Numerical and theoretical analyses of the dynamics of droplets driven by electrowetting on dielectric in a Hele-Shaw cell

2018 ◽  
Vol 839 ◽  
pp. 468-488 ◽  
Author(s):  
Yasufumi Yamamoto ◽  
Takahiro Ito ◽  
Tatsuro Wakimoto ◽  
Kenji Katoh
Keyword(s):  
Theoretical Model ◽  
Contact Line ◽  
Three Dimensional ◽  
Simulation Method ◽  
Movement Speed ◽  
Electrowetting On Dielectric ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Droplet Movement ◽  
Hele Shaw Cell

Droplet movement by electrowetting on dielectric (EWOD) in a Hele-Shaw cell is analysed theoretically and numerically. We propose a simple theoretical model for the motion, which describes well the voltage dependency of droplet speed below the saturation voltage as measured experimentally. The simulation method for numerical analyses is constructed by using the Young–Lippmann equation to represent EWOD and the generalised Navier boundary condition to represent the moving contact line in the context of the front-tracking method. With an adjusted slip parameter, the present full three-dimensional numerical simulation reproduces well the shape evolution and movement speed of droplets as observed experimentally. We verify the proposed theoretical model in numerical experiments with various shapes and voltages. Furthermore, we analyse theoretically the behaviour of the contact line at the onset of droplet motion as observed in the simulation and experiment, and we are able to estimate very well the time scale on which the contact angle changes.

scholarly journals Evaporation of sessile drops: a three-dimensional approach

2015 ◽  
Vol 772 ◽  
pp. 705-739 ◽  
Author(s):  
P. J. Sáenz ◽  
K. Sefiane ◽  
J. Kim ◽  
O. K. Matar ◽  
P. Valluri
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Evaporation Rate ◽  
Three Dimensional ◽  
Complex Case ◽  
Interface Temperature ◽  
Angle Distribution ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Sessile Drops

The evaporation of non-axisymmetric sessile drops is studied by means of experiments and three-dimensional direct numerical simulations (DNS). The emergence of azimuthal currents and pairs of counter-rotating vortices in the liquid bulk flow is reported in drops with non-circular contact area. These phenomena, especially the latter, which is also observed experimentally, are found to play a critical role in the transient flow dynamics and associated heat transfer. Non-circular drops exhibit variable wettability along the pinned contact line sensitive to the choice of system parameters, and inversely dependent on the local contact-line curvature, providing a simple criterion for estimating the approximate contact-angle distribution. The evaporation rate is found to vary in the same order of magnitude as the liquid–gas interfacial area. Furthermore, the more complex case of drops evaporating with a moving contact line (MCL) in the constant contact-angle mode is addressed. Interestingly, the numerical results demonstrate that the average interface temperature remains essentially constant as the drop evaporates in the constant-angle (CA) mode, while this increases in the constant-radius (CR) mode as the drops become thinner. It is therefore concluded that, for increasing substrate heating, the evaporation rate increases more rapidly in the CR mode than in the CA mode. In other words, the higher the temperature the larger the difference between the lifetimes of an evaporating drop in the CA mode with respect to that evaporating in the CR mode.

A theoretical study of two-phase flow through a narrow gap with a moving contact line: viscous fingering in a Hele-Shaw cell

1990 ◽  
Vol 221 ◽  
pp. 53-76 ◽  
Author(s):  
Steven J. Weinstein ◽  
E. B. Dussan ◽  
Lyle H. Ungar
Keyword(s):  
Thin Films ◽  
Contact Angle ◽  
Contact Line ◽  
Viscous Fingering ◽  
Contact Lines ◽  
Fluid Interface ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Hele Shaw Cell

The problem of viscous fingering in a Hele-Shaw cell with moving contact lines is considered. In contrast to the usual situation where the displaced fluid coats the solid surface in the form of thin films, here, both the displacing and the displaced fluids make direct contact with the solid. The principal differences between these two situations are in the ranges of attainable values of the gapwise component of the interfacial curvature (the component due to the bending of the fluid interface across the small gap of the Hele-Shaw cell), and in the introduction of two additional parameters for the case with moving contact lines. These parameters are the receding contact angle, and the sensivity of the dynamic angle to the speed of the contact line. Our objective is the prediction of the shape and widths of the fingers in the limit of small capillary number, Uμ/σ. Here, U denotes the finger speed, μ denotes the dynamic viscosity of the more viscous displaced fluid, and σ denotes the surface tension of the fluid interface. As might be expected, there are similarities and differences between the two problems. Despite the fact that different equations arise, we find that they can be analysed using the techniques introduced by McLean & Saffman and Vanden-Broeck for the thin-film case. The nature of the multiplicity of solutions also appears to be similar for the two problems. Our results indicate that when contact lines are present, the finger shapes are sensitive to the value of the contact angle only in the vicinity of its nose, reminiscent of experiments where bubbles or wires are placed at the nose of viscous fingers when thin films are present. On the other hand, in the present problem at least two distinct velocity scales emerge with well-defined asymptotic limits, each of these two cases being distinguished by the relative importance played by the two components of the curvature of the fluid interface. It is found that the widths of fingers can be significantly smaller than half the width of the cell.

Experimental and theoretical study of dewetting corner flow

2014 ◽  
Vol 762 ◽  
pp. 393-416 ◽  
Author(s):  
Hyoungsoo Kim ◽  
Christian Poelma ◽  
Gijs Ooms ◽  
Jerry Westerweel
Keyword(s):  
Flow Pattern ◽  
Contact Line ◽  
Dynamic Pressure ◽  
Three Dimensional ◽  
Internal Flow ◽  
Pressure Effects ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Corner Flow ◽  
Analytical Results

AbstractWe study a partial dewetting corner flow with a moving contact line at a finite Reynolds number, $0<\mathit{Re}<O(100)$. When the speed of the moving contact line increases, the receding contact line appears with a corner shape that is also observed in a gravity-driven liquid droplet on an incline and on a plate withdrawn from a bath. In the current problem, $\mathit{Re}\,{\it\epsilon}$ is larger than unity, where ${\it\epsilon}$ is the aspect ratio of the flow structure. Therefore, classical lubrication theory is no longer appropriate. We develop a modified three-dimensional lubrication model for the dewetting corner structure at $\mathit{Re}\,{\it\epsilon}>1$ by taking into account the internal flow pattern and by scaling arguments. The key requirement is that the streamlines in the corner are straight and (nearly) parallel. In this case, we can obtain a modified pressure consisting of the capillary pressure and the dynamic pressure. This model describes the three-dimensional dewetting corner structure at the rear of the moving droplets at $\mathit{Re}\,{\it\epsilon}>1$ and furthermore shows that the dynamic pressure effects become dominant at a small half-opening angle. Additionally, this model provides analytical results for the internal flow, which is a self-similar flow pattern. To validate the analytical results, we perform high-speed shadowgraphy and tomographic particle image velocimetry (PIV). We find a good agreement between the theoretical and the experimental results.

Moving contact line

2001 ◽  
Vol 11 (PR6) ◽  
pp. Pr6-199-Pr6-212 ◽  
Author(s):  
Y. Pomeau
Keyword(s):  
Contact Line ◽  
Moving Contact Line ◽  
Moving Contact

scholarly journals Validation and modification of asymptotic analysis of slow and rapid droplet spreading by numerical simulation

2013 ◽  
Vol 715 ◽  
pp. 283-313 ◽  
Author(s):  
Yi Sui ◽  
Peter D. M. Spelt
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Analysis ◽  
Contact Line ◽  
Slip Length ◽  
Interface Shape ◽  
Droplet Spreading ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Line Region ◽  
Modified Theory

AbstractUsing a slip-length-based level-set approach with adaptive mesh refinement, we have simulated axisymmetric droplet spreading for a dimensionless slip length down to $O(1{0}^{\ensuremath{-} 4} )$. The main purpose is to validate, and where necessary improve, the asymptotic analysis of Cox (J. Fluid Mech., vol. 357, 1998, pp. 249–278) for rapid droplet spreading/dewetting, in terms of the detailed interface shape in various regions close to the moving contact line and the relation between the apparent angle and the capillary number based on the instantaneous contact-line speed, $\mathit{Ca}$. Before presenting results for inertial spreading, simulation results are compared in detail with the theory of Hocking & Rivers (J. Fluid Mech., vol. 121, 1982, pp. 425–442) for slow spreading, showing that these agree very well (and in detail) for such small slip-length values, although limitations in the theoretically predicted interface shape are identified; a simple extension of the theory to viscous exterior fluids is also proposed and shown to yield similar excellent agreement. For rapid droplet spreading, it is found that, in principle, the theory of Cox can predict accurately the interface shapes in the intermediate viscous sublayer, although the inviscid sublayer can only be well presented when capillary-type waves are outside the contact-line region. However, $O(1)$ parameters taken to be unity by Cox must be specified and terms be corrected to ${\mathit{Ca}}^{+ 1} $ in order to achieve good agreement between the theory and the simulation, both of which are undertaken here. We also find that the apparent angle from numerical simulation, obtained by extrapolating the interface shape from the macro region to the contact line, agrees reasonably well with the modified theory of Cox. A simplified version of the inertial theory is proposed in the limit of negligible viscosity of the external fluid. Building on these results, weinvestigate the flow structure near the contact line, the shear stress and pressure along the wall, and the use of the analysis for droplet impact and rapid dewetting. Finally, we compare the modified theory of Cox with a recent experiment for rapid droplet spreading, the results of which suggest a spreading-velocity-dependent dynamic contact angle in the experiments. The paper is closed with a discussion of the outlook regarding the potential of using the present results in large-scale simulations wherein the contact-line region is not resolved down to the slip length, especially for inertial spreading.

Depletion of λ-DNA near moving contact line

2016 ◽  
Vol 236 ◽  
pp. 50-62
Author(s):  
Hongrok Shin ◽  
Ki Wan Bong ◽  
Chongyoup Kim
Keyword(s):  
Contact Line ◽  
Moving Contact Line ◽  
Moving Contact

Inertial effects on the flow near a moving contact line

2021 ◽  
Vol 924 ◽  
Author(s):  
Akhil Varma ◽  
Anubhab Roy ◽  
Baburaj A. Puthenveettil
Keyword(s):  
Contact Line ◽  
Inertial Effects ◽  
Moving Contact Line ◽  
Moving Contact

Abstract

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