Lee Joohee, Park Jun Kwon, Hong Jiwoo, Lee Sang Joon, Kang Kwan Hyoung, Hwang Hyung Ju
Department of Mathematics, Chung-Ang University, Seoul 156-756, Republic of Korea.
Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Sep;90(3):033017. doi: 10.1103/PhysRevE.90.033017. Epub 2014 Sep 30.
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%.
我们研究了介电基底上静止水滴在交流电润湿（EW）驱动下的轴对称振荡特性。在交流电润湿中，水滴的小振幅振荡不同于自由振荡水滴的瑞利线性模式。在本文中，我们证明了由于电场和固体基底的存在而导致的静止水滴时间平均接触角的变化是造成这种差异的主要原因。我们将区域摄动法与林德斯特德 - 庞加莱方法相结合，推导出共振频率的渐近公式。理论分析表明，共振频率是时间平均接触角的函数。共振频率的每个模式都是ε(1)的线性函数，ε(1)是时间平均接触角余弦的大小。本研究中最主要的模式，即基模n = 2，随ε(1)线性减小。将理论模型的结果与实验和数值模拟的结果进行了比较。摄动解与数值模拟之间的平均共振频率偏差为4.3%，而摄动解与实验之间的平均共振频率偏差为1.8%。
