The linear and nonlinear dynamics of an interface separating a thin liquid film and a hydrodynamically passive ambient medium, subject to normal electrostatic forcing, are investigated. A reduced-order model is developed for the case where both fluids are taken to be leaky dielectrics (LD). Cases of time periodic as well as steady forcing are studied. In the former case, an important result is the elucidation of two forms of resonant instability than can occur in LD films. These correspond to an inertial resonance due to mechanical inertia of the fluid and an inertialess resonance due to charge capacitance at the interface that is similar to mechanically forced films with an insoluble surfactant. In the case of steady forcing, the long-time dynamics exhibits spontaneous sliding as the interface approaches the wall, for the two limiting cases of a perfect conductor–perfect dielectric pair as well as a pair of perfect dielectrics. Under these limits, only the normal component of the Maxwell stress at the interface is significant and the interface dynamics resembles that of a Rayleigh–Taylor unstable interface. For a general pair of leaky dielectrics studied in the limit of fast relaxation times, the presence of interfacial charge prevents the onset of sliding. For the special case when the square of the conductivity ratio equals the permittivity ratio, the interface exhibits cascading structures, similar to those reported for the long-wave Marangoni instability.

中文翻译：

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周期性和稳态场下薄漏电介质膜的静电强迫

研究了分离薄液膜和流体动力学被动环境介质的界面的线性和非线性动力学，受法向静电力的影响。针对两种流体都被视为泄漏电介质 (LD) 的情况开发了降阶模型。研究了时间周期性和稳定强迫的情况。在前一种情况下，一个重要的结果是阐明了 LD 薄膜中可能出现的两种形式的谐振不稳定性。这些对应于由于流体的机械惯性引起的惯性共振和由于界面处的电荷电容引起的无惯性共振，类似于具有不溶性表面活性剂的机械强制膜。在稳定强迫的情况下，随着界面接近壁面，长时间动力学表现出自发滑动，对于完美导体-完美电介质对以及一对完美电介质的两个极限情况。在这些限制下，只有界面处麦克斯韦应力的法向分量是显着的，并且界面动力学类似于瑞利-泰勒不稳定界面的动力学。对于在快速弛豫时间极限下研究的一对一般泄漏电介质，界面电荷的存在阻止了滑动的开始。对于电导率比的平方等于介电常数比的特殊情况，界面呈现级联结构，类似于长波 Marangoni 不稳定性所报道的结构。只有界面处麦克斯韦应力的法向分量是显着的，并且界面动力学类似于瑞利-泰勒不稳定界面的动力学。对于在快速弛豫时间极限下研究的一对一般泄漏电介质，界面电荷的存在阻止了滑动的开始。对于电导率比的平方等于介电常数比的特殊情况，界面呈现级联结构，类似于长波 Marangoni 不稳定性所报道的结构。只有界面处麦克斯韦应力的法向分量是显着的，并且界面动力学类似于瑞利-泰勒不稳定界面的动力学。对于在快速弛豫时间极限下研究的一对一般泄漏电介质，界面电荷的存在阻止了滑动的开始。对于电导率比的平方等于介电常数比的特殊情况，界面呈现级联结构，类似于长波 Marangoni 不稳定性所报道的结构。