Continuum models for the contact line problem

Ren, Weiqing; Huang, Dan; Weinan, E

doi:10.1063/1.3501317

Cited by 105 publications

(114 citation statements)

References 63 publications

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“…Hence, the driving force is the interfacial tension, while energy dissipation occurs around the moving contact line (MCL). There are essentially two theoretical models to interpret the physics of the wetting behaviours (Bonn et al 2009;Ren, Hu & E 2010), known as the hydrodynamic model and molecular kinetic theory (MKT).…”

Section: Introductionmentioning

confidence: 99%

Multiscale dynamic wetting of a droplet on a lyophilic pillar-arrayed surface

2013

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Dynamic wetting of a droplet on lyophilic pillars was explored using a multiscale combination method of experiments and molecular dynamics simulations. The excess lyophilic area not only provided excess driving force, but also pinned the liquid around the pillars, which kept the moving contact line in a dynamic balance state every period of the pillars. The flow pattern and the flow field of the droplet on the pillar-arrayed surface, influenced by the concerted effect of the liquid-solid interactions and the surface roughness, were revealed from the continuum to the atomic level. Then, the scaling analysis was carried out employing molecular kinetic theory. Controlled by the droplet size, the density of roughness and the pillar height, two extreme regimes were distinguished, i.e. R ∼ t 1/3 for the rough surface and R ∼ t 1/7 for the smooth surface. The scaling laws were validated by both the experiments and the simulations. Our results may help in understanding the dynamic wetting of a droplet on a pillar-arrayed lyophilic substrate and assisting the future design of pillar-arrayed lyophilic surfaces in practical applications.

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Section: Introductionmentioning

confidence: 99%

Multiscale dynamic wetting of a droplet on a lyophilic pillar-arrayed surface

2013

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“…This macroscopic dissipation was defined by a friction factor local at the contact line, which has the same units as viscosity. Others [8][9][10][11][12] have also discussed the importance of local non-hydrodynamic effects at the contact line, with different interpretations of its microscopic origin. Recently [13] a friction factor was estimated from the molecular kinetic theory by fitting the experimental spreading radius for drops with different viscosity.…”

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confidence: 99%

Universality in dynamic wetting dominated by contact-line friction

2012

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We report experiments on the rapid contact line motion present in the early stages of capillary driven spreading of drops on dry solid substrates. The spreading data fails to follow a conventional viscous or inertial scaling. By integrating experiments and simulations, we quantify a contact line friction (µ f ), which is seen to limit the speed of the rapid dynamic wetting. A scaling based on this contact line friction is shown to yield a universal curve for the evolution of the contact line radius as a function of time, for a range of fluid viscosities, drop sizes and surface wettabilities.

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“…In the presence of moving contact lines, the no-slip boundary condition will lead to a non-integrable force singularity. Several different techniques have been proposed to remove this singularity [38][39][40][41]. In this paper, the dynamic contact line model developed by Ren et al [41] is employed.…”

Section: Boundary Conditions and Contact Line Modelmentioning

confidence: 99%

“…Several different techniques have been proposed to remove this singularity [38][39][40][41]. In this paper, the dynamic contact line model developed by Ren et al [41] is employed. In this model, the mesh velocity of node C is prescribed as a function of the contact angle:…”

Section: Boundary Conditions and Contact Line Modelmentioning

confidence: 99%

Numerical simulation of drop oscillation in AC electrowetting

Zhang

2013

Sci. China Phys. Mech. Astron.

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In this paper, a "macroscopic-scale" numerical method for drop oscillation in AC electrowetting is presented. The method is based on a high-fidelity moving mesh interface tracking (MMIT) approach and a "microscopic model" for the moving contact line. The contact line model developed by Ren et al. [Phys Fluids, 2010, 22: 102103] is used in the simulation. To determine the slip length in this model, we propose a calibration procedure using the experimental data of drop spreading in DC electrowetting. In the simulation, the frequency of input AC voltage varies in a certain range while the root-mean-square value remains fixed. The numerical simulation is validated against the experiment and it shows that the predicted resonance frequencies for different oscillation modes agree reasonably well with the experiment. The origins of discrepancy between simulation and experiment are analyzed in the paper. Further investigation is also conducted by including the contact angle hysteresis into the contact line model to account for the "stick-slip" behavior. A noticeable improvement on the prediction of resonance frequencies is achieved by using the hysteresis model. Electrowetting (EW) is a phenomenon in which the wettability of a droplet on an insulator-coated electrode surface is modified by externally applying electrical voltages. This phenomenon originates from the electrostatic force, which is a direct consequence of the excess charge at the three-phase contact line [1]. A comprehensive review on EW, in both theory and experiment, was presented in the paper by Mugele and Baret [2]. EW can be used to manipulate small volume of liquid very fast and efficiently, with relatively low electrical potential and power consumption. Electrowetting on dielectric (EWOD) avoids the electrolysis of the aqueous solution in EW by coating the electrode surface with a thin dielectric layer. EWOD has been widely used in various applications, including microfluidics [3,4], liquid display [5,6], and microswitches [7,8]. Both DC and AC fields can be used in EW or EWOD.*Corresponding author (email: zhangx@lnm.imech.ac.cn)When a DC field is used, a new equilibrium state with a smaller contact angle will be reached after a spontaneous spreading process. If an AC field is used instead, more interesting and complex features are observed. At low-frequency AC excitation, the hydrodynamic response can follow the periodic change of the electric force at the contact line and the shape oscillation of droplet is observed. If the AC frequency exceeds a critical value for the hydrodynamic response, the droplet behaves just as if it is excited by a DC field. The final state of contact angle and shape depends only on the time-averaged value of the applied voltage. Recently, drop oscillation in AC EW at low frequencies (10-300 Hz) was studied by experiment and theory [9][10][11]. The experiments revealed that the drop oscillation became resonant at certain input AC frequencies and the pattern of shape oscillation was different at each resonance frequency. Th...

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Continuum models for the contact line problem

Cited by 105 publications

References 63 publications

Multiscale dynamic wetting of a droplet on a lyophilic pillar-arrayed surface

Multiscale dynamic wetting of a droplet on a lyophilic pillar-arrayed surface

Universality in dynamic wetting dominated by contact-line friction

Numerical simulation of drop oscillation in AC electrowetting

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