Gambhire P, Thaokar R M
Department of Chemical Engineering, Indian Institute of Technology Bombay.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Sep;86(3 Pt 2):036301. doi: 10.1103/PhysRevE.86.036301. Epub 2012 Sep 4.
The effect of electrical conductivity on the wavelength of an electrohydrodynamic instability of a leaky dielectric-perfect dielectric (LD-PD) fluid interface is investigated. For instabilities induced by dc fields, two models, namely the PD-PD model, which is independent of the conductivity, and the LD-PD model, which shows very weak dependence on the conductivity of the LD fluid, have been previously suggested. In the past, experiments have been compared with either of these two models. In the present work, experiments, analytical theory, and simulations are used to elucidate the dependence of the wavelength obtained under dc fields on the ratio of the instability time (τs=1/smax) and the charge relaxation time (τc=εε0/σ, where ε0 is the permittivity of vacuum, ε is the dielectric constant, and σ is the electrical conductivity). Sensitive dependence of the wavelength on the nondimensional conductivity S2=σ2μ2h0(2)/(ε0(2)φ0(2)δ2) (where σ2 is the electrical conductivity, μ2 is the viscosity, h0 is the thickness of the thin liquid film, φ0 is the rms value of the applied field, and δ is a small parameter) is observed and the PD-PD and the LD-PD cases are observed only as limiting behaviors at very low and very high values of S2, respectively. Under an alternating field, the frequency of the applied voltage can be altered to realize several regimes of relative magnitudes of the three time scales inherent to the system, namely τc, τs, and the time period of the applied field, τf. The wavelength in the various regimes that result from a systematic variation of these three time scales is studied. It is observed that the linear Floquet theory is invalid in most of these regimes and nonlinear analysis is used to complement it. Systematic dependence of the wavelength of the instability on the frequency of the applied field is presented and it is demonstrated that nonlinear simulations are necessary to explain the experimental results.
研究了电导率对漏电介质 - 理想介质（LD - PD）流体界面的电流体动力学不稳定性波长的影响。对于直流电场引起的不稳定性，先前已经提出了两种模型，即与电导率无关的PD - PD模型和对LD流体电导率依赖性非常弱的LD - PD模型。过去，实验是与这两种模型中的任何一种进行比较的。在本工作中，使用实验、解析理论和模拟来阐明在直流电场下获得的波长对不稳定性时间（τs = 1 / smax）与电荷弛豫时间（τc = εε0 / σ，其中ε0是真空电容率，ε是介电常数，σ是电导率）之比的依赖性。观察到波长对无量纲电导率S2 = σ2μ2h0(2) / (ε0(2)φ0(2)δ2)（其中σ2是电导率，μ2是粘度，h0是薄液膜的厚度，φ0是外加电场的均方根值，δ是一个小参数）敏感依赖，并且分别仅在S2的非常低和非常高的值时观察到PD - PD和LD - PD情况为极限行为。在交变电场下，可以改变外加电压的频率以实现系统固有的三个时间尺度，即τc、τs和外加电场的时间周期τf的相对大小的几种状态。研究了由这三个时间尺度的系统变化导致的各种状态下的波长。观察到线性弗洛凯理论在这些状态中的大多数情况下是无效的，并使用非线性分析来补充它。给出了不稳定性波长对外加电场频率的系统依赖性，并证明需要非线性模拟来解释实验结果。
