Nonlinear oscillations of a sessile drop on a hydrophobic surface induced by ac electrowetting

We examine the nature of ac electrowetting (EW)-driven axisymmetric oscillations of a sessile water drop on a dielectric substrate. In ac EW, small-amplitude oscillations of a drop differ from the Rayleigh linear modes of freely oscillating drops. In this paper, we demonstrate that changes in the time-averaged contact angle of the sessile drop attributed to the presence of an electric field and a solid substrate mainly caused this discrepancy. We combine the domain perturbation method with the Lindsted-Poincaré method to derive an asymptotic formula for resonant frequency. Theoretical analysis shows that the resonant frequency is a function of the time-averaged contact angle. Each mode of the resonance frequency is a linear function of ɛ(1), which is the magnitude of the cosine of the time-averaged contact angle. The most dominant mode in this study, that is, the fundamental mode n=2, decreases linearly with ɛ(1). The results of the theoretical model are compared with those of both the experiments and numerical simulations. The average resonant frequency deviation between the perturbation solutions and numerical simulations is 4.3%, whereas that between the perturbation solutions and the experiments is 1.8%.