Electric Field Enhanced Spreading of Partially Wetting Thin Liquid

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Electric Field Enhanced Spreading of Partially Wetting Thin Liquid Films Soubhik Kumar Bhaumik,† Monojit Chakraborty,† Somnath Ghosh,† Suman Chakraborty,‡ and Sunando DasGupta*,† †

Department of Chemical Engineering and ‡Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, 721302, India ABSTRACT: Equilibrium and dynamic electrowetting behavior of ultrathin liquid films of surfactant (SDS) laden water over silicon substrate (with native oxide) is investigated. A nonobtrusive optical method, namely, image analyzing interferometry, is used to measure the meniscus profile, adsorbed film thickness, and the curvature of the capillary meniscus. Significant advancement of the contact line of the liquid meniscus, as a result of the application of electric field, is observed even at relatively lower values of applied voltages. The results clearly demonstrate the balance of intermolecular and surface forces with additional contribution from Maxwell stress at the interline. The singular nature of Maxwell stress is exploited in this analysis to model the equilibrium meniscus profile using the augmented Young
Laplace equation, leading to the in situ evaluation of the dispersion constant. The electrowetting dynamics has been explored by measuring the velocity of the advancing interline. The interplay of different forces at the interface is modeled using a control volume approach, leading to an expression for the interline velocity. The model-predicted interline velocities are successfully compared with the experimentally measured velocities. Beyond a critical voltage, contact line instability resulting in emission of droplets from the curved meniscus has been observed.

1. INTRODUCTION Thin films of partially wetting liquids are relevant in a number of applications including microscale cooling devices, adhesion, paints, etc. They are characterized by the formation of an extended meniscus. Interfacial stress fields determine the shape of the meniscus for isothermal conditions and control flow to replenish phase transfer for nonisothermal conditions. Characterization of the stress fields is therefore essential toward understanding and controlling the equilibrium and dynamic behavior of the meniscus, thereby improving the numerous potential applications. Interfacial stress fields include contributions from the longrange van der Waals dispersion forces between the solid and the liquid, termed as disjoining pressure1
3 and the capillary forces due to surface tension. An excess pressure at the interface created by these forces is described by the augmented Young
Laplace equation. Depending on the relative magnitude of the stress field components, three distinct regions of the meniscus are identified: an adsorbed layer controlled by disjoining pressure, a transition layer controlled by both the disjoining pressure and capillary forces, and a capillary meniscus controlled by the capillary forces only.4 The disjoining pressure has a suction potential and induces a flow toward the contact line. Several studies have been conducted on both the equilibrium and the dynamic behavior of the extended meniscus. A balance of stress fields across the length of the meniscus gives the equilibrium shape of the meniscus. Renk et al.5 used the method of r 2011 American Chemical Society

asymptotic expansions to predict the equilibrium shape of an isothermal meniscus and revealed a smooth transition from the capillary meniscus to the adsorbed layer. The thickness and curvature profiles were experimentally measured using interferometric techniques.6
9 Truong and Wayner10 calculated disjoining pressure theoretically using the DLP theory11 and obtained good agreement between theoretical prediction and experimental results. DasGupta et al.7 evaluated the dispersion constant, in situ, for heptane and pentane menisci on high refractive index glass. For nonisothermal conditions, flow and phase transfer were studied by many researchers using thermodynamics and fluid mechanics. Mass flow rate was related to the gradients of the interfacial stress fields using lubrication approximation. Potash and Wayner4 related the phase transfer to the stress fields following the Kelvin
Clapeyron model and concluded that the pressure drop resulting from the change in shape of the evaporating meniscus was sufficient to replenish the evaporating liquid. Wayner et al.12 calculated the heat transfer coefficient of the interline region of the meniscus. Due to their common dependence on the pressure field, flow and phase transfer were coupled to each other through conservation of mass.13
16 Moosman and Homsy13 used perturbation theory to study the sensitivity of the meniscus profile with respect to heat flux in the case Received: June 21, 2011 Revised: September 9, 2011 Published: September 12, 2011 12951

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Langmuir of a static isothermal profile. The effects of evaporation and condensation on the contact line dynamics have been studied by several researchers.17,18 Shanahan18 explained the spreading of water using the concept of supersaturation and local condensation at the contact line. A detailed review of the literature on flow boiling in small channels, with a focus on the variation of heat transfer coefficient with thermodynamic vapor quality, has been compiled by Garimella and his co-workers.19 It is therefore wellestablished that interfacial stress fields control the overall transport processes in the meniscus. Additional interfacial stress fields arise upon application of external electric fields in the form of Maxwell stress. A common configuration used for applying electric fields is electrowetting on dielectric (EWOD).20 In EWOD, electric fields are applied across a conducting liquid drop placed over a solid substrate with a dielectric layer in between. EWOD has emerged as a flexible method to actively control the wetting behavior of conductive liquids on partially wetting surfaces. Applications of EWOD include the areas of optics, such as adjustable focal lenses,21 liquid display technologies, as well as lab-on-a-chip systems. In the latter area, EWOD has become the most popular platform for so-called “digital” microfluidic systems that are based on the manipulation of discrete drops on microfluidic chip.22
24 Using a large number of individually addressable electrodes, EWOD allows for generating, moving, merging, splitting, mixing, etc., of individual drops. Flow in these systems is actuated through enhanced spreading caused by a reduction in the apparent contact angle. The reduction of apparent contact angle with applied voltage is given by the electrowetting equation,25 which utilizes the concept of a reduced effective liquid
solid interfacial tension caused due to capacitive energy introduced into the system. This thermodynamic or “electrochemical” approach is adequate for explaining EWOD at macroscopic scales and under equilibrium conditions. A detailed description of the microscopic contact line and its dynamics requires a mechanistic or “electromechanical” approach involving Maxwell stress due to the excess charge developed in the vicinity of the three-phase contact line.26
28 EWOD of droplets has been extensively studied in the literature, both experimentally and theoretically. Of late, significant attention has been devoted to investigate heat transfer mechanisms associated with the EWOD process as well. For instance, Kumari and Garimella29 investigated heat transfer during EW-induced droplet motion on a single plate and between two parallel plates, analyzing the heat dissipation capacity of such systems. However, despite the huge literature available on droplet-based electrowetting, electric field assisted spreading of partially wetting thin liquid films is yet to be explored in detail. One significant potential advantage of electrowetting of thin liquid films is the requirement of a lower actuation voltage. The reasons for this low actuation voltage are the low dielectric thickness (e.g., SiO2) leading to high capacitance and the low surface tension of the liquid used. The enhanced effects of electrowetting due to low surface tension have been observed in the case of EWOD of surfactant-laden water droplets on hydrophobic substrate.30,31 In such cases, contact angle reduction of 100° has been achieved with voltage as low as 3 V. This is a promising feature for microfluidic applications relying solely on capillary pumping for continuous supply of liquids. The aim of the present study is to explore the effect of electric field on the extended meniscus of partially wetting liquids under equilibrium and nonequilibrium conditions. The meniscus

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Figure 1. Schematic of the experimental setup with cross sectional view of the EWOD cell.

profile is experimentally measured using image analyzing interferometry. The response of the meniscus is assessed based on the advancement of the contact line at a location corresponding to the zeroth dark fringe or 0.1 μm film thickness (henceforth the term contact line refers to this location). The equilibrium studies reveal significant advancement of the contact line (∼100
150 μm) for voltages as low as 0
3.5 V. Use of an augmented Young
Laplace equation, to model the experimental data for film thickness, leads to the in situ evaluation of dispersion constant. The dynamics of the electrowetting is explored next by measuring the velocities of the moving contact line. The maximum velocity for 4 V has been observed to be 20 μm/s, significant for microfluidic applications. The interplay of the different forces at the interface is modeled using a control volume approach. Beyond a critical voltage, contact line instability leading to the ejection of microdroplets is observed. The observations and modeling demonstrate considerable promise of electric field enhanced spreading and wetting of partially wetting thin liquid films in microfluidic applications.

2. EXPERIMENTAL SECTION 2.1. Experimental Setup. The experimental setup along with the cross sectional view of the EWOD cell is illustrated in Figure 1. The EWOD cell consists of a bottom base assembly and a top cover with a Teflon gasket in between. The base assembly is essentially a stainless steel (SS) annular plate with a thin Teflon casing. A silicon wafer with an underlying conducting SS plate fits exactly into a sleeve provided at the inner end of the casing. On the top of the base assembly, a thicker Teflon gasket is placed on the Si wafer with additional O rings for sealing. The top cover is provided with a glass window for viewing the meniscus from the top and for optical measurements. A microtube inserted into a vertical hole in the upper plate allows controlled liquid feed to form a liquid pool on the wafer. A platinum wire is inserted through the side wall and is immersed in the liquid to serve as an electrode. The plate under the Si wafer serves as the other electrode. The whole assembly is mounted on a microscope stage below the objective along with a CCD camera on top. Silicon is used as the substrate due to its conductivity (1.56  10
3 S/m) and highly polished reflecting surface. The naturally occurring native oxide film on the silicon surface constitutes the dielectric layer. The low thickness of the native oxide leads to high capacitance and significant 12952

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EWOD at relatively low voltages. An aqueous solution of 0.1 M NaCl and 0.1 times the critical micellar concentration (cmc) of surfactant SDS is used as the conducting liquid. SDS surfactant enhances the wettability necessary to obtain discernible fringe patterns for interferometric studies. The surface tension of the solution has been measured as 0.033 N/m, using the pendant drop method. 2.2. Experimental Procedure. Due to its significant surface energy, Si surface is highly susceptible to contamination by adsorption from the ambient. Presence of adsorbed impurities prevents free motion of the meniscus by altering the surface energy and initiating pinning effects. Cleanliness is therefore extremely important for the accuracy and repeatability of the results. The entire cleaning procedure and assembling of the set up are performed in a Class 100 laminar flow hood. Si wafer is first cleaned using piranha solution (30% dilute H2O2 and 98% pure H2SO4 in the ratio of 1:1), thoroughly rinsed in deionized water, and dried in a jet of pure nitrogen. The cell is assembled and mounted on the microscope stage below the objective. The whole experimental setup is tilted by an angle 13° and connected to a DC supply. Monochromatic light of λ = 546 nm is used to illuminate the filmcovered Si surface. Using the CCD camera, an image of the bare surface of wafer is captured first, to be used as reference. An appropriate amount of solution is injected into the microtube such that a pool of liquid is formed halfway up the wafer and submerges the platinum wire. The pool is allowed to equilibrate. Naturally occurring interference fringes appear due to reflection of light from the liquid
vapor and the liquid
solid interfaces. Both equilibrium and dynamics of the meniscus behavior are studied as functions of the applied voltages. The range of voltage for the EWOD experiments was fixed on the basis of an estimate of the dielectric breakdown voltage obtained through separate experiments conducted on sessile droplets of 0.1 M NaCl solution on similar Si wafers with native oxide layer. The value of dielectric breakdown voltage was observed to be 12 V. For equilibrium studies, the meniscus is subjected to different applied voltages in the range of 0
3.5 V, which is well within the dielectric breakdown voltage of the SiO2 layer. The voltage is increased gradually in increments of 0.5 V. For each increment, the voltage is kept constant for considerable time, allowing the liquid to equilibrate. Images of the equilibrium meniscus for each voltage are captured. The flow of current is not detected (using an ammeter with a resolution of 1 microampere) during the experiments and the potential difference is kept well within 12 V. Dynamics of the electrowetting phenomenon is studied by capturing the video of the advancing meniscus in between the equilibrium states. Separate EWOD runs are conducted for 2, 4, and 6 V. For each run, continuous movies of the moving meniscus are captured using the CCD camera. From the movies, images of the meniscus are extracted at distinct intervals, using video converter software Xilisoft HD Video Converter (5.1), enabling frame by frame analysis of the advancing meniscus. The interface velocity is defined at a position corresponding to the film thickness of 0.1 μm and is measured at every 3 s using a frame by frame analysis of the captured video.32 The movement of the meniscus in a typical run lasts for about 30 s before the next equilibrium shape is attained. The velocity at time t is calculated as u¼

sðt þ ΔtÞ
sðt
ΔtÞ 2Δt

ð1Þ

where s(t) is the displacement of the interface at time t after voltage application and Δt is the time step for the central difference scheme (0.5 s). 2.3. Image Analysis. The reflectivity images captured from the microscope through the CCD camera are digitized into 626 (horizontal)  469 (vertical) pixels and assigned one of 256 possible gray values representing intensity from zero (black) to 255 (white). The gray value at each pixel is a measure of the reflectivity. Thus, each microscopic pixel acts as an individual light sensor to measure the local

film thickness. With the 20 objective and the CCD camera settings used in the experiments, each pixel represents the average reflectivity of a region of 0.29 μm diameter. For each image, line profiles of the gray values are extracted in a direction normal to the contact line, using Image-Pro-Plus software (version 6.0). The real peaks/valleys are identified by scanning after filtering noise from the raw data. The relative gray values are calculated by drawing interpolatory envelopes of maxima and minimas.7
9 Using the relation for relative gray value with thickness, thickness profiles are obtained from experimental data. The fact that the extended meniscus merges smoothly to an adsorbed flat film is used to estimate the adsorbed film thickness from the gray value data, the gray value corresponding to a bare surface, and the peak and valley envelopes. The error associated with the film thickness measurements are estimated to be (0.01 μm for the transition and capillary region of the meniscus and (10% for the adsorbed region.8,32 The slope and curvature are calculated on the basis of the first- and second-order derivatives of the thickness with respect to distance. The curvature attains a constant value once the effect of disjoining pressure becomes negligible. This has been shown by a number of experimental and theoretical studies.5
7,9,15 Therefore, the thickness data in the thicker portion of the film can be expressed by a seconddegree polynomial. For thinner zones, a higher order polynomial is used to capture the intricate details of the transport phenomena in the transition region along with the possible presence of curvature gradients.

3. RESULT AND DISCUSSION 3.1. Equilibrium Studies. Reflectivity images of the equilibrium meniscus at different applied voltages between 0 and 3.5 V are shown in Figure 2. With increasing voltage, the fringes move forward, indicating advancement of the contact line. A shift of 135 μm is observed for an applied voltage of 3.5 V. Along with the overall shift in the fringe pattern, interfringe spacings increase as well, indicating spreading and decrease in curvature, as will be discussed subsequently. The film retracts toward its original position on withdrawal of voltage, with marginal hysteresis in some cases. This is attributed to the pinning effects of the contact line region, especially around dust particles on the substrate when the voltage is progressively reduced. However, with repeated cleaning, the effects are minimized and reproducible data within the accuracy levels described before are obtained. The thickness profiles of the equilibrium meniscus are plotted in Figure 3 for applied voltages of 0, 2, and 3 V. The meniscus progressively advances with an increase in voltage. However, the thickness of the adsorbed layer remains approximately constant, implying that the Maxwell stress does not influence the flat adsorbed layer. It can be inferred that the Maxwell stress is singular at the junction of the curved meniscus with the flat adsorbed layer.33
36 The net effect can be visualized as a horizontal point force pulling the interline junction along the adsorbed layer without altering its thickness. The above mechanism is distinct from that of normal spreading, where the advancing front is accompanied by an increase in the thickness of the adsorbed layer.18,19 The incremental advancement of the contact line Δx0 (at position corresponding to a film thickness of 0.1 μm or zeroth fringe) is measured. A plot of Δx0 versus V2 (Figure 4) shows a straight line, indicating a quadratic relationship of displacement with voltage. The curvature profiles of the equilibrium meniscus for different values of applied voltages are plotted in Figure 5. The constant curvature at the capillary 12953

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Figure 2. Interferometric images of meniscus (an aqueous solution of 0.1 cmc SDS and 0.1 M NaCl) showing forward movement with applied potential at (a) 0 V, (b) 0.5 V, (c) 1.0 V, (d) 1.5 V, (e) 2.0 V, (f) 2.5 V, (g) 3.0 V, and (h) 3.5 V. Here B (h) minus A (a) is equal to 135 μm.

end of the meniscus decreases with an increase in applied voltage. The extended meniscus showing the various regions, namely, a flat adsorbed layer, a transition region, and a capillary meniscus, is illustrated in Figure 6. During electrowetting, fringe electric field present near the microscopic contact line (at the wedge like portion) induces charges at the liquid
vapor interface.26,27 For conducting liquid, tangential electric field components vanish, leaving only the normal components. The surface charge density, Fe is related to the electric field (E) as Fe = εE. The electrostatic interaction at the interface gives rise to an effective electrostatic pressure given as Pel ¼

1 2 εE 2

ð2Þ

where E =
3j is the electric field, j is the electrostatic potential, ε is the dielectric permittivity of the dielectric layer. Pel is a function of the local charge distribution which decays with distance (r) from the wedge tip or the interline junction with the flat adsorbed layer. Pel scales as Pel ∼ 1/r with its effect confined to a distance typically equal to the dielectric layer thickness.28,33
36 In the present case, the effect of Maxwell stress is highly localized (over a distance ∼50 Å) at the interline junction with the flat adsorbed layer and hence is too small to be resolved in the continuum limit. Using the augmented Young
Laplace equation, the pressure jump across the liquid
vapor interface at equilibrium can be expressed as Pl
Pv ¼

B d2 δ 4
σ 2 dx δ

ð3Þ

Figure 3. Equilibrium thickness profiles showing spreading of the meniscus with an increase in applied potential difference. The meniscus gets less steep, signifying a decrease in curvature at the thicker end.

where Pl is the liquid pressure, Pv is the pressure of vapor phase, σ is the surface tension, δ is the film thickness, x is the coordinate along the substrate, and B is the retarded dispersion constant. The first term represents the disjoining pressure, signifying the change in excess free energy per unit area with change in film thickness. Here disjoining pressure includes contributions only from the apolar London
van der Waals dispersion forces. Additional polar interactions37 are neglected due to the relatively high thickness of the liquid film. 12954

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Figure 6. Schematic diagram of the extended meniscus showing the action of Maxwell stress. Here ψ is the applied electric potential. The liquid
vapor interface and the liquid dielectric interface form equipotential surfaces. Charges get induced at the liquid vapor interface near the interline, giving rise to normal stress gradients, as shown by the arrows (exaggerated).

Figure 4. Effect of voltage on contact line displacement.

Figure 5. Curvature profiles of the equilibrium meniscus for different voltages.

The curvature assumes a constant value at the capillary meniscus. Using the methodology of DasGupta et al.,7 the augmented Young
Laplace equation is written for a point in the capillary meniscus and for another point in transition region. At equilibrium, the effective liquid pressure (Pl) is the same everywhere and the following equation applies σ

d2 δ B
¼ σK∞ dx2 δ4

ð4Þ

where K∞ is the constant curvature at the capillary end of the meniscus. During electrowetting, the effective pressure jump near the adsorbed thin film region comprises of the disjoining pressure augmented by the electrostatic pressure due to Maxwell stress. In order to account for this modified suction potential of the adsorbed region, the constant curvature at the capillary end of the meniscus decreases, as has been measured experimentally. These values of curvatures are used in the right-hand side of eq 4, and therefore, the effect of Maxwell stress is implicitly accounted for in the model equation.

Figure 7. Comparison of theoretical and experimental slopes for (a) 0 V and (b) 3 V.

The following nondimensional variables are introduced next to modify eq 4 to obtain eq 6: δ η¼ δ0 12955


1=2 K∞ Z¼x δ0

ð5Þ

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Figure 8. Reflectivity images for different temporal instants for an applied voltage of 4 V at (a) 0 s, (b) 6 s, (c) 12 s, (d) 18 s, (e) 24 s, and (f) 28 s.


 d2 η B 1 σ 2
¼1 dZ σK∞ δ0 4 η4

ð6Þ

Equations 4
6 are valid for an equilibrium condition when no evaporation or condensation is taking place and no heat is added to the system from outside, Q = 0. A dimensionless variable, α, is defined next α¼

B σK∞ δ0 4

ð7Þ

α is a measure of the deviation from the equilibrium situation because of sensitivity of the system to extremely small variations in the local temperature. For the equilibrium case, Q = 0 and α =1. Using the boundary condition that at η = α, dη/dZ = 0, eq 6 can be integrated to obtain the expression for the slope of the meniscus as rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dδ 2 α 8 ¼ ðK∞ δ0 Þ0:5 2η þ ð8Þ þ α dx 3 η4 3 Hence, if the curvature at the thicker end of the meniscus K∞, along with B, δ0, and σ are known, the slope can be directly calculated as a function of the film thickness, using only the augmented Young
Laplace equation. The value of parameter (α) corresponding to the closest match between theoretical and experimental slopes (Figure 7) is used to calculate the value of the dispersion constant, in situ for each of the voltages (0
3.5 V). The value of the retarded dispersion constant without electric field (V = 0) thus obtained is equal to
1.3  10
29 N m2. This value is compared against the theoretically calculated value of the

retarded dispersion constant calculated using the DLP theory for water, SiO2, and air systems.10,11,38 For an adsorbed layer thickness of 50 nm, the value predicted using DLP is
0.6  10
29 N m2, which is reasonably close to the in situ measured value. The presence of surfactant and NaCl in the experimental solution as well as traces of adsorbed impurities present can significantly lower the values of the dispersion constant, as has been reported by many researchers.9,10,39 The values of in situ dispersion constant at different electric fields (0
3.5 V) are tabulated, along with relevant parameters of the meniscus in Table 1. It can be seen that the value of B remains almost constant irrespective of the applied voltage. 3.2. Dynamic Studies. The velocities of the advancing film have been recorded until the time it reaches a new equilibrium position, as described in the Experimental Section. A typical sequence for 4 V is shown in Figure 8. The velocity versus time plot is shown in Figure 9 for different voltages. The meniscus velocity is initially high and drops steeply with time as the meniscus tends to attain a new equilibrium shape. The velocities are higher for higher voltages. This may be attributed to the higher magnitudes of Maxwell stress, which is a function of the applied voltage. The experimental observations of the present study clearly show a time scale of movement of the film that is large compared to the spreading of a drop in EWOD. As the system sizes becomes smaller, the surface area to volume ratio increases rapidly. As a result, the surface forces become important and the effects of inertial forces diminish progressively. Thus, an approximate order of magnitude analysis between the relevant forces present in the drop (of principal dimension in millimeters) and that of the ultrathin film (of principal 12956

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Table 1. Effect of EWOD on the Meniscus Parameters x0 (μm)

δo (nm)

K∞ (m
1)

α

B  1029 (N m2)

0

0

47

81

0.94


1.29

0.5

4.64

51

72

0.95


1.39

55

68

0.98


1.13

voltage (V)

1

11.6

1.5

22

59

55

0.91


1.32

2

34

55

54

0.90


1.23

2.5

50

51

53

0.92


1.35

3

74

51

45

0.96


1.37

135

53

35

0.95


1.32

3.5

Figure 10. Evolution of meniscus thickness profile with time, for an applied voltage of 4 V.

Figure 9. Interface velocity as a function of time for different applied voltages. The dotted lines are a guide to the reader’s eyes only.

dimension less than a micrometer) can be made to compare the system velocities under the application of electric field (Maxwell stresses) during EWOD. The velocity for the drop can be approximated (from a balance of the inertial and electrostatic forces) as u ∼ (ε0εr/2Fdh)1/2  V, where d is the dielectric thickness, εr the dielectric constant of the system, ε0 is the permittivity in a vacuum, h is the principal dimension of the drop (∼1 mm), and V is the applied voltage. On the other hand, the velocity of the ultrathin film can be obtained (from a balance of the viscous and electrostatic forces) as u ∼ (ε0εr/2μd)(V2h/l), where μ is the viscosity of the liquid and h is the thickness of the thin film (0.1
1 μm). Using typical values for the parameters it can be seen that the velocity scale of thin films is ∼1000 times smaller than that of the drops, and this explains the relatively sluggish response of the thin film to the application of electric field compared to typical values for droplets in electrowetting. A model based on the pressure gradients between the capillary meniscus and the adsorbed layer is developed to gain insight into the dynamics of flow in such thin films. It is clear that the curvature and hence the pressure gradient in the film changes continually during this process (Figures 10 and 11). A control volume spanning the meniscus region between the adsorbed layer and the capillary meniscus is considered herein. Since the momentum of mass in such a control volume is very low, a

Figure 11. Evolution of meniscus curvature profile with time, for an applied voltage of 4 V.

quasisteady state for all the time instants is assumed. Due to the small curvature, the zone is almost flat and the flow can be calculated on the basis of the lubrication approach as12 dPl d2 u ¼μ 2 dy dx

ð9Þ

Imposing boundary conditions of no shear at the interface and no slip at the wall, velocity distribution in the film is given as ! !
 2
 2 1 dPl y 1 Pcap
P2 y uðyÞ ¼
δy ≈
δy μ dx 2μ 2 Lmen 2 ð10Þ where Lmen refers to the length of the control volume, subscript 2 refers to the interline location near the adsorbed layer, and y 12957

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Figure 12. Comparison of theoretical and measured interline velocities during spreading, for an applied voltage of 4 V. The dotted line is a guide to the reader’s eyes only.

Figure 13. Contact line instability ejecting out satellite droplets.

refers to the distance normal to the substrate. The interfacial velocity is obtained as
 1 Pcap
P2 2 δ ð11Þ uint ¼
4μ Lmen where δ refers to the average film thickness in the control volume. The pressures Pcap and P2 are calculated using the augmented Young
Laplace equation (eq 3). The velocities can therefore be predicted from an analysis of the fringe data at any time instant by evaluating the pressure gradient using eq 3. It is to be noted that a uniform value of dispersion constant equal to
1.3  10
29 N m2 is used for all calculations. Here we consider the sequence for an applied potential difference of 4 V. The evaluated velocities are then compared with the measured velocities. Figure 12 shows the close match between the experimentally measured values of the interline velocity and that predicted from eq 11, for an applied voltage of 4 V. It is to be emphasized that the comparison is achieved without taking recourse of any adjustable parameter. The velocities initially increase, as the effect of Maxwell stress sets a forward motion of the film. However, the associated change in curvature at the thicker end of the meniscus acts as a stabilizing factor, thereby reducing the velocity until it attains the new equilibrium position. For an applied potential of 4 V, the maximum velocity attained is 20 μm/s and the advancing meniscus reaches a new equilibrium

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position after about 28 s at a distance of 287 μm. The significant movement of the film upon application of a relatively small voltage (compared to the EWOD of discrete drops) is encouraging for further application. 3.3. Effects at Higher Voltages. For voltages beyond 4 V, effects of electrowetting get more pronounced. Beyond 6 V, the contact line becomes unstable, ejecting small satellite liquid droplets with characteristic lateral spacing, and starts retracting spontaneously (Figure 13). Fringes clearly visible at lower values of the potential difference disappear, indicating high contact angle during retraction. This type of contact line instability has been previously reported.36,40
42 Beyond a threshold voltage, the surface tension can no longer balance the repulsion of like charges at the liquid vapor interface, resulting in emission of satellite droplets.28 The threshold voltage for onset of instability is a function of the surface tension. The loss of mass results in retraction of the meniscus. Liquid drops formed are stable as the capillary pressure acting inward counter the electrostatic forces acting outward. To some extent, this is the limit of stable operation of a device working on the principles of electric field enhanced spreading of liquid films and will depend on intrinsic factors like liquid
solid combination and their properties (e.g., surface tension) as well as external factors such as surface cleanliness and purity of the liquid.

4. CONCLUSIONS Enhanced spreading of a thin film of surfactant (0.1 cmc SDS) laden water (an aqueous solution of 0.1 M NaCl) on Si substrate, with the passivating oxide layer, at relatively low values of applied voltages is studied in detail. The shape, curvature, and other important parameters of the equilibrium meniscus at different applied voltages (0
3.5 V) are accurately measured using image analyzing interferometry and improved data analysis. The results clearly show considerable advancement of the meniscus front and reduction of curvature at the capillary end of the meniscus. The advancement for an applied voltage of 3.5 V is measured to be ∼135 μm. However, the adsorbed layer thickness remains almost unchanged. A force balance based on disjoining pressure and capillary pressure is used to examine the meniscus shape and to evaluate, in situ, the values of the dispersion constant. The effect of Maxwell stress during the advancement of the meniscus on the application of electric field is implicitly accounted for in the analysis through the drop in constant curvature at the capillary meniscus. The value of dispersion constant is obtained as
1.3  10
29 N m2 and is found to be invariant with the electric field. The dynamic behavior including the magnitude of the interface velocities of the moving meniscus is studied by frame by frame analysis of the interferometric images during advancement. The velocities for an applied voltage of 4 V are found to be as high as 20 μm/s. Using a control volume approach, an expression for velocity in terms of instantaneous pressure gradients (dispersion, capillary as well as the effects of Maxwell stress) is obtained, and the predicted velocities are successfully compared with the experimentally measured velocities. For higher voltages beyond 6 V, contact line instability is observed. ’ AUTHOR INFORMATION Corresponding Author

*E-mail [email protected]; sunando.dasgupta@gmail. com. 12958

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dx.doi.org/10.1021/la202317f |Langmuir 2011, 27, 12951–12959