Electro-dewetting and Wetting of an Extended Meniscus

Subscriber access provided by NAGOYA UNIV

Interfaces: Adsorption, Reactions, Films, Forces, Measurement Techniques, Charge Transfer, Electrochemistry, Electrocatalysis, Energy Production and Storage

Electro-dewetting and Wetting of an Extended Meniscus Sri Ganesh Subramanian, Monojit Chakraborty, Srinivas Tenneti, and Sunando DasGupta Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00967 • Publication Date (Web): 27 Jul 2018 Downloaded from http://pubs.acs.org on July 29, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Electro-dewetting and Wetting of an Extended Meniscus Sri Ganesh Subramanian, Monojit Chakraborty*, Srinivas Tenneti, Sunando DasGupta1 Department of Chemical Engineering, Indian Institute of Technology Kharagpur - 721302, India

*

Currently at the School of Mechanical Engineering and Birck Nanotechnology Center

Purdue University, West Lafayette, IN, 47907 USA 1

Corresponding author

Email: [email protected]; Ph: +91 - 3222 – 283922

1|P a g e

ACS Paragon Plus Environment

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 32

ABSTRACT: We report the intriguing movements of an extended liquid meniscus on a silicon substrate under the influence of sinusoidal AC voltages at different operating frequencies. As opposed to droplet electrowetting, wherein the droplet spreads and experiences oscillations at the free surface, the application of AC voltage to a thin liquid film results in distinct and uniform dewetting, in conjunction with augmented wetting. Image analyzing interferometry is used for the precise measurement of the film thickness profile, and other associated parameters. We postulate that the classical Young-Lipmann equation fails to explain the dynamics of an extended meniscus and evince that the dynamics of film displacement could be successfully explained by considering the product of the applied electric field and its gradient, as opposed to the existing consideration of a square dependence on the applied voltage. The physics of the hitherto unreported phenomena is elucidated by developing a mathematical model, taking into consideration all the germane forces governing the dynamics of the thin liquid film. We affirm that the present study would serve as a fundamental background for a fascinating mode of liquid actuation, with inherent application potential in several existing and novel microfluidic systems.

2|P a g e


Page 3 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

INTRODUCTION: Electrowetting1,2 has been associated with Microelectromechanical systems (MEMS) and Nanoelectromechanical systems (NEMS) due to its inherent potential for fluid manipulation at the microscale. Recently, the dynamics of electrowetting has been studied and applied for various operations involving paper,3 liquid infused films,4 storage and harvesting of energy,5 and hot-spot cooling6,7. Although droplets appear to be promising candidates for microfluidic operations, it would be more advantageous if there were a particular volume of liquid, which offers the benefits of a microfluidic regime and at the same time, possesses an inherently larger volume so as to cater to multiple demands simultaneously. One such interesting mode of liquid-handling at the microscale with additional application potential involves the use of thin liquid films (TLF)8,9. However unlike droplets, the application of TLF to microfluidic platforms and specifically for lab-on-a-chip devices is relatively unexplored. One of the intriguing phenomena associated with TLF is the Huh-Scriven paradox, wherein it was identified that the existence of a no-slip boundary condition for the case of an extended meniscus could induce extensive and unaccountable energy dissipation at the translating contact-line10. Alternatively, one plausible solution to the paradox is to carefully delineate the different regimes in a liquid meniscus and consider the relevant forces governing each element of the liquid11. Therefore, inspired by the multi-scale physics associated with the dynamics of TLF, studies pertaining to the response of a liquid meniscus subjected to thermal,12,13 electrical,14,15 and magnetic field16 have been reported. The aforementioned studies on the dynamics of TLF reflect the intricacies of the physics at the contact-line region of an extended meniscus, under certain perturbations; specifically, the electric field, and highlight the inherent potential associated with the direct applicability of TLF in microscale processes.

3|P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 32

It is well established that the existing theory on the electrowetting of droplets considers a square-dependency on the voltage for the contact-line motion, which in-turn is consistent with the Lippmann’s law6. The classical theory clearly underlines the fact that the effect of the electric field on the droplet would only result in its net spreading, irrespective of the polarity of the applied voltage. Moreover, the existing theory is inadequate to explain the experimentally observed dynamics of TLF, because of the multi-scale physics involved in the description of a TLF, wherein the applicable forces differ based on the varying orders of thicknesses along the meniscus. Therefore, the inherent multi-functionality of a TLF, coupled with the need to develop the governing dynamics for thin-film-electrowetting, forms the motivating factor to explore the response of TLF subjected to time-varying electrical potentials, e.g., “low-voltage and low-frequency (LVLF)” sinusoidal AC waveform. In the present study, we developed a theoretical model coupled with an aid from the simulation ambiance, for the successful explanation of the observed phenomena. The model includes the net effect of the electric field and its gradient, considering the appropriate forces pertinent to the different regions of an extended meniscus. Furthermore, we evince that the experimental observations of sequential wetting and dewetting of the TLF near the three-phase contactline, are significantly different from the existing works on TLF and droplets.

MATERIALS AND METHODS: The experimental system was similar to the previously reported studies on TLF.14,15 The system consists of a closed cell (Figure 1) enclosing a thoroughly cleaned silicon wafer, with an extended meniscus of a solution containing DI water, 0.1 M NaCl and 0.3 CMC sodium dodecyl sulfate (SDS) and a vapor space above the liquid. A minimum concentration (0.3 CMC) of the surfactant was chosen to realize an adequate reduction in the surface tension of the liquid while ensuring that at such lower concentration the Marangoni stress is not generated due to additional surface tension gradient. At this concentration, the surfactant 4|P a g e


Page 5 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

molecules, in presence of an external field, would not be able to generate additional tangential velocity, due to the fact that their rate of displacement is not sufficient enough to induce additional stresses in the extended meniscus.17–19 Furthermore, we affirm that irrespective of the type of the surfactant used (anionic, cationic, non-ionic), the dynamics of the extended meniscus would be qualitatively the same, due to the fact that the concentration of the surface active molecules is not sufficient enough to impel a secondary phenomenon.18,20 The main purpose of the closed cell is to isolate the system and minimize the influence of external perturbations and impurities, including dust particles from the surroundings, which otherwise would adversely affect the experiments. The addition of surfactant lowers the interfacial tension and promotes better spreading, and enhances the clarity for viewing and analyzing the film for the magnification used herein. The viscosity of the liquid was measured to be 9 × 10-4 (Pa. s), using a rheometer (Anton Paar MCR 302). The surface tension of the solution was measured by the pendant drop technique using a goniometer (290-G1 Ramehart™, Germany) and was found to be 33 mN/m. The curved liquid meniscus was continuously monitored using a CCD camera (LEICA™ DFC 450) mounted on a microscope (LEICA™ DM-LM) using a 20× objective, wherein each pixel of the digitized image represents an area with an equivalent diameter of 0.486 µm. Monochromatic light of wavelength (λ = 543.5 nm) was used as the light source. The silicon wafer (which is used as the substrate in the present work) possesses an inherently high surface energy, thereby making it highly vulnerable to contamination. Hence, stringent cleaning protocols were followed throughout the experiment. Every component of the experimental cell was left overnight in pure ethanol, for effective cleaning. The silicon wafer was subjected to Piranha cleaning by dipping it in a reactive mixture of 30% H2O2 with 98% pure H2SO4 in the proportion of 1:3 by volume, for the removal of organic contaminants from the surface of the wafer. The wafer was subsequently rinsed with DI water to remove traces 5|P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 32

of the Piranha solution, followed by rinsing in a mixture of 1:1 ethanol and DI water. The wafer was blow dried with hot air and filtered nitrogen alternatively and was finally placed under nitrogen blanket so as to prevent contamination. The setup was cleaned and assembled inside a Class-100 Laminar Flow Hood (MFD-V-W-2400, Micro Flow Devices India Private Limited) to ensure that the system was mostly free of dust particles.

Figure 1. Schematic of the experimental setup The liquid was introduced through a capillary tube (microtube in Figure 1), embedded into the Teflon spacer using a 10 ml syringe. The Teflon spacer and casing, ensure that the silicon wafer remains electrically insulated. Successful positioning of the system and further adjustment for proper viewing was accomplished by the use of LEICA™ FELM platform.

6|P a g e


Page 7 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

The entire sequence of the movement of the liquid film was recorded in the form of a movie clip, using the CCD camera. Images were extracted from the captured videos using Xilisoft HD video converter v.5.1 with a time interval of 0.05 s. The image resolution obtained for the 20× magnification was 1280×960 (pixels). The profile of the light intensity of each pixel, along a line perpendicular to the fringes, was expressed in terms of their gray values having the intensities in the range [0,255] using ImageJ

®

v. 2. In each image, the positions of the

dark fringes were located and compared with their corresponding positions in the subsequent image. This process was repeated for the whole length of the experimentation time. After obtaining the relative distance traveled by the film at any given instance of time, the instantaneous velocity, average velocity, and acceleration of the extended meniscus were all calculated using a MATLAB® (v. R2015 a) subroutine.

THEORETICAL MODEL Thin liquid films are generally divided into three regions: an adsorbed thin film region, wherein the intermolecular forces dominate; the capillary region, with a predominant capillary force, and the transition region, which lies medially between these two regions; as depicted in Figure 2(a).

7|P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 32

Figure 2. (a) Schematic of the thin liquid film on the silicon substrate. (b) Temporal variations in the applied field, its gradient, and the net force for the case of 1 Hz

The aforementioned multi-scale attributes of the TLF, coupled with a plane-wave form of an electric field (spatially and temporally varying electric field) have been carefully considered for developing the governing dynamics pertaining to the present case. In the present formulation, a plane-wave for the electrical field is considered because, unlike classical “Electrowetting-on-dielectric” (EWOD), wherein a relatively thick layer of dielectric (few microns in thickness) is spread over the substrate, the native oxide layer on the silicon substrate (with a thickness of 20-35 Å, measured using an ellipsometer: Sentech SE400adv) itself acts as the dielectric. More importantly, the thicknesses of the electric double layer (EDL), the dielectric, and the adsorbed thin film are all comparable in the present case. Hence, it is reasonable to consider the electrical field as a localized body force, along the entire adsorbed thin film region and a part of the transition region close to the contact-line (the entire region to the right-hand-side of the point - (2) in Figure 2 (a)), as opposed to the 8|P a g e


Page 9 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

electric field being considered as a point force (at the contact line), in droplet electrowetting.20 This consideration results in delineation of the formulation into two regions – one, that is not directly affected by the electrical field (the capillary region and the remaining part of the transition region), and the other being responsible for the contact-line movement (the adsorbed thin film region and a part of the transition region). A two-dimensional Cartesian coordinate system has been used for the present model, and the flow is assumed to be incompressible. A unidirectional electric field (x-direction) has been chosen as the dominant driving force. Since the electric field is considered to be a localized body force (due to the aforementioned reasons), the magnitude of the field is initially derived as follows (tensors are denoted in bold-face). From the fundamental Lorentz’ force law,21 r r r r F = q(E + v × B)

(1)

where, the force per unit volume is given as

r r r r f =σE + J×B

(2)

r where, σ is the charge density, q is the charge of a particle, v is the instantaneous velocity r of the particle, J is the current density of the medium. Applying Gauss’ law and Ampere’s law for the medium, r σ ∇⋅E =

(3)

r r r ∂E ∇ × B = µ J + µε ∂t

(4)

ε

r

where, µ and ε represent the permeability and permittivity of the medium, respectively. E

r

and B are the electric and magnetic fields respectively, and t denotes the time. Substituting equations (3) and (4) in (2),

9|P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 32

r r r r 1 r r  ∂E  r f = ε (∇.E)E + (∇ × B) × B − ε  ×B µ  ∂t 

(5)

Invoking Faraday’s law of induction, r r ∂B ∇×E = − ∂t

(6)

and the Poynting vector, which represents the directional energy flux density (the rate of energy transfer per unit area) of an electromagnetic field; r r r r ∂ r r ∂E r r ∂B ∂E r r (E × B ) = ×B + E× = × B − E × (∇ × E ) ∂t ∂t ∂t ∂t

(7)

Using Gauss’s law of magnetism and post-elimination of the curls, an equation is obtained comprising both the electric and magnetic field terms. Since the present formulation involves the effect of the electrical field alone, the magnetic field components have been neglected and the resultant equation can be written as: r r r r r r 1 f = ε (∇.E)E + (E.∇ )E  − ∇ (ε E 2 ) 2

(8)

Considering a one-dimensional plane wave type formulation for the electrical field21 r V E(x, t) = 0 sin ( kx − ω t ) iˆ

(9)

δ0

2π where k is the wave number   λ

 , λ is the wavelength corresponding to the frequency of  

the applied voltage, ω (= 2πf) denotes the angular frequency, f is the frequency of the wave,

δ 0 is the thickness of the native oxide layer, V0 denotes the applied voltage, and iˆ is the unit vector along the x-direction. It is to be noted that when we apply a voltage to the system, we are not specifically applying an x-directional field. The field is oriented along the three principal axes. For brevity, we define the co-ordinate system as follows: the x-direction is along the horizontal path, parallel to the substrate, the y-direction is along the upward direction and the z-direction is on the 10 | P a g e


Page 11 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

plane of the substrate but perpendicular to the principal direction of motion of the thin film. Upon application of an electric field, in presence of a dielectric, the charges in the dielectric would polarize and redistribute themselves,21 resulting in a change in the magnitude of the electric field (giving rise to a net electric field), which is proportional to the applied voltage, and inversely proportional to the thickness of the dielectric1,2,21,22 and the electric field is still oriented along the three principal axes. However, the forces due to the y and z directional electric fields are countered by the normal reaction forces from the bottom wall (the substrate) and the side-walls of the setup respectively, whereas the x-directional electric field could manifest along the extended meniscus. Therefore, although we have applied a general non-directional electric field, the resultant manifestation of the effective component is along the x-direction only. Hence the x-directional electric field was represented as depicted in equation (09). Substituting the relevant terms would yield the x-directional electrodynamic force as r ε V0 2 k G fx = sin ( 2kx − 2ω t ) = sin ( 2kx − 2ω t ) = Θ sin ( 2 kx − 2ω t ) 2 2 2 (δ 0 ) (δ 0 )

where, G =

ε V0 2 k 2

and Θ =

(10)

G

(δ 0 )

2

The above equation implies that although the electrodynamic force is proportional to the square of the voltage, the proportionality is different for the frequency part. We emphasize that the net effect of the electrodynamic force is not due to the applied electric field alone, but also due to its gradient. The reason for considering the gradient of the electric field, instead of a direct square-dependence, is solely because, for a complete sine wave, in the first quartercycle, the electric field is positive, and the gradient of the electric field is also positive (as depicted in Figure 2(b)). For the second quarter-cycle, although the electric field is positive, the gradient is negative, and this pattern repeats for the third and the fourth quarter-cycles as

11 | P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 32

well. Therefore, the product of the electric field and its gradient alternates between a positive and a negative value resulting in the forward and backward movement of the meniscus. Furthermore, numerical simulations also verified the reversal in the direction of motion of the film, thereby confirming the spatial variance of the electrical field, for a given frequency (see supplementary information – S1). The relative distribution of the electrical field along the length of the liquid meniscus results in a part of the film experiencing a net body force that alternates in accordance with the direction of the net force.1,23 This results in spreading and retraction of the liquid film, engendering the wetting and dewetting of the TLF on the substrate. Hence, we ascertain that the present formulation can be used to explain the retraction of the liquid meniscus which has been observed, in case of an input AC voltage, wherein the charge carriers reverse direction with time, for a specified operating frequency (as observed from the numerical simulations in the supplementary information - S1). The hydrodynamics of the TLF can be described by the application of lubrication theory, and neglecting the inertial terms in comparison to the viscous terms in the Stokes regime (see supplementary information – S2, for the initial steps in the theoretical model). The applicability of lubrication theory is also well justified, due to the nature of thin-film evolution along the spatial domain. To model the dynamics of the corresponding liquid flow, a control volume approach is used. The control volume for the present formulation is located between the points 1 and 2, in Figure 2(a) comprising of the liquid element between the capillary and adsorbed thin film regions. The governing equation for liquid flow in a thin film has been extensively studied by Potash and Wayner.12,24 Utilization of the lubrication theory and substitution of the relevant terms, would result in the transformation of the Navier-Stokes (x-component) equation into the generalized governing equation of the form,

12 | P a g e


Page 13 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

η

∂ 2u dP G = − ρ g sin (θ ) − sin ( 2kx − 2ωt ) 2 2 ∂y dx (δ 0 )

(11)

where, η is the dynamic viscosity of the liquid, ρ is the density of the liquid, g is the local acceleration due to gravity, θ is the angle of inclination of the setup with the horizontal, u is the component of velocity along the x-direction, P denotes the pressure and ( x, y ) are the local coordinates. The pressure gradient along the entire expanse (the region between the points 1 and 2, in Figure 2(a)) includes the contribution from both, the capillary region and the adsorbed thin film region. Therefore, the inclusion of intermolecular and surface tension forces (curvature obtained by considering the small slope approximation), would result in a pressure gradient of the form,

  2 2 2  dP ∂ ∂δ B εκ  4kT   zφ1   zφ2  −κδ  − = γ lv 2 − +    tanh   tanh  e 3 dx ∂x  123 6πδ 2 ze 4 4 ∂x { π       14444444244444443  II  I  III

(12)

where, γ lv is the surface tension at the liquid-vapor interface, B is the dispersion constant (between the silicon oxide and the liquid solution used in the present work),

∂ 2δ represents ∂x 2

 8π e 2 z 2 n  the curvature of the liquid meniscus, ε is the permittivity of the medium, κ 2 =   is  ε kT  the reciprocal of the Debye length for the case of symmetrical electrolytes, k is the Boltzmann constant, T is the absolute temperature, ze denotes the charge of an ionic species  eψ  in the solution, φ j =  j  where, j = 1, 2, and ψ j denotes the zeta potentials and kT  

δ represents the film thickness. It is to be noted that, in equation (12), the terms II and III

13 | P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 32

denote contributions from the Van der Waals’ component of disjoining pressure, and the electrostatic component of disjoining pressure respectively.25 We evaluated the magnitude of the electrostatic component of disjoining pressure and observed that it was at least 1-2 orders of magnitude lower than the van der Waals’ component of disjoining pressure. However, in order to capture the underlying physics, and to develop a generalized equation, both the terms are incorporated in the equation for disjoining pressure. Substitution of the relevant terms would result in the transformation of the Navier-Stokes (xcomponent) equation into the generalized governing equation of the form, I 64444444444447444444444444 8 II 8 2 6474 2 2  ∂  ∂δ B εκ  4kT   zφ1   zφ2  −κδ   +  γ lv 2 −   − ρ g sin (θ )   tanh   tanh  e 3  ∂x  ∂x 6 2 ze 4 4 πδ π       ∂ 2u   η 2 = −  ∂y III 64447444 8 { f (y) G − sin ( 2kx − 2ωt ) 2

(δ )

0 144444444444444 42444444444444444 3

≠ f (y)

(13) The body force term due to the applied electric field in the generalized equation (term III, on the right-hand-side of equation (13)), disappears for the case of droplets. This is due to the absence of a differentiating length-scale in droplets, wherein the electric double layer and the dielectric layer, have significant variation in their thicknesses. We conjecture that upon selection of the dominating terms via a comparative scaling analysis (see supplementary

information – S3), the present equation can be used to explain the dynamics of the droplets, as well. Since the right-hand-side of equation (13) is not a function of ‘y’, we could integrate the equation between appropriate limits, after incorporating certain simplifying conditions. It is

14 | P a g e


Page 15 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

to be noted that the term I of equation (13) signifies the pressure difference in the film due to its inherent spatiotemporal evolution, wherein different forces manifest themselves based on the thickness of the pertinent regions. On the other hand, term III could be construed as an electrodynamic pressure arising from the net electric field. Since the application of the timevarying voltage would substantiate itself by causing a net variation in the curvature of the liquid meniscus, we could, therefore, consider a dynamic coupling between the first and third terms on the right-hand side of equation (13), resulting in:

η

∂ 2u  ∂  = −  [ Pnet ] + ρ g sin (θ )  2 ∂y ∂x 1444 424444 3

(14)

f (x)

Therefore, the final equation for calculating the average velocity of the TLF (in accordance with the methodology reported in literature,14–16), could be obtained by integrating equation (14) with the appropriate boundary conditions (no slip at the wall, and no shear at the interface), and is given as,

U avg = −

U avg = −

U avg =

1

ηδ

δ

∫ 0

 y2  f (x)  − δ y dy  2 

δ2 [ f (x)] 3η

 δ 2  ( Π − γ lv K inf ) + ρ g sin (θ )   3η  ∆L 

(15)

where, Π is the net disjoining pressure (which includes contributions from both, Van der Waals and electrostatic disjoining pressures), ∆L is the distance between the capillary and adsorbed thin film region (between points 1 and 2 in Figure 2(a)) and Kinf denotes the experimentally obtained constant curvature of the capillary region for a set of specified operating conditions, which is a function of the applied voltage and frequency. 15 | P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 32

The in-situ evaluation of the dispersion constant (B) is performed at the start of the experiment, following an established methodology

15,26

and found to be – 6.4×10-29 N m2.

Taking an average value of the film thickness for the control volume, the contact-line velocities are obtained for all the experimental cases experiencing different magnitudes of the net force. We achieved an excellent agreement between the velocity calculated using equation (15) with the experimentally obtained one (error 1−4 %) as shown in Figure 3. The increase in velocity of the extended meniscus with the operating frequency is elucidated subsequently.

Figure 3. Comparison between the theoretical and experimental velocities of the TLF (The

dashed-line is only a guide to the reader’s eye)

16 | P a g e


Page 17 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

RESULTS AND DISCUSSION: We performed the entire sets of experiments between 1 Vpp (Voltage peak-to-peak) to 3 Vpp in steps of 1 Vpp and between 100 m Hz to 1 Hz in steps of 100 m Hz. Beyond 3Vpp, we observed instabilities along the contact-line region, which made it difficult to capture the images and analyze the phenomena. Beyond 1 Hz the dynamics of the film became very fast and could not be effectively captured with the present setup. The dynamic changes in the flow parameters such as velocity and acceleration as well as the thickness and curvature of the moving meniscus are evaluated as a function of both the applied voltage and the frequency. It is interesting to note that the film experiences a cyclic forward and backward motion and traverses the same distance in both the directions, implying negligible hysteresis. The physics pertaining to the movement of the thin liquid film has been elucidated by initially describing the dynamics at different instants of time, followed by selecting a dominant time-frame and comparing the dynamics of the extended meniscus, subjected to different voltage-frequency combinations. Oscillating Frequencies of the Liquid Meniscus:

Although it is well established that, the application of an AC voltage to a droplet would result in a significant decrease in hysteresis (when compared to the case of DC electrowetting),27–29 we observed (see Figure 4) that the effect of frequency-dominance is further intriguing in the case of thin liquid films, wherein the input and output frequencies corresponding to the film movement are almost the same (± 3-5% variance) (see Supplementary Information S4 and

S5). Unlike droplets subjected to a sinusoidal AC voltage, the frequency of the forward and backward movements of the extended meniscus was exactly equal to the input frequency of the AC voltage (implying negligible hysteresis). The input frequency was obtained from the function generator, whereas the output frequency was obtained by analyzing the dynamics of 17 | P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 32

the temporal film-displacement using a MATLAB subroutine, which measured the forward and backward distances traversed by the film and the corresponding time taken for the net movement. The measurements were repeated for 10 cycles for each of the voltage-frequency combinations. In case of droplets, the governing equation for AC Electrowetting is considered to have a square-dependence on the applied voltage1,20 and therefore for a given voltage, the maximum and minimum values of the electrodynamic force is purely dependent on the value of

D (1 − cos ( 2ωt ) ) , where D =

ε 0.ε r 2 V and hence, the range is between [0,2 D ].20 The output 2d γ lv

frequency of the droplet is calculated as the net displacement of the droplet from its initial equilibrium position, and the number of cycles it traverses per unit time, for a specific voltage. Therefore when the magnitude of the applied force lies between [0, 2 D ], the droplet would spread: once when the force ranges between [0, D ] and the second time when the force ranges between [ D , 2 D ]. Thus the output frequency is twice that of the input frequency because, irrespective of the input frequency, the drop always traverses the same distance twice in the same direction, owing to the nature of the resultant force. It is also fascinating to note that, given the correctness of the existing equation, the output electrodynamic force would have a relative magnitude range between [0, 1], which is only a part of the actual sine wave and cannot be used to explain the backward movement of the droplet or TLF. On the other hand, for the case of TLF, the range of the electrodynamic force is solely dependent on the sine of the angle for a given voltage with a range between [- Θ , Θ ] (equation (10)). Therefore the film traverses in the backward direction when the force is between [- Θ , 0] and in the forward direction when the force is between [0, Θ ]. Although the film traverses in both the directions, for a given direction, the film traverses only once owing to the magnitude of

18 | P a g e


Page 19 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

the resultant net force and therefore, the film has an output frequency, exactly matching the input frequency.

Figure 4. Variation in output frequency as a function of input frequency with applied

voltages. (The dashed-line is only a guide to the reader’s eye). Furthermore, in order to explore the effect of the residual surface-charge, we varied the pH of the solution from 1 to 11 (using diluted buffer solutions (Merck)) while maintaining the composition of the salt and surfactant constant. We observed no significant changes in the forward and backward movement of the meniscus. Film Thickness:

The thickness of the thin-film (as presented in Figure 5) is another important parameter to assess the concomitant effect of the frequency and the applied voltage on film-dynamics. For brevity, we classified the dynamics of the extended meniscus into three distinct instants, viz.

19 | P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 32

the initial, final and the peak time. The initial ( time0I ) and the final time ( timefI ), correspond to time depicting the characteristic behaviour of the film (film thickness, film curvature, and slope), at the beginning and the end of a specific frequency, respectively. Simply put, for the case of 100 mHz, the initial time corresponds to t = 0s, and the final time corresponds to t =10s. These two values help us in understanding how the film responds to the applied voltage, just at the beginning, and how the film comes to rest, at the end of each cycle. On the other hand, we observed that the film behaves in a slightly different manner when the time was (t =) 5s, that is, at the end of the first half-cycle and the beginning of the second halfcycle. We observed that, at the end of the first half-cycle, the film still experienced a forward movement, because it continued to respond to the forward half-cycle of the applied voltage, due to its forward momentum. However, the initiation of the backward half-cycle results in a localized accumulation of liquid along the film. In other words, the film experiences a rapid change in the direction of the impetus and accumulates locally for a short period of time. This accumulation causes an instantaneous increase in the thickness of the entire film and to highlight this phenomenon, the instant when the driving impetus changes its direction, is named as the peak time (‫݁݉݅ݐ‬P*) and the corresponding film thickness is termed as the peak film thickness. We also descried that the application of an AC voltage does not induce any significant hysteresis in the motion of the extended meniscus, therefore the behaviour of the film at time0I and timefI are identical. The variation in the peak film-thickness as a function of the operating frequency is presented in Figure 5(b). The observed variation in the dynamics of the extended meniscus could be attributed to the effect of viscosity, which is inherently dependent on the magnitude and duration of the applied voltage, for a given frequency. It is well established that the viscosity of a polar liquid would increase with the electric field, due to the local displacement of ions and their collective accumulation near the electrode (the solid-liquid interface).30–32 20 | P a g e


Page 21 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Furthermore, the augmentation in the value of viscosity is only possible provided the ions exhibit a net displacement from their initial position and accumulate at a particular expanse.31 For the case of time-varying electric potentials, the drift velocity of the ions may not be sufficiently large so as to displace the particles from their mean position, within the time period of oscillation. This is to mean that, if the time-period of oscillation is large enough (for the case of lower frequencies), the ions would be subjected to the actuating voltage for a significantly larger time, which would in-turn propel the ions to drift to a newer positions and cause accumulation, thereby resulting in an increase in the viscosity of the liquid. On the other hand, if the frequency of the applied voltage is sufficiently large (lower time period), the actuating voltage might not exert significant influence on the ions so as to cause a net drift, which could be sufficient enough to initiate any discernible change in the viscosity of the liquid. In order to evince this postulation for the present case, we compare the time period of the applied frequency and the drift-time for one of the species, viz. sodium ion. The drift velocity of sodium ion, for an applied voltage of 1 V (2 Vpp), and at 25o C is 5.19 × 10−8 m/s.33 The time taken for sodium ion to travel from the vapor-liquid interface of the transition region

td =

to

the

surface

of

the

silicon

wafer,

could

be

obtained

as:

LT 100 ×10 −9 ≈ ≈ 1.927 s ; where, td is the drift-time, LT is the characteristic length of vd 5.19 ×10−8

the transition region, and vd is the drift-velocity of sodium ion. Therefore, for the case of 100 mHz, the duration of the applied voltage per cycle is 10 s, which would imply that the forward and backward half-cycles have a respective duration of 5s; this time-span is significantly larger than the drift-time of sodium ions. On the other hand, for the case of 1 Hz, the duration of the applied voltage per cycle is about 1s, which is lower than the time taken for the sodium ions to drift from one place to the other. Therefore, the apparent increase in

21 | P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 32

the viscosity of the liquid, at the adsorbed film-region and a part of the transition region, would be relatively larger for the case of 100 mHz when compared to 1 Hz. Simply put, for the case of 100 mHz, the nature of film displacement could be attributed to the effect of viscosity, which would prolong the effect of the forward half-cycle, thereby causing a relatively slower accumulation of the fluid along the length of the film, which would consequentially result in a lower increase in the film thickness, at the peak-time. On the other hand, for the case of 1 Hz, the duration of the applied voltage per cycle is one order of magnitude lower than that of the previous case, and hence the net effect of retarding forces is not as impactful as that of the first case, and therefore a relatively larger rise in the filmthickness at a specific location is evident. These observations are in-line with the existing literature, wherein pronounced effects of an applied electric field and the operating frequency, on the dynamics of polar-liquids, have been observed and reported by various researchers.30,31

Figure 5. (a) Spatiotemporal variation of the film thickness at 100 m Hz and 3Vpp. The

legends are indicative of various instants of time (in seconds). (b) Effect of frequency on film thickness, for an applied voltage of 2 Vpp.

22 | P a g e


Page 23 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Film Curvature:

The film-curvature, velocity, and acceleration of the moving meniscus play an important role in understanding the dynamics of film-evolution and displacement, respectively. We observed as in14,15 that an increase in the curvature of the liquid meniscus at the capillary region resulted in a decrease in the thickness of the adsorbed thin film region (as depicted in Figure 6(a) and Table 1). We attribute this increase in film-curvature (at the peak-time) to the sudden change in the direction of the applied voltage, leading to a localized accumulation of liquid owing to its viscosity, 30–32 as stated previously. TABLE 1: Thickness of the adsorbed thin-film as a function of the applied voltage-

frequency combination Combination

Adsorbed Film Thickness (nm) Peak

Voltage Frequency (mHz) (Vpp)

(at maximum curvature and film

Final (at the end of one cycle)

thickness)

2

100

49

53

2

200

47

53

2

600

45

49

2

1000

43

49

The variation of the peak-curvature (curvature at peak-time) with different operating frequencies and applied voltages is depicted in Figure 6 (b and c), wherein we discern a clear 23 | P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 32

rise in the peak curvature with a decrease in frequency and increase in voltage. These results are in agreement with the theoretical model which demonstrates that there exists a region (the edge of the transition region and the entire adsorbed thin film region, as described previously), wherein the electric field manifests itself as a bulk force and hence results in the deformation of the curved meniscus.

Figure 6. (a) Dynamic variation in the film curvature as a function of the film thickness. The

legends are indicative of different instants of time (in seconds). Variation of peak-curvature at (b) Different frequencies and 2 Vpp and (c) Different voltages and 100 m Hz

24 | P a g e


Page 25 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Velocity and Acceleration of the Liquid Film:

The analysis of the present phenomena, led to the revelation of several fascinating dynamics, one such observation was that the velocity and acceleration of the liquid meniscus also follow a sinusoidal trend, as depicted in Figure 7 (a through d). The determination of the local velocity and acceleration of the liquid meniscus was accomplished by taking the first and second derivative of the film-displacement with respect to the time lapse as mentioned earlier.

25 | P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 32

Figure 7. Temporal variation in velocity and acceleration of the liquid meniscus as a function

of the applied voltage at a frequency of 1 Hz (a), (c) and the operating frequency (b), (d) at an applied voltage of 2 Vpp. It is to be noted that the difference in behavior of the curve at

100 mHz, is due to its significantly larger time period (10 s).

Interestingly, as predicted by our theoretical model, we descried an increase in the velocity of the thin-film with an increase in the applied voltage-frequency combination, as depicted in Figure 8 (a and b). This is due to the fact that, at the highest applied voltage, the magnitude of the driving force is the largest, and at the highest frequency, the viscous resistance is the lowest,30–32 thereby resulting in greater velocity and acceleration of the extended meniscus. We observed that the velocity of the liquid meniscus almost doubled, when the frequency is varied from 100 mHz to 1 Hz, for any given value of the applied voltage. The rise in acceleration is also more pronounced with an increase in the operating frequency. It is to be noted from the plots below (Figure 8), that the maximum value of the velocity and acceleration occurs for the 3Vpp and 1 Hz combination.

Figure 8. Effect of frequency and voltage on the (a) velocity and (b) acceleration of the

liquid meniscus 26 | P a g e


Page 27 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

These observations reveal the maneuverability of thin liquid films subjected to time-varying electric voltages and suggest that an extended meniscus could be manipulated in several ways, based on the nature of the impetus. We infer that the present and future studies on the dynamics of a liquid meniscus subjected to various waveforms of an AC voltage could be used for the design and fabrication of efficient microfluidic platforms, eliminating the need for internal mixers and complex fabrication procedures.

CONCLUSION: The dynamics of an extended meniscus was studied in presence of a sinusoidal AC electric field, wherein the film was found to move in both forward and backward directions, due to the nature of the resultant force acting on the meniscus. The variation in film parameters such as film thickness, curvature, velocity, and acceleration were studied as functions of the applied voltage and the operating frequency. The effect of the operating frequency was found to be more pronounced at lower values of the frequency, which resulted in slower velocities of the liquid meniscus. It was also observed that, unlike droplets, the output frequency of the TLF was exactly the same as that of the input frequency, as predicted by the theoretical formulation. The proposed model takes into account the spatial variation of the electric field and its gradient and hence suggests that the direction of motion of a TLF could be reversed resulting in partial dewetting of the substrate. The incorporation of all the germane forces governing the dynamics of a liquid meniscus has enabled us in developing a multi-functional mathematical formulation, that could be used to explain the dynamics of thin liquid films and those of droplets, as a limiting case. However, we note that the dynamics of an extended meniscus at higher frequencies (> 1 Hz) and ultra-low frequencies (< 100 mHz) are yet to be explored which would be a part of the future work. We also affirm that the negligible effect

27 | P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 32

of hysteresis, coupled with the ability to translate an extended meniscus in both the directions, will lay the background for novel applications in several microfluidic operations.

Acknowledgments: The authors gratefully acknowledge the financial support provided by the Indian Institute of Technology Kharagpur, India [Sanction Letter No.: IIT/SRIC/ATDC/CEM/2013-14/118, dated 19.12.2013]. Supporting Information: The supporting information consists of the results from the

numerical simulation; the initial steps associated with the theoretical model; a comparative scaling analysis of the governing equation demonstrating the applicability of the present formulation for the case of droplets as well; videos depicting the dynamics of the extended meniscus for two different frequencies, i.e. 1 Hz and 100 mHz while maintaining the voltage at a constant value of 2Vpp.

REFERENCES (1)

Mugele, F.; Baret, J.-C. Electrowetting: From Basics to Applications. J. Phys.

Condens. Matter 2005, 17 (28), R705–R774. (2)

Quilliet, C.; Berge, B. Electrowetting: A Recent Outbreak. Curr. Opin. Colloid

Interface Sci. 2001, 6 (1), 34–39. (3)

Kim, D. Y.; Steckl, A. J. Electrowetting on Paper for Electronic Paper Display. ACS

Appl. Mater. Interfaces 2010, 2 (11), 3318–3323. (4)

Hao, C.; Liu, Y.; Chen, X.; He, Y.; Li, Q.; Li, K. Y.; Wang, Z. Electrowetting on Liquid-Infused Film (EWOLF): Complete Reversibility and Controlled Droplet

28 | P a g e


Page 29 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Oscillation Suppression for Fast Optical Imaging. Sci. Rep. 2014, 4 (6846), 1–7. (5)

Krupenkin, T.; Taylor, J. A. Reverse Electrowetting as a New Approach to HighPower Energy Harvesting. Nat. Commun. 2011, 2 (448), 1–7.

(6)

Berthier, J. Micro-Drops and Digital Microfluidics, 2nd ed.; Elsevier: Oxford, 2013.

(7)

Paik, P. Y.; Pamula, V. K.; Chakrabarty, K. A Digital-Microfluidic Approach to Chip Cooling. IEEE Des. Test Comput. 2008, 25 (4), 372–391.

(8)

Craster, R. V.; Matar, O. K. Dynamics and Stability of Thin Liquid Films. Rev. Mod.

Phys. 2009, 81 (3), 1131–1198. (9)

Oron, A.; Davis, S. H.; Bankoff, S. G. Long-Scale Evolution of Thin Liquid Films.

Rev. Mod. Phys. 1997, 69 (3), 931–980. (10)

Huh;, C.; Scriven, L. E. Hydrodynamic Model of Steady Movement of a Solid / Liquid / Fluid Contact Line. J. Colloid Interface Sci. 1971, 35 (1), 85–101.

(11)

Bonn, D.; Eggers, J.; Indekeu, J.; Meunier, J. Wetting and Spreading. Rev. Mod. Phys. 2009, 81 (2), 739–805.

(12)

Potash, M.; Wayner, P. C. Evaporation from a Two-Dimensional Extended Meniscus.

Int. J. Heat Mass Transf. 1972, 15 (10), 1851–1863. (13)

Kundan, A. Condensation on Highly Superheated Surfaces : Unstable Thin Films in a Wickless Heat Pipe. Phys. Rev. Lett. 2017, 118 (094501), 1–6.

(14)

Bhaumik, S. K.; Chakraborty, M.; Ghosh, S.; Chakraborty, S.; Dasgupta, S. Electric Field Enhanced Spreading of Partially Wetting Thin Liquid Films. Langmuir 2011, 27, 12951–12959.

(15)

Chakraborty, M.; Chatterjee, R.; Ghosh, U. U.; Dasgupta, S. Electrowetting of

29 | P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 32

Partially Wetting Thin Nanofluid Films. Langmuir 2015, 31 (14), 4160–4168. (16)

Tenneti, S.; Subramanian, S. G.; Chakraborty, M.; Soni, G.; DasGupta, S. Magnetowetting of Ferrofluidic Thin Liquid Films. Sci. Rep. 2017, 7 (44738), 1–13.

(17)

Raccurt, O.; Berthier, J.; Clementz, P.; Borella, M.; Plissonnier, M. On the Influence of Surfactants in Electrowetting Systems. J. Micromechanics Microengineering 2007,

17, 2217–2223. (18)

Gurkov, T. D.; Dimitrova, D. T.; Marinova, K. G.; Bilke-crause, C.; Gerber, C.; Ivanov, I. B. Ionic Surfactants on Fluid Interfaces : Determination of the Adsorption ; Role of the Salt and the Type of the Hydrophobic Phase. Colloids Surfaces A

Physicochem. Eng. Asp. 2005, 261, 29–38. (19)

Karakashev, S. I.; Ivanov, I. B. Ionic Surfactants and Ion-Specific Effects : Adsorption , Micellization , Thin Liquid Films. In Surfactant Science and Technology: Retrospects

and Prospects; 2014; pp 1–70. (20)

Li, F.; Mugele, F. How to Make Sticky Surfaces Slippery : Contact Angle Hysteresis in Electrowetting with Alternating Voltage. Appl. Phys. Lett. 2008, 92 (244108), 1–3.

(21)

J, Griffiths, D. Introduction to Electrodynamics, 3rd ed.; Prentice Hall International: New Jersey, 1999.

(22)

Ramos Antonio. Electrokinetics and Electrohydrodynamics in Microsystems; Springer US: Italy, 2011.

(23)

Sharma, M.; Resta, R.; Car, R. Dipolar Correlations and the Dielectric Permittivity of Water. Phys. Rev. Lett. 2007, 98, 247401(1-4).

(24)

Wayner, P. C.; Kao, Y. K.; Lacroix, L. V. The Interline Heat-Transfer Coefficient of an Evaporating Wetting Film. Int. J. Heat Mass Transf. 1976, 19, 487–492. 30 | P a g e


Page 31 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(25)

Deryaguin, B.; Churaev, N.; Muller, V. Surface Forces; Kitchener, J. A., Ed.; Springer Science+Business Media LLC, 1985.

(26)

Derjaguin, B V, Churaev, N.V, Rabinovich, Y. . The Modern State of the Macroscopic Theory of Molecular Forces and the Results of Its Experimental Verification for Thin Interlayers. Adv. Colloid Interface Sci. 1988, 28, 197–244.

(27)

Hong, J. S.; Ko, S. H.; Kang, K. H.; Kang, I. S. A Numerical Investigation on AC Electrowetting of a Droplet. Microfluid. Nanofluidics 2008, 5 (2), 263–271.

(28)

Lee, J.; Park, J. K.; Hong, J.; Lee, S. J.; Kang, K. H.; Hwang, H. J. Nonlinear Oscillations of a Sessile Drop on a Hydrophobic Surface Induced by Ac Electrowetting. Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys. 2014, 90 (3), 33–36.

(29)

Nagiel, I.; Fair, R. AC Electrowetting Actuation of Droplets on a Digital Microfluidic Platform, Duke University, 2007.

(30)

Honda;, T.; Sasada, T. The Mechanism of Electroviscosity. I. Electrohydrodynamic Effect on Polar Liquids. Jpn. J. Appl. Phys. 1977, 16 (10), 1775–1783.

(31)

Andeade, E. N.; Dodd, C. The Effect of an Electric Field on the Viscosity of Liquids.

Proc. R. Soc. A Math. Phys. Eng. Sci. 1945, 187 (1010), 296–337. (32)

Johari, G. P. Effects of Electric Field on the Entropy , Viscosity , Relaxation Time , and Glass-Formation. J. Chem. Phys. 2013, 138 (154503), 1–7.

(33)

Koneshan, S.; Rasaiah, J. C.; Lynden-Bell, R. M.; Lee, S. H. Solvent Structure, Dynamics, and Ion Mobility in Aqueous Solutions at 25 °C. J. Phys. Chem. B 1998,

102 (21), 4193–4204.

31 | P a g e


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

GRAPHICAL ABSTRACT

100 μm

Wetting

De-wetting

100 μm

Fcapillary

FvdW

Fcapillary 1s

Electric Force

FvdW

6s

Electric Force 2.5 s

7.5 s

5s

10 s


Page 32 of 32

Electro-dewetting and Wetting of an Extended Meniscus

Recommend Documents