Numerical simulation of drop oscillation in AC electrowetting

Abstract

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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