Field-assisted Contact Line Motion in Thin Films - ACS Publications

Subscriber access provided by Kaohsiung Medical University

Field-assisted Contact Line Motion in Thin Films Udita Uday Ghosh, and Sunando DasGupta Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b04322 • Publication Date (Web): 17 Apr 2018 Downloaded from http://pubs.acs.org on April 17, 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 40 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

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

Field-assisted Contact Line Motion in Thin Films

Udita Uday Ghosh and Sunando DasGupta* Chemical Engineering Department Indian Institute of Technology Kharagpur, India

*

Corresponding author e-mail: [email protected]

1 ACS Paragon Plus Environment

Page 2 of 40

Page 3 of 40 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

Abstract The balance of intermolecular and surface forces plays a critical role in the transport phenomena near the contact line region of an extended meniscus in several technologically important processes. Externally applied fields can alter the equilibrium and stability of the meniscus with concomitant effects on its shape, spreading characteristics and may even lead to an oscillation. This article provides a detailed account of the present and past efforts in exploring the behavior of curved thin liquid films, subjected to mild thermal perturbations, heat input, electrical and magnetic fields for pure as well as colloidal suspensions - including the effects of particle charge and polarity. The shape-dependent intermolecular force field has been evaluated in-situ, by a non-obtrusive optical technique utilizing the interference phenomena and subsequent image processing. The critical role of disjoining pressure is identified along with the determination of the Hamaker constant. The spatial and temporal variation of the capillary forces are evaluated for the advancing and receding meniscus. The Maxwell stress induced enhanced spreading during electrowetting, at relatively lower voltages, as well as that due to the application of magnetic field are discussed with their distinctly different characteristics and application potentials. The use of the augmented Young-Laplace equation elicited additional insights into the fundamental physics for flow in ultra-thin liquid films.


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

Introduction

The interplay and delicate balance of a number of forces near the three phase contact line, where the liquid, solid and the gas phases are in close proximity, plays a pivotal role in several technologically important processes. In most of the cases, the process dynamics and efficiency of a system are controlled by the transport phenomena taking place in the meniscus region of the extended thin film. These systems can be broadly categorized based on the final applications (a) Phase change processes involving boiling, evaporation, condensation and the associated surface cooling – Thin films of the liquid over a surface with elevated temperature plays a crucial role in the boiling process, encompassing the phenomena associated with the nucleation, growth and subsequent detachment of the bubble. The forces at the contact line are governed by the substrate properties which in turn heavily influence the bubble detachment phenomenon.

1–6

These forces are also of critical importance, as the system size gets

smaller and the surface forces start to dominate, as in microfluidic applications. For example, the shape change of the corner meniscus provides the suction for the continuous supply of the liquid towards the hot end of a micro heat-pipe that relies on the alternating evaporation-condensation cycles for heat dissipation. Moreover, the use of digital microfluidics to transport droplets of the coolant towards the hot spot and subsequent evaporation is being used for effective thermal management of electronic devices7–9 (b) Ink-jet printing, surface coatings, paints – Self-assembly of colloidal particles dispersed in liquids can be observed in a variety of everyday processes (e.g. the formation of a coffee stain). This basic phenomenon of solvent evaporation induced specific arrangement of particles is central to industrial processes like ink-jet printing, surface coatings and paints. The aesthetics and durability of the final products are governed by the contact line dynamics of the colloidal suspensions, the meniscus configurations and the physical characteristics of the meniscus (thickness, liquid nature etc.)10,11 (c) DNA linearization – A large number of diagnostic techniques and genome sequencing studies require manipulation of DNA strands. Primarily, this involves, linearization of DNA strands which necessitates coating the surface with a layer of straightened or linearized DNA. The quality of the coating processes are governed by the liquid meniscus characteristics which affect the 3 ACS Paragon Plus Environment

Page 4 of 40

Page 5 of 40 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

properties of the immobilized DNA strands on the surface12,13 Recent advancements also involve utilization of confinements for DNA stretching where in the dynamics of the liquid DNA source within the nano/micro-confinement plays an important role14 (d) Adhesives – Design of adhesives and manipulation of the strength of adhesion plays an integral part in many devices. These can be achieved by controlling the morphology of the liquid bridges formed when a liquid adheres to a substrate. Switchable adhesion devices inspired by the leaf beetle,15,16 have also been proposed. Thus, the dynamics of the contact line and the associated contact line dissipation17 are central to the transport processes for both the extended meniscus regions of partially wetting thin films as well as to the droplets undergoing shape changes18 under the influence of external forces.19 Thin films of partially wetting liquids are characterized by the formation of an extended meniscus with a non-evaporating adsorbed thin film, where intermolecular forces (e.g. the long-range van der Waal’s forces) dominate, a relatively thicker meniscus region, with capillary forces being prominent and a transition region in between. The evaluated curvature profiles clearly showed a flat film (zero curvature) in the adsorbed section and increases rapidly in the transition region and stabilizing to a constant value. The beginning of this constant curvature region is termed as the thicker end of the meniscus. Interfacial stress fields control the shape of the meniscus and the internal fluid flow to replenish phase transfer in non-isothermal conditions. Characterization of the stress fields is therefore essential towards the understanding of the equilibrium and dynamic behaviour of the meniscus, for successful applications. Liquid droplets have been studied extensively and its shape is closely related to the wetting state of the substrate - liquid combination. For a nearly non-wetting system, exhibiting a large contact angle, the liquid component retains its spherical shape owing to the effect of surface tension. Stability of thin liquid films is closely linked with their wetting properties and is an important aspect of investigation for complex fluids like polymers, liquid crystals, bio-fluids etc. The forces and the related mechanisms of film rupture have been covered elsewhere in a detailed dedicated review.20 The author mentioned two prevailing theoretical approaches to describe the van der Waals interactions between the condensed media, namely the microscopic 4 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 6 of 40

approach of London and Hamaker and the more rigorous, macroscopic, Lifshitz theory with the later providing better predictions for more complex dielectrics. Receding contact lines of such liquid films during dewetting and rupture are governed by the underlying dissipation routes/channels (hydrodynamic/molecular kinetic theory).21 However, the system of interest for the present article is the intermittent wetting system, wherein the liquid partially wets the solid to form a leading meniscus with a curvature that changes with the decreasing film thickness, essentially becoming equal to zero in the flat adsorbed portion of the extended meniscus. These three wetting states are shown schematically in Figure 1. For spherical surfaces, the pressure jump across the liquid-vapor interface is generally written as, ∆ P = Pl − Pv =

2σ R

(1)

where, σ is liquid-vapor interfacial tension and (R) is the radius of curvature. Equation (1) is the well-known Young Laplace equation (Thomas Young (1805) and PierreSimon Laplace (1806)).

Figure 1 Classification of (i) wetting scenarios based on the magnitudes of the contact angles (θ) as non-wetting, partially wetting and completely wetting films. The extended meniscus region (not to scale) can be observed for the partially wetting and wetting films and can be divided into three spatial regions in decreasing order of film thickness as capillary region, transition region and adsorbed region (ii) Disjoining pressure isotherms for (A) non-wetting (B) partially wetting and (C) complete wetting.


Page 7 of 40 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 Young Laplace equation works fairly well for droplets but for regions closer to the contact line, it fails to capture the necessary physics as additional forces, namely the long range intermolecular forces, start to play a dominant role. To incorporate the effect of these long-range van der Waals forces, and other intermolecular interactions in the intrinsic meniscus region, the Young Laplace equation is modified by including an additional pressure jump at the liquid-vapor interface (disjoining pressure). The additional term denotes the meniscus shape dependent interfacial force field and plays an important role in the spreading and transport in the extended meniscus. The modified equation is known as the augmented Young Laplace equation and will be further discussed in the next sections. The Disjoining Pressure The crossover from the bulk liquid to the intrinsic meniscus region is associated with a significant change in the length-scale, wherein the thickness of the thin film changes from sub-micron levels to a few hundreds of angstroms in the adsorbed portion of the extended meniscus. At this scale, the long-range intermolecular forces start to play an important role and to take into account their effect the concept of disjoining pressure was first introduced by Derjaguin22 as an equivalent pressure difference (Π) to be included to the Young-Laplace equation, defined as Π =−

A

(2)

δn

where δ is the film thickness and A is the modified Hamaker constant or the dispersion constant, depending on the thickness of the adsorbed film. The modified Hamaker constant, A is equal to A/6π, and n = 3 where the adsorbed film thickness is less than 500 Å. For higher thicknesses (retarded region), the dispersion constant B is to be used instead of the Hamaker constant with a value of n = 4. This additional pressure term is known as the ‘disjoining’ pressure which is a result of the interaction of the three phases leading to the separation of the solid and the vapor by an intervening liquid film. The values of the Hamaker (or the dispersion) constant is negative for a wetting film, signifying the predominance of the attractive forces between the liquid and solid substrate and positive for a non-wetting situation. The parameter A is the classical Hamaker constant, and its system specific value can be 6 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 8 of 40

estimated from the respective refractive indices and dielectric constants of the solid, liquid and vapor phases.23,24 Truong and Wayner

22

theoretically calculated both the

‘Hamaker constant’, A and the ‘retarded dispersion force constant’, B, as a function of the film thickness and have performed careful experiments that support the theoretically predicted trends. It was also shown that the value of the Hamaker constant (or the dispersion constant) gradually decreased with increase in the film thickness, e.g., reducing to a value of about one fifth (for a thickness of 100 nm) as compared to that for a thickness of 1 nm. It is to be noted that for the results reported in the present article, the values of the Hamaker/Dispersion constants were evaluated in situ for a specific system and then used for all experiments involving the system. It must be stated here that the expression given above (equation (2)) for disjoining pressure considers only the attractive van der Waals forces25, that are also called the dispersion forces. The origin of the van der Waals forces is quantum mechanical in nature and for a detailed discussion on this, the readers may refer to an excellent treatise by Israelachvili.26 It is to be mentioned that the effect of disjoining pressure reduces drastically with increase in film thickness and may not play a significant role for thicknesses above 50 nm. Some researchers mentioned values even lower than this and it was shown that even for non-polar liquids, the Lifshitz theory may break down for distances comparable to the molecular diameter of the liquids. Pioneering experiments by Horn and Israelachvili27 with mica surface and silicone oil octamethylcyclotetrasiloxane (OMCTS) showed the presence of oscillatory force wherein the force alternated between attraction and repulsion with separation distance. These oscillatory forces were termed as solvation or structural forces. Amplitude of the oscillatory force was found to increase drastically as the surfaces approached each other whereas the nature of decay of the oscillation was found to be a function of the bulk liquid property and fairly independent of the surface properties.28 Subsequently, the structural forces were also investigated in terms of the flexibility of the liquid molecule and the higher degree of molecular flexibility seemed to oppose the structure formation and its sustenance beyond the primary layers of liquid. Thus, two distinct behaviors were reported wherein long-range oscillatory solvation forces was observed for tetrachloromethane, benzene, cyclohexane, and OMCTS whereas iso-octane, n-octane exhibited short-range solvation forces.28,29 For a detailed discussion of the intermolecular forces in different systems, the reader is referred to the book by Israelachvili26 wherein it was also 7 ACS Paragon Plus Environment

Page 9 of 40 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

mentioned that “Repulsive van der Waals forces also occur across thin liquid hydrocarbon films in alumina and quartz. The thicknesses of such films were varied either by pressing a gas bubble in the liquid against the solid surface or by changing the vapor pressure above the film. The measured variation of the repulsive pressure with thickness in the range 0.5 to 80 nm was found to be in excellent agreement with theory. Once again, retardation effects are evident for films thicker than 5 nm.” It was

further noted that “such repulsive pressure is often referred to as the disjoining pressure of a film.”

However, the expression for disjoining pressure (equation (2)) is limited to non-polar liquids since for common polar liquids like water, the strong polarity leads to significant dipole-dipole interactions and the associated experimental data (optical and spectral data) for evaluation of Hamaker constant is scanty. There exists only a handful of studies which predict a logarithmic correlation30,31 of disjoining pressure with film thickness for polar liquids. The dominant dipole-dipole interactions in polar liquids give rise to the formation of a counter charge layer over a polar molecule, and these charged layers are cumulatively referred to as the electrical double layer. The attraction between two oppositely charged polar molecules and the repulsion between similarly charged polar molecules forms the second component of disjoining pressure32, commonly known as the electrostatic component. It is relevant in microdevices like micro-channels and in MEMS wherein charged wall surfaces with minimal inter-wall spacing causes overlapping of electrical double layers that affect the flow of liquids within such devices. The third component of the disjoining pressure33 arises from the ordering of molecules at the interface and is therefore liquid specific. It is of significance in polymolecular water films34, nanofluids35–40 and alcohols. For this particular component, the disjoining pressure isotherm for a film of thickness δ, assumes the following form:

Π s (δ ) = b exp (-δ /λ)

(3)

where, b and λ represent the magnitude and range of action of the forces, respectively. This particular form of disjoining pressure isotherm has been validated32 and the


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 40

substrate specific parametric values have been determined41 using experiments 42–45 as well as simulations. 46–53 The interactions between the three phases especially for long-chain molecules are yet to be addressed completely and may lead to inaccuracies in the estimation of disjoining pressure since all possible types of interactions are not included. Additionally, the thin film is a multi-scale entity and the limits of the bulk, transition and adsorbed region cannot be demarcated with confidence. Nanoscale models are better suited for the thinner adsorbed region whereas the continuum models can readily capture the physics in the bulk liquid. The transition region falls in a mesoscale and a single model incorporating the transport processes of the three regions is still absent and it is difficult to predict film thickness for a such a multi-scale system. The study of the transport processes in an extended meniscus is a multifaceted problem and a rapidly evolving area of research. The experiments require precise control of the conditions and the measurements need to be non-obtrusive (e.g., optical) to handle the extremely sensitive nature of the phenomena near the interline. It is worth mentioning that a temperature perturbation in the range of one hundredths of a centigrade is sufficient to cause the system to deviate from equilibrium with associated changes in the thickness and the shape of the extended meniscus. Additionally, another important parameter is the cleanliness of the system including the purity of the liquids used. The presence of even minute dust particles or adsorbed contaminants on the substrate significantly alters the substrate surface energy and subsequently the meniscus shape. A detailed discussion of the cleaning techniques normally used will be presented in the experimental section. The optical techniques used generally depend on the changes in the states of polarization of a circularly polarized light when it gets reflected from a film covered surface (ellipsometry)24 or the interference phenomena associated with reflection form a solid surface with a curved liquid film and subsequent analysis of the images (Image Analyzing Interferometry). The aim is to accurately measure the shape and dynamics of the thin film

at

equilibrium

and

under

the

effect

of

externally

applied

force-

fields/perturbations, for pure liquid thin films and colloidal films. The next section enumerates the experimental54 details.


Page 11 of 40 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

Experimental System A schematic of the generic experimental setup50–53 is shown in Figure 2, which was modified depending on the nature of the external perturbations (heat, electric or magnetic field) being applied. It comprised of a substrate (glass/ silicon wafer) with a pool of the working liquid (shown in yellow in Figure 2) in an enclosed experimental cell. The cell is made of two matching stainless steel (SS) plates, separated by Teflon gaskets and casing (creating a space for the liquid and its vapor above the working substrate), with a circular glass viewing port at the top. The enclosure with the Teflon gaskets and SS screws provides effective isolation of the substrate from the environment and the glass cover enables continuous visualization of the liquid film. The setup has the provision of attaching a strip heater (for thermal perturbation), electrical connections (for the use of electric field) depending upon the objective of the experiments. Surface energy of clean silicon surface is very high and it is prone to the accumulation of dust and surface contaminants. This severely interfered with the spreading of the liquid films and the interferometric fringes, compromising the accuracy of the measurements (undesired pinning of the contact line, patterns around dust particles, etc.). Hence, a rigorous cleaning protocol was followed involving surface contaminant elimination by piranha treatment that involved dipping the substrate in a mixture of sulfuric acid and hydrogen peroxide in a volumetric ratio of 3:1, followed by multiple wash in de-ionized water (Millipore, USA) and the working liquid, and subsequently drying in pure nitrogen. The thoroughly cleaned and dried experimental cell after being charged with the requisite amounts of the working liquid was placed under the microscope and the interferometric fringes were readily observed upon illumination by monochromatic light (λ = 546 nm).


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

Figure 2 Schematic of the experimental setup.

A number of techniques and instrumental methods have been utilized for visualization and film thickness measurement in the region close to the contact line that include interferometry,55,56 ellipsometry24 and confocal microscopy.57 Each method has its own advantages and limitations. For example, even though ellipsometry is an extremely accurate thickness measurement technique, it is not suitable for a curved meniscus (in the transition and the capillary region of the extended meniscus).

Figure 3 Algorithm for thin film thickness and curvature evaluation, where the different notations have the following meaning, G - gray value, G - relative gray value, RL reflectivity, δ - film thickness, K- curvature; nl, nv, ns are the refractive indices of the liquid, vapor and solid respectively, λ -wavelength of the monochromatic light used for illumination.


Page 12 of 40

Page 13 of 40 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

It has been shown that interferometry coupled with digitization and image analysis provides an efficient methodology for thickness measurement for the entire extended meniscus with high precision, especially in the transition region (± 0.01 µm). Therefore, the film characteristics (thickness, curvature and velocity) were evaluated using ‘Image Analysing Interferometry’ and the steps are briefly shown in the flow chart in Figure 3. Details of the process are available in the literature.54,56,58–60 It must be mentioned here that the effect of varying numerical aperture on the interfringe distance becomes significant for high numerical aperture microscope objectives.61 It is emphasized that for all the studies reported in this article, the microscope objectives used are either 10X or 20X with a numerical aperture of 0.25 and 0.4 respectively. Thus, for the values of the slopes, numerical aperture and surface tilt encountered in the present study, results can be used without incorporation of any corrections. Briefly, the method consisted of digitizing the reflectivity images into a large number of horizontal and vertical pixels and assigning one of 256 possible gray values representing intensity from zero (black) to 255 (white) to each pixel. Since the gray value at each pixel was a measure of the reflectivity, each microscopic pixel acted as an individual light sensor and was used in conjunction with the equations provided in Figure 3 to measure the film thickness at every pixel.56,58–60 For each image, line profiles of the gray values were extracted and the relative gray values are calculated by drawing interpolatory envelopes of maxima and minimas. Using the relation for relative gray value with thickness (shown in the schematic presented in Figure 3), the thickness profiles were obtained. The fact that the extended meniscus merged 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 was estimated to be ± 0.01 µm for the transition and capillary region of the meniscus and ± 10 % for the adsorbed region. Once the film thickness profile was accurately measured, the slope, curvature and other pertinent parameters could be evaluated. The video of the dynamic meniscus (in response to external perturbations) were analyzed


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

in a frame-by-frame manner to measure the velocities of the meniscus during spreading, retraction as well as during oscillatory motions.56,58–60

Figure 4 An overview of the factors influencing the behaviour of the extended liquid meniscus.

Effects of External Fields on the Meniscus Pure Liquids Thermal Perturbation – Evaporation/Condensation In a number of investigations,31,62,63 the transport processes within an extended film was studied to obtain the film thickness profiles, pressure and heat flux variations. The term interline was used to designate the junction of (adsorbed) non-evaporating thin film with the evaporating region. The ratio of the local to interline thickness was predicted and correlated to the interline heat-transfer coefficient. Interestingly, the heat transfer co-efficient showed significant variation near the interline. It was zero at the interline and increased significantly near the interline region and gradually decreased towards the thicker part of the film in the evaporating region.31,62,63 The subsequent studies established the role of disjoining pressure to model the pressure jump at the liquid-vapor interface with the help of the augmented Young Laplace equation24,63,64 which is expressed as,


Page 14 of 40

Page 15 of 40 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

Pl − Pv = − σ K −

A

(4)

δ3

In a carefully planned series of experiments, the extended meniscus was subjected to alternate cycles of evaporation and condensation.56 To realize this, a strip heater was intermittently (10minutes) used to supply heat and the film behavior was characterized. Subsequently, the strip heater was deactivated and the response of the film was noted again. The film was found to recede during the activated state of the heater (signifying evaporation) with a decrease in the adsorbed film thickness whereas it was found to move forward (with an increase in adsorbed film thickness) as soon as the heater was deactivated (condensation). These internal flows induced by the presence/absence of the thermal perturbation were principally governed by the curvature gradient within the film and the suction potential at the adsorbed section of the meniscus. The delicate balance between these two was expressed by a dimensionless parameter 'α' ( = 4 − B / σ K ∞δ 0 4 ) which denoted the ratio of the suction potential (− ⁄ ) to the capillary force ( ) as shown in Figure 5 during the evaporation/condensation cycle of a heptane meniscus on glass substrates. The points that lie in the region above the diagonal denote condensation since, the suction pull is more than the capillary pull and as a result of this imbalance, the film will move forward leading to an increase in the adsorbed film thickness (pertinent values are reported in Table I). Table I Variation of capillary pressure and suction potential for an extended meniscus subjected to thermal perturbations. δ0 (m-1)

B/δ04 (Pa)

K∞ (m-1)

σK∞ (Pa)

α = 4 − B/ σK∞ δ04

Near equilibrium

3.39×10-8

8.02

392.62

7.90

1.004

Evaporation

1.2×10-8

4.00

452.03

9.10

0.814

Condensation

3.9×10-8

5.57

258.77

5.21

1.017


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 40

It has been shown with a large number of images taken at very small-time intervals that it was possible to capture a case extremely close to equilibrium (the fifth point in Figure 5, with a value of α very close to unity. The slope of the film was expressed as a function of α as,

dδ 2 α4 8 = − ( K ∞ δ 0 ) 1/ 2 2η + − α ; η = δ δ0 dx 3 η3 3 where, K∞ and

(5)

δ0 are the capillary end curvature and the adsorbed film thickness

respectively. Herein, the value of α is evaluated by minimizing of error between the theoretically predicted and experimentally evaluated slopes. This in turn enabled evaluation of the Hamaker (or the dispersion) constant, the disjoining pressure and subsequently the net pressure gradient within the film.

Figure 5 (A) The interplay of the capillary force with the suction potential signifying condensation and evaporation for a thermally perturbed heptane meniscus on glass.56 (B) Decrease in the thickness of the adsorbed film on addition of heat to the system in zero gravitational field (horizontal substrate).65

The study established the utility of the augmented Young-Laplace equation in capturing the physics of the evaporation-condensation cycles as evidenced by the dimensionless parameter. The associated high heat transfer from the transition region underscored the importance of the extended meniscus as far as the overall efficiency of the heat transfer processes was concerned.36


Page 17 of 40 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

It must be also stated here that, the force per unit area acting on a film driven by Marangoni flow can be expressed as(equation 6)

τ=

d γ d γ dT = dx dT dx

66

, (6)

The contribution of the Marangoni flow can be estimated from the temperature gradient encountered in similar low heat flux situations which were of the order of 0.1 C/mm. Considering the length of the extended meniscus under consideration (O ∼ 100 µm), dT/dx was of the order of 10-2 ºC

67

. An order of magnitude analysis of the

relative effects of the Marangoni flow and curvature gradient induced flow has been performed, wherein it was found that the flow due to the curvature gradient was at least two orders of magnitude higher and thus the effect of surface tension gradient (Marangoni flows) on contact line movement was not taken into account. Numerical studies were also carried out to explore the transient response of thin films during evaporation and the results were compared with the experimental results68 wherein the spatial film thickness profiles were determined using a reflectometer. The effect of the disjoining pressure was included using the Gregory’s expression69 that accounted for the retardation and non-retardation effects. As expected intuitively, the decay in film thickness was exponential in the capillary and transition region albeit with distinctly different decay exponents. The response of the capillary region mapped closely with the experimentally measured results indicating that the basic transport mechanism is controlled by viscous forces.70 In a series of earlier publications,

71–73

not described herein, the effect of heat flux on

the liquid meniscus profile on a flat, horizontal surface were described in detail. It was demonstrated that with the addition of heat to the system, the thickness of the adsorbed film decreased drastically with a concomitant increase in the slope and curvature of the liquid meniscus (Figure 5(B). The capillary pumping capacity of an extended meniscus (in terms of capillarity and disjoining pressure) was evaluated through the introduction of a transport model based on the augmented Young-Laplace equation and kinetic theory. However, the studies presented in this article described the combined effect of the opposing body force (gravity, the set-up was always tilted at angle 13-15º) and the assistive capillary, suction potential and electric/magnetic 16 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

forces on the transport process and therefore the set-up was always tilted at angle 1315º. It must be stated here that the studies discussed so far are restricted to pure liquid films. Additional complexities are expected on the introduction of additional components, such as colloidal particles and will be addressed in the separately under 'Colloidal Films'. Corner Meniscus - Oscillations and Instabilities A Constrained Vapor Bubble Loop Thermosyphon (CVBLT), provides an interesting system to study the behavior of thin liquid films in a groove that plays an important part during the application of micro heat pipes and heat spreaders. Both analytical models74–76 and experimental studies67,77,78 (Figure 6(A)) were conducted to predict and measure the heat transfer characteristics of film evaporation on a microgroove surface and to optimize the groove design for the prediction of the onset of dry-out in such devices. However, the evaporating film started to show instabilities in the form of oscillations. This was explored in two novel experimental arrangements, a CVBLT and a vertical constrained vapor bubble, (VCVB) wherein the critical heat input that triggers meniscus instability and initiates oscillation of the meniscus was measured along with the film thickness and the meniscus shape dependent interfacial force field during oscillations.79,80 The working liquid was chosen to be pentane with a relative low boiling point of 36oC for the first study whereas for the second VCVB, HFE-7000 was used. The important parameters (contact angle, curvature, profiles for both the advancing and receding films) and the velocities of the oscillating film were measured. Three stages were observed during oscillation of the film upon subjecting it to increasing heat loads. The first stage showed the constancy of the contact angle for the heat input range of 0 to 0.88 W and a relatively stable film. In the second stage (heat input ~ 2.33W) the film remained stable, however the apparent contact angle increased to 2.4 ͦ with a distinct increase in curvature. The final stage for high heat input (~2.34W) is characterized by the onset of instabilities with oscillations in the contact angle about a mean value. A force balance for the oscillating meniscus involving the intermolecular, and shape governing forces were used to describe the oscillating velocity.


Page 18 of 40

Page 19 of 40 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

Films/ Menisci were found to recede towards the corner with an increase in heat load and at higher heat loads, film oscillation was observed. These oscillations were faster in the proximity of the heater and such oscillating films were characterized by the magnitude of the film velocity. A positive value of the film velocity / contact line velocity implied the film moved towards the flat film whereas a negative value implied movement towards the cell corner. This study79 was however restricted to film thickness greater than 0.1 µm since at higher velocity of oscillating meniscus, the evaluation of meniscus characteristics became difficult and inaccurate. In a subsequent study, oscillating menisci (HFE-7000) below thicknesses 0.1µm was been studied using interferometry.80 This enabled characterization of the adsorbed region. The thickness of the adsorbed region of an oscillating film in a CVB system increased with the advancement of the film and decreased during film recession (Figures 6 (C) and (D)). A single oscillation cycle comprised of an advancement (evaporation by heaters) and recession (condensation by coolers) of the film. The measured film movements and the generated internal pressure gradient that helped in driving the flow of the coolant liquid towards the corner showed marked oscillatory behavior at higher heat fluxes. The oscillating phenomena were described using a macroscopic interfacial force balance that relates the viscous losses to interfacial forces and the apparent contact angles.81


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

Figure 6 (A) Schematic of the experimental set up for constrained vapor bubble systems to study oscillating meniscus80 (B) Film thickness profiles79 at varying heat loads and at higher loads (indicated by arrows) the meniscus experiences oscillations. Curvature profile during an oscillation cycle showing meniscus (C1) Advancement 66 and (C2) Recession.66 Reproduced with permission from DasGupta et al.79,80

Contact line velocities of the oscillating film were obtained and were found to be directly proportional to the difference between the instantaneous force acting on the curved film and the reference force. Using an augmented Young-Laplace pressure jump model, the effect of the excess free energy at the contact line was established. The experimentally68 determined thickness profiles for Pentane meniscus as a function of applied heat input is shown in Figure 6 (B) and the theoretically predicted evaluations were in close agreement.


Page 20 of 40

Page 21 of 40 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

Applications of Electric Field – Without Evaporation Electrolyte containing droplets have been subjected to electric field to design efficient microscale devices.82,83 Such electric field induced droplet actuation has been traditionally studied using techniques such as ‘Electrowetting on a dielectric (EWOD)’84 and ‘di-electrophoresis’. In EWOD, a conducting electrolyte droplet is placed on a dielectric covered conductive substrate. In some cases, the dielectric layer is protected by an additional thin layer of hydrophobic coating (Teflon). On application of external voltage, the reduction in the substrate surface energy is manifested by a reduction in the droplet contact angle as it spreads to balance the effective interfacial tension at the liquid-dielectric layer interface. The study of the effect of the electric field on the extended meniscus of partially wetting liquids under equilibrium and non-equilibrium conditions is relatively recent and has opened up a new paradigm in electrowetting. The focus was on the electric field induced spreading of an extended meniscus on a dielectric covered conducting substrate. The results clearly demonstrated the delicate balance of the intermolecular and surface forces with additional contribution from the Maxwell stress at the contact line. The origin of the Maxwell stress is attributed to the excess charge developed in the vicinity of the three-phase contact line.84–86 It was shown that the effect of the applied electric field induced Maxwell stress was highly localized (over a distance ∼50 Å) at the interline junction and acted as a line force near the contact line resulting in enhanced spreading while maintaining the thickness of the flat adsorbed layer constant.58 To investigate the effect of electric field on partially wetting liquid films, the set-up in Figure 2 was modified by including the provision of precise application of electric field through two platinum wires – one dipped in the electrolyte solution and the other connected to the substrate (silicon) covered with a naturally occurring layer of native oxide (SiO2), of thickness in the range of 30-50 angstroms that acted as the dielectric. On application of voltage (0-3V) to the meniscus, the spacing between the consecutive fringes58 increased (Figure 7 (A)), indicating spreading of the film. This was accompanied by a concomitant decrease in the film curvature at the capillary end whereas the adsorbed layer thickness remained unaltered (Figure 7(B)).


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

Figure 7 (A) Experimentally observed increase in fringe spacing with an increase in applied voltage and the corresponding decrease in (B) capillary region curvature (C) enhancement in contact line spreading velocity with increase in driving force (applied voltage) (D) dynamic reduction in the capillary end curvature of a liquid meniscus at a specific applied voltage (4V). Reproduced with permission from DasGupta et al.,58

The velocity of the extended meniscus on application of the electric field was also evaluated by a frame-by-frame analysis of the video depicting the meniscus spreading. As the electric field induced Maxwell stress was the major driving force for the meniscus movement, the velocities were found to increase with an increase in the applied voltage (Figure 7(C)). For a specific voltage, the capillary end curvature reduced progressively with time indicating that the pressure gradient also varies temporally within the film (Figure 7(D)). The applied voltage could thus be used to modulate the physical and dynamic characteristics (shape and spreading) of the meniscus for a specific liquid and substrate combination. To incorporate the effect of the applied field, the electrostatic pressure induced change in the capillary film shape and thickness were measured experimentally and used for the evaluation of the effective pressure with the help of the augmented Young-Laplace equation. The electric field induced enhanced wetting of a partially wetting film and the associated flow was distinguished by negligible hysteresis and increase in the efficiency of the


Page 22 of 40

Page 23 of 40 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

electrowetting process. Additionally, the magnitude of voltage required for thin film spreading were about an order or two lesser in magnitude (few volts compared to tens of volts, even hundred volts) as compared to that for droplet actuation. Electrowetting of Evaporating Meniscus The concurrent effects of the evaporation induced retraction and electric field induced spreading of an extended evaporating meniscus was further explored in a related study57 with water containing a surfactant SDS (sodium dodecyl sulfate of 0.1 critical micellar concentration) as the working fluid. The surfactant was used to enhance the spreading of the meniscus and to obtain sharp interferometric fringes for further processing. On switching the strip heater, recession of the meniscus started immediately. The retraction of the meniscus was clearly evident (Figure 8(A)) with a decrease in the inter-fringe spacing and concomitant increase in the curvature at the thicker end of the meniscus. Once the film assumed a new position after retraction, in response to the applied heat load, an electric field was applied in increments of 2V up to a maximum of 8V. Electrowetting acted counter to the recession of the evaporating meniscus and caused the film to advance and reached a new location at steady state that was ahead of the initial location (at zero heat flux), completely countering the effect of the heat induced retraction of the meniscus for low heat fluxes (Q1= 0.12 W, Q2= 0.24 W).


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

Figure 8 (A) Interferometric images showing the recession during evaporation of liquid menisci countered by the advancement of the meniscus on application of electric field (B) Displacement of the meniscus with increasing voltages at specific heat loads, Q1= 0.12 W, Q2= 0.24 W and Q3 = 0.33 W. The vertical line at ∆x0 = 0 indicates the reference meniscus position in absence of applied electric field and heat flux. Reproduced with permission from DasGupta et al.,87

It was also observed that the curvature at the thicker end of the meniscus decreased progressively with increase in the applied voltage denoting electric field assisted spreading of the meniscus. The augmented Young–Laplace equation was used to model the interfacial phase transfer using lubrication approximation to obtain the mass flow rate, in a slightly tapered thin film. The interfacial mass flux was expressed as functions of the superheat, pressure jump, and the film thickness. The resulting model equations were solved numerically and compared with the experimental data to obtain an in situ estimate of the modified Hamaker constant and demonstrate appreciable enhancement of the mass and evaporative flux during electrowetting. Thus the beneficial effect of electrowetting at relatively low voltages (as compared to electrowetting on dielectric) worked in tandem with the suction potential of thin films and would be beneficial for hot-spot cooling. The strategy can be used for effective


Page 24 of 40

Page 25 of 40 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

heat dissipation from electronic components, highlighting the potential of electrowetting in micro-cooling applications. Colloidal Films Effect of Colloidal Particles on Thin Film Dynamics Colloidal suspensions play a major role in several industrial processes10,88 like surface coatings, paints and inkjet printing.89 The presence of the particles may significantly alter the interfacial transport processes in an extended meniscus and ultimately play a role in the rupture or cracking of thin films upon drying that reduces the quality and durability of such coatings. The presence of particles may give rise, among others, evaporation induced assembly of deposited colloidal particles. A prime example of such particle deposition pattern being the coffee ring effect, the shape and presence of which is increasingly being used in a number of detection and quantification studies. Various factors influence the process of thin film dynamics of colloidal systems - the prime examples are the wetting nature of the substrate, that of the liquid (polar or apolar) and the size of the particles along with their surface charges. The analysis of the change in the contact line dynamics of an extended meniscus of a colloidal suspension of both polar and apolar liquids would therefore be interesting from both fundamental and application point of view. To conduct these sensitive experiments, the existing system (Figure 2) was used with the meniscus of a dispersion of colloidal particles in liquids of different natures. The individual response of each of these three components (the particle, substrate and the liquid) and their cumulative interactions determined the shape of the liquid meniscus and controlled the evaporation. The gradual evolution of the meniscus shape with the corresponding movement of the contact line for colloidal films was investigated as a function of different particle diameters (0.055 µm; 1µm) and liquid polarity (apolar isopropyl alcohol (IPA) and relatively polar, water as the experimental liquids).60 The experimental procedure comprised of placing known volumes of the diluted colloidal suspensions in the form of droplets (1µL, 0.01(w/w) %) on the freshly cleaned silicon wafers and the evaporating colloidal films were observed using optical microscopy. Introduction of colloidal particles altered the film thickness at the capillary region, the film thickness increased further with an increase in particle diameters from 0.055 µm to 1µm. Similar effects could also be observed by 24 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 26 of 40

increasing the polarity of the liquid. The capillary region curvature (K ͚) also increased with particle addition and increase in liquid polarity, keeping in tune with the film thickness trend (Table II). Table II Variation in film thickness and curvature on introduction of colloidal particles in polar and apolar liquids. Particle Diameter

Percentage increase in capillary region curvature (K ͚ )

0.055µm

1µm

Apolar (IPA)

16.15 %

31.62%

Polar (Water)

53.20 %

60.74%

These changes in the film curvature were a reflection of the imbalance in the internal pressure in the film. This was shown to be caused by the electrostatic component of the disjoining pressure (Π) that dominated the process as the liquid polarity increased, whereas the structuring of the particles also contributes towards an additional increase in the disjoining pressure. An amalgamation of these effects led to an increase in the disjoining pressure with the introduction of particles and in a relatively polar liquid as predicted by the augmented Young-Laplace equation (shown in Figure 9(A)).

Figure 9 (A) Enhancement in the disjoining pressure on addition of particles and with an increase in the liquid polarity and (B) corresponding reduction in contact line velocity (Uf). The symbols ▲ and ■ represent IPA and water respectively. Reproduced with permission from DasGupta et al.60


Page 27 of 40 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 internal pressure imbalance provided the necessary spatial pressure gradient that drove the contact line dynamics. Therefore, an increase in the disjoining pressure also implied that the effective driving force within the film decreases on introduction of the colloidal particles and with an increase in solvent polarity. Thus, the reduction in the effective driving force led to a decline in the contact line velocity (Uf) which was in close agreement with the experimentally obtained trends shown in Figure 9(B). Electrowetting of Nanofluid Films Previous studies point to a decrease in the contact angle and the actuation voltage along with an increase in wetting90 during EWOD of droplets containing nanoparticles, postulated to be caused by the modification of the interfacial energy due to nanoparticle adsorption at the solid−liquid interface.91 With an increase in the particle concentration, the actuation voltages were lowered because of the altered effective permittivity of the system. Another interesting aspect was the absence of contact angle saturation92 and together they highlighted the altered electrowetting behaviour of droplets of nanofluids in EWOD. It was envisaged that the electrowetting phenomena of a partially wetting liquid meniscus would likewise be substantially altered in terms of the spreading and contact line dynamics, if nanoparticles (charged and uncharged) were present in the solution.59 The study also explored the effect of the polarity reversal of the electrodes and the effect of particle properties on the contact line velocity and characteristics of the electrowetted meniscus. The major results are presented in Figure 10. The primary configuration of the electrowetting setup as shown in Figure 10 (A) comprised of a platinum wire, acting as one of the electrodes and being connected to the negative end of the power source (Configuration I) whereas in the reversed polarity configuration, Configuration II, the platinum wire was connected to the positive end of the source. Clear advancement of the meniscus on introduction of the nanoparticles was observed and magnitude of this advancement increased further upon application of electric field. The same trend could be noticed for the contact line velocity wherein the introduction of the nanoparticles and the application of electric field worked in unison to enhance the velocity. .


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

Figure 10 (A) Configuration of the electrowetting setup for studying the effect of reversal of electrode polarity (B) Contact line velocity variation in presence of nanoparticles(30 nm in diameter, carboxylate modified, 0.05% (w/w)) and electric field. Reproduced with permission from DasGupta et al.59

In the electrolyte-surfactant nanosuspension, negatively charged nanoparticles were surrounded by a layer of positive counter-ions and the polarity of the electrode governed the direction of migration of these anions. This gave rise to two distinct situations in Configuration I, these anions moved rapidly towards the adsorbed thin region and this flow also dragged the liquid in the same direction. This flow, depending on the polarity of the platinum wire electrode, would add to or oppose the electric field induced (Maxwell stress) flow which was intrinsically directed towards the contact line. On reversal of polarity, the anions dragged the fluid towards the capillary region, opposing the electric field induced flow and thus, the overall contact line velocity underwent a reduction as represented in Figure 10 (B). Additionally, the effects of the physical size of the particles (diameter) and the particle weight fraction on the phenomena were reported. A decrease in particle diameter or decrease in particle concentration implied a decrease in the effective surface area for the attachment of counter-ions or decrease in the number density of the available counter-ions. Therefore, the effective fraction of the anions, remaining 27 ACS Paragon Plus Environment

Page 28 of 40

Page 29 of 40 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

unused in the solution, increased. Thus, the contact line velocity decreased with a decrease in particle diameter as well as with particle loading. A control volume formulation was used in the study wherein the effects of the capillary pressure gradients and the Maxwell stress were incorporated to form an expression for the contact line velocity and compared with the experimental data. Magnetowetting As was discussed before, the efficiency of electrowetting depended on the chemical and more importantly the physical nature (in terms of the cleanliness, smoothness etc.) of the substrate. The phenomenon of contact line pinning was probed, both theoretically and experimentally in a number of publications.93–96

Contact line

pinning essentially affected the response of the system to electrical actuation and hysteresis. Electrowetting also required physical contact with the liquid, which created difficulties in microscale systems and in in-vivo applications. In this respect, use of magnetic field has started to become an attractive alternative recently.97,98 However, the application of magnetic field to actuate flow in extended meniscus is almost non-existent. The magnetic field is a non-contact, non-obtrusive method as well as being a body force it acts on the entire film (unlike the Maxwell stress) making magnetowetting an even better proposition. The associated experiments99 were based on the premise that on application of a magnetic field to a ferromagnetic liquid on a solid substrate, the surface energy of the system would change and that would be manifested not only through a change in the shape of the meniscus but might result in spreading as well. In the experimental system, a ferrofluid (with a nanoparticle concentration of 0.8% (v/v), procured from Ferrotec™) diluted in a suitable solvent, (n-heptane, to reduce its inherent viscosity) was used. The suspension was introduced in a sealed chamber tilted at a suitable angle to aid the formation of the liquid meniscus. This set up was similar to that used for electrowetting experiments with the difference that the field was applied by the accurate positioning of a Ceramic-5 magnet (external field intensity of 3950 Gauss) such that the first dark fringe coincided with the centre of the magnet. Therefore, the thinner adsorbed region was situated to the right of the centre of the magnet whereas the thicker capillary region was on its left. The magnetic force (F/V) that acted on the film due to the applied magnetic field was expressed as,


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

F  1     ∂Br =     Br ⋅  V  µ0     ∂r

  ∂Br  + Bz ⋅    ∂z

    ∂Bz   rˆ +  Br ⋅      ∂r

Page 30 of 40

  ∂Bz  + Bz ⋅    ∂z

    zˆ   

(5)

where, Br and Bz were the radial and axial components respectively of the applied magnetic field, rˆ and zˆ were the unit vectors along the radial and axial directions respectively,

µ0 is the permeability of vacuum. Magnetic force being a volumetric

force acted over the entire film and its effect was dependent on the thickness of the film region in consideration.

Figure 11 (A) Image sequence depicting the thin film on exposure to magnetic field at the initial (t = 0s) and final instant (t = 34s). (B) Spatio-temporal behavior of the thin film thickness when subjected to magnetic field (C) Variation in film curvature in presence of magnetic field with film thickness. Reproduced with permission from DasGupta et al.,92

The shape dependent interfacial force-field was evaluated using image analyzing interferometry (Figure 11 (A)) and the movement of the contact line was also quantified. Two events occur simultaneously; initially the thinner adsorbed region (and transition region) receded while the thicker capillary region advanced for a time period of few seconds. The net effect of these two events caused a spike in the 29 ACS Paragon Plus Environment

Page 31 of 40 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

curvature close to the contact line region. However, the advancing liquid flow from the capillary region dominated the receding motion and a bulk motion of the entire film towards the region right to the magnetic centre was noted to occur. The spike in curvature (Figures 11 (B) and (C)) and the changes in adsorbed and capillary region film thicknesses were functions of the applied magnetic field intensity and the axial distance of the magnet from the film although it was independent of field direction.

Figure 12 (A) Schematic of the advancing extended thin ferrofluid film on the application of different magnetic forces, β1 and β2 where β2 > β1 (B) Comparison between the theoretical and experimental velocity of the ferrofluid film at different magnetic field intensities. Reproduced with permission from DasGupta et al.,92

The increase in the net movement (advancement) of the contact line with an increase in the applied magnetic field intensity (Figure 12 (A)) was quantified in terms of the average velocity of the film. The thin film dynamics was modeled using a control volume approach and the effect of the magnetic field (β) was incorporated as a body force term in the governing equation. The predictions of the average film velocity were found to agree well with the experimental results (Figure 12 (B)) (details are available in,92). 30 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

Other parameter that may possibly affect this phenomenon is the particle properties (aspect ratio, concentration etc.) and may be explored further. Summary and Future Scope Extended thin film menisci are ubiquitous in several processes of technological importance. This article provides an insight into the complex transport processes involving delicate balances of intermolecular and surface forces near the thin film region of an extended meniscus. The goal is to provide a summary of the exciting research in this domain and delineate the future aspects in this ever expanding area. We provide a detailed discussion on the progress in developing techniques that utilize external field based manipulation of thin films encompassing basic disciplines such as interfacial force fields, heat transfer, mass transfer and applied areas like surface coatings, paints, inkjet printing etc. It presents the fundamental physics in terms of the intermolecular forces governing the shape and the behaviour of thin films including the contact line dynamics in presence of applied fields. The interferometry based nonobtrusive measurement technique aided by image analysis provided experimental insight along with improved data analysis in an area of vastly reduced length scale. The nature of the applied field may be as diverse as simple thermal perturbation to the comparatively complex, e.g., pulsed electric field, magnetic fields etc. The behaviour of the colloidal suspensions and their altered dynamics in terms of the nature of the particles and the associated characteristics during electrowetting are discussed as well. We envisage that in the near future application of external fields at a precise location will be used to augment the fundamental transport mechanisms and usher in a paradigm shift in a number of micro-scale applications.

Associated Content The authors declare no competing financial interest. Author Information: Corresponding author e-mail: [email protected]


Page 32 of 40

Page 33 of 40 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

References (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)

(15) (16) (17) (18) (19) (20) (21) (22) (23)

(24)

Dhir, V. K. Boiling Heat Transfer. Annu. Rev. Fluid Mech. 1998, 30 (1), 365–401. Demiray, F.; Kim, J. Microscale Heat Transfer Measurements during Pool Boiling of FC-72: Effect of Subcooling. Int. J. Heat Mass Transf. 2004, 47 (14–16), 3257–3268. Nikolayev, V. S.; Janeček, V. Impact of the Apparent Contact Angle on the Bubble Departure at Boiling. Int. J. Heat Mass Transf. 2012, 55 (23–24), 7352–7354. Raghupathi, P. A.; Kandlikar, S. G. Contact Line Region Heat Transfer Mechanisms for an Evaporating Interface. Int. J. Heat Mass Transf. 2016, 95, 296–306. Stephan, P.; Hammer, J. A New Model for Nucleate Boiling Heat Transfer. Heat Mass Transf. 1994, 30 (2), 119–125. Dhir, V. K.; Warrier, G. R.; Aktinol, E. Numerical Simulation of Pool Boiling: A Review. J. Heat Transfer 2013, 135 (6), 61502. Kim, J. Spray Cooling Heat Transfer: The State of the Art. Int. J. Heat Fluid Flow 2007, 28 (4), 753–767. Chinnov, E. A.; Ron’shin, F. V.; Kabov, O. A. Two-Phase Flow Patterns in Short Horizontal Rectangular Microchannels. Int. J. Multiph. Flow 2016, 80, 57–68. Sodtke, C.; Stephan, P. Spray Cooling on Micro Structured Surfaces. Int. J. Heat Mass Transf. 2007, 50 (19–20), 4089–4097. Routh, A. F. Drying of Thin Colloidal Films. Reports Prog. Phys. 2013, 76 (4). Xu, P.; Mujumdar, A. S.; Yu, B. Drying-Induced Cracks in Thin Film Fabricated from Colloidal Dispersions. Dry. Technol. 2009, 27 (5), 636–652. Douville, N.; Huh, D.; Takayama, S. DNA Linearization through Confinement in Nanofluidic Channels. Anal. Bioanal. Chem. 2008, 391 (7), 2395–2409. Michalet, X. Dynamic Molecular Combing: Stretching the Whole Human Genome for High-Resolution Studies. Science (80-. ). 1997, 277 (5331), 1518–1523. Roy, T.; Szuttor, K.; Smiatek, J.; Holm, C.; Hardt, S. Stretching of Surface-Tethered Polymers in Pressure-Driven Flow under Confinement. Soft Matter 2017, 13, 6189– 6196. Vogel, M. J.; Steen, P. H. Capillarity-Based Switchable Adhesion. Proc. Natl. Acad. Sci. 2010, 107 (8), 3377–3381. Macner, A. M.; Steen, P. H. Adaptive Adhesion by a Beetle: Manipulation of Liquid Bridges and Their Breaking Limits. Biointerphases 2014, 9 (1), 11001. Bostwick, J. B.; Steen, P. H. Stability of Constrained Capillary Surfaces. Annu. Rev. Fluid Mech. 2015, 47 (1), 539–568. Van Lengerich, H. B.; Steen, P. H. Energy Dissipation and the Contact-Line Region of a Spreading Bridge. J. Fluid Mech. 2012, 703, 111–141. Bostwick, J. B.; Steen, P. H. Response of Driven Sessile Drops with Contact-Line Dissipation. Soft Matter 2016, 12 (43), 8919–8926. Saramago, B. Thin Liquid Wetting Films. Curr. Opin. Colloid Interface Sci. 2010, 15 (5), 330–340. Bertrand, E.; Blake, T. D.; De Coninck, J. Dynamics of Dewetting. Colloids Surfaces A Physicochem. Eng. Asp. 2010, 369 (1–3), 141–147. Derjaguin, B. V. Some Results from 50 Years’ Research on Surface Forces. Prog. Coll. Poly. Sci. 1987, 74 (1), 17–30. Hough, D. B.; White, L. R. The Calculation of Hamaker Constants from Liftshitz Theory with Applications to Wetting Phenomena. Adv. Colloid Interface Sci. 1980, 14 (1), 3–41. Truong, J. G.; Wayner, P. C. Effects of Capillary and van Der Waals Dispersion Forces on the Equilibrium Profile of a Wetting Liquid: Theory and Experiment. 32 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

(25) (26) (27) (28) (29)

(30) (31) (32) (33) (34) (35) (36)

(37) (38)

(39) (40)

(41) (42)

(43) (44) (45) (46)

J.Chem.Phys. 1987, 87 (7), 4180–4188. Wang, H.; Pan, Z.; Chen, Z. Thin-Liquid-Film Evaporation at Contact Line. Front. Energy Power Eng. China 2009, 3 (2), 141–151. Israelachvili, J. N. Intermolecular and Surface Forces: Third Edition. Intermol. Surf. Forces Third Ed. 2011, 1–676. Horn, R. G.; Israelachvili, J. N. Direct Measurement of Structural Forces between Two Surfaces in a Nonpolar Liquid. J. Chem. Phys. 1981, 75 (3), 1400–1411. Christenson, H. K. Experimental Measurements of Solvation Forces in Nonpolar Liquids. J. Chem. Phys. 1983, 78 (11), 6906–6913. Christenson, H. K.; Gruen, D. W. R.; Horn, R. G.; Israelachvili, J. N. Structuring in Liquid Alkanes between Solid Surfaces: Force Measurements and Mean-Field Theory. J. Chem. Phys. 1987, 87 (3), 1834–1841. Potash, M.; Wayner, P. C. Evaporation from a Two-Dimensional Extended Meniscus. Int. J. Heat Mass Transf. 1972, 15, 1851–1863. Holm, F. W.; Goplen, S. P. Heat Transfer in the Meniscus Thin-Film Transition Region. J. Heat Transfer 1979, 101 (8), 543–547. Churaev, N. V. Surface Forces in Wetting Films. Adv. Colloid Interface Sci. 2003, 103, 197–218. Derjaguin, B. .; Churaev, N. V. Structural Component of Disjoining Pressure. J. Colloid Interface Sci. 1974, 49 (2), 249–255. Hall, A. C. Optical Studies of Thin Films on Surfaces of Fused Quartz. J. Phys. Chem. 1970, 74 (1), 2742–2746. Wasan, D. T.; Nikolov, A. D. Spreading of Nanofluids on Solids. Nature 2003, 423, 156–159. Chengara, A.; Nikolov, A. D.; Wasan, D. T.; Trokhymchuk, A.; Henderson, D. Spreading of Nanofluids Driven by the Structural Disjoining Pressure Gradient. J. Colloid Interface Sci. 2004, 280, 192–201. Nikolov, A.; Kondiparty, K.; Wasan, D. Nanoparticle Self-Structuring in a Nanofluid Film Spreading on a Solid Surface. Langmuir 2010, 26 (29), 7665–7670. Kondiparty, K.; Nikolov, A.; Wu, S.; Wasan, D. Wetting and Spreading of Nanofluids on Solid Surfaces Driven by the Structural Disjoining Pressure : Statics Analysis and Experiments. Langmuir 2011, 27, 3324–3335. Nikolov, A.; Wasan, D. Wetting – Dewetting Films : The Role of Structural Forces. Adv. Colloid Interface Sci. 2014, 206, 207–221. Lim, S.; Zhang, H.; Wu, P.; Nikolov, A.; Wasan, D. Journal of Colloid and Interface Science The Dynamic Spreading of Nanofluids on Solid Surfaces – Role of the Nanofilm Structural Disjoining Pressure. J. Colloid Interface Sci. 2016, 470, 22–30. Churaev, N. V.; Derjaguin, B. V. Inclusion of Structural Forces in the Theory of Stability of Colloids and Films. J. Colloid Interface Sci. 1985, 103 (2), 542–553. Viani, B. E.; Low, P. F.; Roth, C. B. Direct Measurement of the Relation between Interlayer Force and Interlayer Distance in the Swelling of Montmorillonite. J. Colloid Interface Sci. 1983, 96 (1), 229–244. Israelachvili, J. N. Forces between Surfaces in Liquids. Adv. Colloid Interface Sci. 1982, 16 (1), 31–47. Rabinovich, Y.; Derjaguin, B.; Churaev, N. Direct Measurements of Long-Range Surface Forces in Gas and Liquid Media. Adv. Colloid Interface Sci. 1982, 16, 63–78. Israelachvili, J. N. Measurement of Forces between Surfaces Immersed in Electrolyte Solutions. Faraday Discuss. Chem. Soc. 1978, 65, 20–24. S.Mitlin, V.; Sharma, M. M. A Local Gradient Theory for Structural Forces in Thin Fluid Films. J. Colloid Interface Sci. 1993, 157, 447–464.


Page 34 of 40

Page 35 of 40 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

(47) (48) (49)

(50) (51) (52) (53) (54) (55)

(56)

(57)

(58)

(59) (60)

(61) (62) (63) (64) (65)

(66) (67)

Boinovich, L. B.; Emelyanenko, A. M. Forces due to Dynamic Structure in Thin Liquid Films. Adv. Colloid Interface Sci. 2002, 96 (1–3), 37–58. Besseling, N. A. M. Theory of Hydration Forces between Surfaces. Langmuir 1997, 13 (7), 2113–2122. Kornyshev, A. A.; Leikin, S. Fluctuation Theory of Hydration Forces: The Dramatic Effects of Inhomogeneous Boundary Conditions. Phys. Rev. A 1989, 40 (11), 6431– 6437. M.L. Belaya, M. V. F. and V. G. L. Hydration Forces as a Result of Non-Local Water Polarizability. Chem. Phys. Lett. 1986, 126 (3,4), 361–364. Marcelja, S.; Gruen, D. W. R. Spatially Varying Polarization in Water. J.Chem.Soc.,Faraday Trans. 1983, 79 (2), 225–242. Ninham, B. W. Long-Range vs. Short-Range Forces. The Present State of Play. J. Phys. Chem. 1980, 84 (12), 1423–1430. Marčelja, S.; Radić, N. Repulsion of Interfaces due to Boundary Water. Chem. Phys. Lett. 1976, 42 (1), 129–130. Dasgupta, S.; Plawsky, J. L.; Wayner, P. C. Interfacial Force Field Characterization in a Constrained Vapor Bubble Thermosyphon. AIChE J. 1995, 41 (9), 2140–2149. Panchamgam, S. S.; Gokhale, S. J.; Plawsky, J. L.; DasGupta, S.; Wayner, P. C. Experimental Determination of the Effect of Disjoining Pressure on Shear in the Contact Line Region of a Moving Evaporating Thin Film. J. Heat Transfer 2005, 127 (3), 231–243. Argade, R.; Ghosh, S.; De, S.; Dasgupta, S. Experimental Investigation of Evaporation and Condensation in the Contact Line Region of a Thin Liquid Film Experiencing Small Thermal Perturbations. Langmuir 2007, No. 10, 1234–1241. Shin, D. H.; Allen, J. S.; Choi, C. K.; Lee, S. H. Visualization of an Evaporating Thin Layer during the Evaporation of a Nanofluid Droplet. Langmuir 2015, 31 (4), 1237– 1241. 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. Chakraborty, M.; Chatterjee, R.; Ghosh, U. U.; Dasgupta, S. Electrowetting of Partially Wetting Thin Nanofluid Films. Langmuir 2015, 31 (14), 4160–4168. Ghosh, U. U.; Chakraborty, M.; De, S.; Chakraborty, S.; DasGupta, S. Contact Line Dynamics during the Evaporation of Extended Colloidal Thin Films: Influence of Liquid Polarity and Particle Size. Langmuir 2016, 32 (48), 12790–12798. Sheppard, C. J. R.; Larkin, K. G. Effect of Numerical Aperture on Interference Fringe Spacing. Appl. Opt. 1995, 34 (22), 4731. 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. Renk, F. J.; Wayner, P. C. An Ewaporating Ethanol Meniscus Part I : Experimental Studies. 2014, 101 (February 1979), 55–58. Wayner, P. C.; Jr. The Effect of Interfacial Liquid Films Mass Transport on Flow in Thin Liquid Films. Colloids and Surfaces 1991, 52, 71–84. DasGupta, S.; Schonberg, J. A.; Wayner, P. C. Investigation of an Evaporating Extended Meniscus Based on the Augmented Young–Laplace Equation. J. Heat Transfer 1993, 115 (1), 201–208. Fanton, X.; Cazabat, A. M.; Quéré, D. Thickness and Shape of Films Driven by a Marangoni Flow. Langmuir 1996, 12 (24), 5875–5880. Anand, S.; De, S.; Dasgupta, S. Experimental and Theoretical Study of Axial Dryout Point for Evaporation from V-Shapes Microgrooves. Int. J. Heat Mass Transf. 2002, 34 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

(68)

(69) (70)

(71)

(72)

(73)

(74) (75) (76)

(77) (78) (79) (80)

(81)

(82) (83) (84) (85) (86) (87) (88)

45 (7), 1535–1543. Hanchak, M. S.; Vangsness, M. D.; Byrd, L. W.; Ervin, J. S. Thin Film Evaporation of N-Octane on Silicon: Experiments and Theory. Int. J. Heat Mass Transf. 2014, 75, 196–206. Gregory, J. Approximate Expressions for Retarded Van Der Waals Interaction. J. Colloid Interface Sci. 1981, 83 (1), 138–145. Hanchak, M. S.; Vangsness, M. D.; Ervin, J. S.; Byrd, L. W. Model and Experiments of the Transient Evolution of a Thin, Evaporating Liquid Film. Int. J. Heat Mass Transf. 2016, 92, 757–765. DasGupta, S.; Kim, I. Y.; Wayner, P. C. Use of the Kelvin-Clapeyron Equation to Model an Evaporating Curved Microfilm. J. Heat Transfer 1994, 116 (November), 1007–1015. DasGupta, S.; Schonberg, J. A.; Wayner, P. C. Investigation of an Evaporating Extended Meniscus Based on the Augmented Young–Laplace Equation. J. Heat Transfer 1993, 115, 201–208. Sunando, D.; Schonberg;, J. A.; Kim;, I. Y.; Wayner, P. C. Use of the Augmented Young-Laplace Equation to Model Equilibrium and Evaporating Extended Menisci. J. Colloid Interface Sci. 1993, 157, 332–342. Ayyaswamy, P. S.; Catton, I.; Edwards, D. K. Capillary Flow in Triangular Grooves. J. Appl. Mech. 1974, 41 (2), 332–336. Stephan, P. C.; Busse, C. A. Analysis of the Heat Transfer Coefficient of Grooved Heat Pipe Evaporator Walls. Int. J. Heat Mass Transf. 1992, 35 (2), 383–391. X;, X.; Carey;, V. P. Film Evaporation from a Micro-Grooved Surface - An Approximate Heat Transfer Model and Its Comparison with Experimental Data. J.Thermophysics 1990, 4, 512–520. Swanson, L. W.; Peterson, G. P. The Interfacial Thermodynamics of Micro Heat Pipes. J. Heat Transfer 1995, 117 (February 1995), 195–201. D.Wu.; G.P., P. Investigation of the Transient Characteristics of a Micro Heat Pipe. J. Thermophys. 1991, 5 (2), 129–134. Zheng, L.; Plawsky, J. L.; Wayner, P. C.; DasGupta, S. Stability and Oscillations in an Evaporating Corner Meniscus. J. Heat Transfer 2004, 126 (2), 169–178. Plawsky, J. L.; Panchamgam, S. S.; Gokhale, S. J.; Wayner, P. C.; DasGupta, S. A Study of the Oscillating Corner Meniscus in a Vertical Constrained Vapor Bubble System. Superlattices Microstruct. 2004, 35 (3–6), 559–572. Chatterjee, A.; Plawsky, J. L.; Wayner, P. C. Disjoining Pressure and Capillarity in the Constrained Vapor Bubble Heat Transfer System. Adv. Colloid Interface Sci. 2011, 168 (1–2), 40–49. Wang, H.; Chen, L.; Sun, L. Digital Microfluidics: A Promising Technique for Biochemical Applications. Front. Mech. Eng. 2017, 1, 1–16. Choi, K.; Ng, A. H. C.; Fobel, R.; Wheeler, A. R. Digital Microfluidics. Annu. Rev. Anal. Chem. 2012, 5 (1), 413–440. Mugele, F.; Baret, J.-C. Electrowetting: From Basics to Applications. J. Phys. Condens. Matter 2005, 17 (28), R705–R774. Kang, K. H. How Electrostatic Fields Change Contact Angle in. Langmuir 2002, No. 10, 10318–10322. Buehrle, J.; Herminghaus, S.; Mugele, F. Interface Profiles near Three-Phase Contact Lines in Electric Fields. Phys. Rev. Lett. 2003, 91 (8), 86101. Bhaumik, S. K.; Chakraborty, S.; DasGupta, S. Electrowetting of Evaporating Extended Meniscus. Soft Matter 2012, 8 (44), 11302. Larson, R. G. In Retrospect: Twenty Years of Drying Droplets. Nature. 2017, pp 466–


Page 36 of 40

Page 37 of 40 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

(89) (90)

(91) (92)

(93) (94)

(95)

(96) (97)

(98)

(99)

467. Park, J.; Moon, J. Control of Colloidal Particle Deposit Patterns within Picoliter Droplets Ejected by Ink-Jet Printing. Langmuir 2006, 22 (8), 3506–3513. Chakraborty, D.; Sai, G.; Chakraborty, S.; Dasgupta, S. Effect of Submicron Particles on Electrowetting on Dielectrics ( EWOD ) of Sessile Droplets. J. Colloid Interface Sci. 2011, 363 (2), 640–645. Orejon, D.; Sefiane, K.; Shanahan, M. E. R. Young-Lippmann Equation Revisited for Nano-Suspensions. Appl. Phys. Lett. 2013, 102 (20), 100–103. Dash, R. K.; Borca-Tasciuc, T.; Purkayastha, A.; Ramanath, G. Electrowetting on Dielectric-Actuation of Microdroplets of Aqueous Bismuth Telluride Nanoparticle Suspensions. Nanotechnology 2007, 18, 1–6. Lu, Z.; Preston, D. J.; Antao, D. S.; Zhu, Y.; Wang, E. N. Coexistence of Pinning and Moving on a Contact Line. Langmuir 2017, 33 (36), 8970–8975. Wang, A.; McGorty, R.; Kaz, D. M.; Manoharan, V. N. Contact-Line Pinning Controls How Quickly Colloidal Particles Equilibrate with Liquid Interfaces. Soft Matter 2016, 12, 8958–8967. Hong, S. H.; Fontelos, M. A.; Hwang, H. J. The Contact Line of an Evaporating Droplet over a Solid Wedge and the Pinned–unpinned Transition. J. Fluid Mech. 2016, 791, 519–538. Weon, B.; Je, J. Self-Pinning by Colloids Confined at a Contact Line. Phys. Rev. Lett. 2013, 110 (28303), 1–4. Lehmann, U.; Hadjidj, S.; Parashar, V. K.; Vandevyver, C.; Rida, A.; Gijs, M. A. M. Two-Dimensional Magnetic Manipulation of Microdroplets on a Chip as a Platform for Bioanalytical Applications. Sensors Actuators, B Chem. 2006, 117 (2), 457–463. Long, Z.; Shetty, A. M.; Solomon, M. J.; Larson, R. G. Fundamentals of MagnetActuated Droplet Manipulation on an Open Hydrophobic Surface. Lab Chip 2009, 9 (11), 1567–1575. Tenneti, S.; Subramanian, S. G.; Chakraborty, M.; Soni, G.; DasGupta, S. Magnetowetting of Ferrofluidic Thin Liquid Films. Sci. Rep. 2017, 7 (44738), 1–13.


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

TOC Graphic:


Page 38 of 40

Page 39 of 40 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

Biographies

Sunando DasGupta Professor Sunando DasGupta is presently a professor of Chemical Engineering and Head of the Advanced Technology Development Centre at the Indian Institute of Technology Kharagpur, India. He has joined the Indian Institute of Technology Kharagpur after obtaining his PhD from the Rensselaer Polytechnic Institute, USA. His research interests are in the fields of interfacial phenomena, microscale transport processes, digital microfluidics, and biomicrofluidics. Prof. DasGupta is a Fellow of the National Academy of Engineering, India, and is a Senior Associate of the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy.

Udita Uday Ghosh Udita Uday Ghosh is a PhD student in the Department of Chemical Engineering at the Indian Institute of Technology Kharagpur, India. Her research interests include droplet microfluidics, colloids and interfacial phenomena particularly crack formation in colloidal films.


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

Acknowledgements SDG would like to acknowledge the inspiring role of Prof. Peter C. Wayner Jr. of the Rensselaer Polytechnic Institute. We are indebted to the former and present members of the Microscale/Microfluidics Laboratory group at the Indian Institute of Technology Kharagpur. The authors duly acknowledge the support extended by the Department of Information Technology (DIT) India, Department of Science and Technology (DST) India, Indian Institute of Technology Kharagpur, Intel and the Indian Space Research Organization (ISRO).


Page 40 of 40

Field-assisted Contact Line Motion in Thin Films - ACS Publications

Recommend Documents