the increment of U leads to the decrease in θ. As demonstrated in Figure 4, cos θ − cos θ0 is proportional to U2 at low voltages. However, when the applied voltage is large enough (∼1.25 V), a saturation in the contact angle occurs. The contact angle saturation is generally observed in electrowetting. Although many explanations of contact angle saturation have been proposed, it is not yet clearly understood. Some explanations of contact angle saturation are plausible on steel surfaces under ultralow voltages, including the zero effective solid−liquid interfacial tension33 and increment of the electric resistance of the liquid 3843
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Figure 5. (a) Temporal evolution of the contact angle (θ) of the spreading drop under the applied voltage ranging from 0.8 to 1.75 V. (b) Temporal evolution of the base diameter (d) of the spreading drop under the applied voltage ranging from 0.8 to 1.75 V. (c) Variation of the characteristic times (τ) determined from contact angle measurements under the applied voltage ranging from 0.8 to 1.75 V. In the inset, the characteristic times (τ) are determined from base diameter measurements.
Figure 6. (a) Temporal evolution of the contact angle of the spreading drop with different volume ranging from 3 to 12 μL. Symbols: experimental results. Line: simulation outcomes with exponential decay. (b) Temporal evolution of the base diameter of the spreading drop with different volume ranging from 3 to 12 μL. Symbols: experimental results. Line: simulation outcomes with exponential decay. (c) Variation of the characteristic times (τ) determined from contact angle measurements with different volumes ranging from 3 to 12 μL. In the inset, the characteristic times (τ) are determined from base diameter measurements.
originates from the electrical migration of ions, and the increment in electric field enhances the migration velocity in regime II. E. Effects of Drop Size. It has been reported that the drop size can affect the spreading dynamics.22 Our simple model also reveals that the relaxation time can be altered by the drop volume associated with electrical migration resistance. To investigate the effects of the drop size on the electrowetting dynamics of drops, the variations of the contact angle and base diameter with time are measured. As designated in Figure 6 with an applied voltage of 1.25 V, the differences between the final value and the initial value, including contact angle Δθ = θ0 − θf and base diameter Δd = df − d0, are insensitive to the drop volume, ranging from 3 to 12 μL. That is, θf and df are
essentially determined by the applied voltage. However, the spreading dynamics does vary substantially with the drop size. It is evident that the drops with smaller volumes reach the final state faster than those with larger volumes. The influence of the drop size on the spreading dynamics is different in different regimes. As shown in the semilogarithmic plots of Figure 6a,b, the period of regime I grows as the drop volume is increased. Under the same voltage, the larger drop volume leads to a weaker electrical field in the drop, which results in a smaller electrical pulling force. The exponential changes in regime II are also identified in the variations of the contact angle and base diameter for different drop sizes. The 3844
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Langmuir relaxation time τ gained from the contact angle is depicted in Figure 6c whereas that attained from the base diameter is illustrated in the inset. Evidently, the relaxation time rises with increasing drop volume. Moreover, a linear relationship between τ and Vl is observed. This result is consistent with our simple theory and indicates that a larger liquid volume yields a greater resistance to ion migration.
(2) Frumkin, A.; Gorodetskaya, A.; Kabanov, B.; Nekrasov, N. Electrocapillary phenomena and the wetting of metals by electrolytic solutions. I. Phys. Z. Sowjetunion 1932, 1, 255−284. (3) Chen, L.; Bonaccurso, E. Electrowetting - From statics to dynamics. Adv. Colloid Interface Sci. 2014, 210, 2−12. (4) Hendriks, B. H. W.; Kuiper, S.; Van, A. M. A. J.; Renders, C. A.; Tukker, T. W. Electrowetting-Based Variable-Focus Lens for Miniature Systems. Opt. Rev. 2005, 12, 255−259. (5) Kuiper, S.; Hendriks, B. H. W. Variable-focus liquid lens for miniature cameras. Appl. Phys. Lett. 2004, 85, 1128−1130. (6) Shamai, R.; Andelman, D.; Berge, B.; Hayes, R. Water, electricity, and between...On electrowetting and its applications. Soft Matter 2008, 4, 38−45. (7) Hayes, R. A.; Feenstra, B. J. Video-speed electronic paper based on electrowetting. Nature 2003, 425, 383−385. (8) Fair, R. B. Digital microfluidics: is a true lab-on-a-chip possible? Microfluid. Nanofluid. 2007, 3, 245−281. (9) Miller, E. M.; Wheeler, A. R. Digital bioanalysis. Anal. Bioanal. Chem. 2009, 393, 419−426. (10) Cho, S. K.; Moon, H. J. Electrowetting on Dielectric (EWOD): New Tool for Bio/Micro Fluids Handling. Biochip J. 2008, 2, 79−96. (11) Mugele, F.; Baret, J.-C. Electrowetting: from basics to applications. J. Phys: Condens. Matter 2005, 17, R705−R714. (12) Cho, S. K.; Moon, H. J.; Kim, C. J. Creating, Transporting, Cutting, and Merging Liquid Droplets by Electrowetting-Based Actuation for Digital Microfluidic Circuits. J. Microelectromech. Syst. 2003, 12, 70−80. (13) Berge, B. Électrocapillarité et mouillage de films isolants par l’eau. CRAS 317 Série II 1993, 317, 157. (14) Peykov, V.; Quinn, A.; Ralston, J. Electrowetting: a model forcontact-angle saturation. Colloid Polym. Sci. 2000, 278, 789−93. (15) Quilliet, C.; Berge, B. Electrowetting: a recent outbreak. Curr. Opin. Colloid Interface Sci. 2001, 6, 34−39. (16) Blake, T. D.; Haynes, J. M. Kinetics of Liquid/Liquid Displacement. J. Colloid Interface Sci. 1969, 30, 421−423. (17) Blake, T. D.; Clarke, A.; Stattersfield, E. H. An Investigation of Electrostatic Assist in Dynamic Wetting. Langmuir 2000, 16, 2928− 2935. (18) Berge, B.; Peseux, J. Variable focal lens controlled by an external voltage: An application of electrowetting. Eur. Phys. J. E 2000, 3, 159− 163. (19) Decamps, C.; De Coninck, J. Dynamics of Spontaneous Spreading under Electrowetting Conditions. Langmuir 2000, 16, 10150−10153. (20) Bavière, R.; Boutet, J.; Fouillet, Y. Dynamics of droplet transportinduced by electrowetting actuation. Microfluid. Nanofluid. 2007, 4, 287−294. (21) Roques-Carmes, T.; Hayes, R. A.; Feenstra, B. J.; Schlangen, L. J. M. Liquid behavior inside a reflective display pixel based on electrowetting. J. Appl. Phys. 2004, 95, 4389−4396. (22) Hong, J.; Kim, Y. K.; Kang, K. H.; Oh, J. M.; Kang, I. S. Effects of Drop Size and Viscosity on Spreading Dynamics in DC Electrowetting. Langmuir 2013, 29, 9118−9125. (23) Kornyshev, A. A.; Kucernak, A. R.; Marinescu, M.; Monroe, C. W.; Sleightholme, A. E. S.; Urbakh, M. Ultra-Low-Voltage Electrowetting. J. Phys. Chem. C 2010, 114, 14885−14890. (24) Chen, L. Q.; Li, C. L.; van der Vegt, N. F. A.; Auernhammer, G. K.; Bonaccurso, E. Initial Electrospreading of Aqueous Electrolyte Drops. Phys. Rev. Lett. 2013, 110, 026103. (25) Annapragada, S. R.; Dash, S.; Garimella, S. V.; Murthy, J. Y. Dynamics of Droplet Motion under Electrowetting Actuation. Langmuir 2011, 27, 8198−8204. (26) Chou, T.-H.; Hong, S.-J.; Sheng, Y.-J.; Tsao, H.-K. Wetting Behavior of a Drop Atop Holes. J. Phys. Chem. B 2010, 114, 7509− 7515. (27) Wang, Z. J.; Chang, C.-C.; Hong, S.-J.; Sheng, Y.-J.; Tsao, H.-K. Capillary Rise in a Microchannel of Arbitrary Shape and Wettability:Hysteresis Loop. Langmuir 2012, 28, 16917−16926.
IV. CONCLUSIONS The spreading dynamics of a water droplet on stainless steel under ultralow voltage is investigated. It takes about 1 min to reach the equilibrium state, and no hydrolysis occurs. Once the applied voltage is switched off during the electrowetting process, the spread is halted and the drop does not retract. The spreading dynamics can be divided into three regimes: regime I, slow spreading; regime II, rapid growth of the base diameter; regime III, slowly reaching the plateau. The electrowetting dynamics can be explained by the electromechanical mechanism. In the beginning, the local density of ions near the contact line is small. The weak electrical pull leads to slow changes in the contact angle and base diameter. As time proceeds, ions migrate from the bulk to electrodes. As a result of the accumulation of charges in the vicinity of the contact line, the electrical pulling force is increased and gives rise to the rapid decay of the contact angle and the rapid growth of the base diameter. SE simulations are performed to compare the dynamic observation with the equilibrium shape. The agreement between the experimental results and simulation outcomes indicates that the overdamped electrowetting dynamics can be considered to be a quasi-equilibrium process. The effects of both electric field and drop size on the spreading dynamics are explored. It is found that the variation of both the contact angle and base diameter with time in regimes II and III can be well described by the exponential change with a characteristic time (τ) for the specified electric field and drop size. A simple model is proposed to depict such electrowetting dynamics. The charge accumulation near the contact line can be followed by the loss of ion concentration in the bulk of the drop. According to the exponential decay of the bulk density, the characteristic time grows with the drop volume but is inversely proportional to the electric field. The experimental results agree well with the prediction of our simple theory. When the applied voltage is high enough, the charge carriers are eventually absent in the bulk of the drop and the electric resistance reaches its maximum. Contact angle saturation is therefore observed.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail: [email protected]. *E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research work is supported by the Ministry of Science and Technology of Taiwan.
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REFERENCES
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