We analyze the interfacial instability of a thin film confined between a rigid surface and a pre-stretched elastic sheet, triggered by non-uniform electro-osmotic flow. We derive a nonlinear viscous$-$elastic equation governing the deformation of the elastic sheet, describing the balance between viscous resistance, the dielectric and electro-osmotic effects, and the restoring effect of elasticity. Our theoretical analysis, validated by numerical simulations, shows several distinct modes of instability depending on the electro-osmotic pattern, controlled by a non-dimensional parameter representing the ratio of electro-osmotic to elastic forces. We consider several limiting cases and present approximate asymptotic expressions predicting the electric field required for triggering of the instability. Through dynamic numerical simulations of the governing equation, we study the hysteresis of the system and show that the instability can result in an asymmetric deformation pattern, even for symmetric actuation. Finally, we validate our theoretical model with finite-element simulations of the two-way coupled Navier equations for the elastic solid, the unsteady Stokes equations for the fluid, and the Laplace equation for the electric potential, showing very good agreement. The mechanism illustrated in this work, together with the provided analysis, may be useful in toward the implementation of instability-based soft actuators for lab-on-a-chip and soft-robotic applications.

中文翻译：

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电渗流驱动的软微流态薄膜的界面不稳定性

我们分析了由不均匀的电渗流触发的，限制在刚性表面和预拉伸弹性片材之间的薄膜的界面不稳定性。我们得出非线性粘性$-$弹性方程式，用于控制弹性片的变形，描述了粘滞电阻，介电和电渗透效应以及弹性恢复效应之间的平衡。我们的理论分析（通过数值模拟验证）显示了几种不同的不稳定模式，具体取决于电渗模式，并由代表电渗与弹性力之比的无量纲参数控制。我们考虑了几种极限情况，并给出了近似渐近表达式，预测了引发不稳定性所需的电场。通过控制方程的动态数值模拟，我们研究了系统的滞后现象，并表明，即使进行对称致动，不稳定性也会导致不对称变形。最后，我们通过对弹性固体的双向耦合Navier方程，对于流体的非稳态Stokes方程以及对电势的Laplace方程的有限元模拟，验证了我们的理论模型。这项工作中说明的机制以及所提供的分析，可能有助于实现针对芯片实验室和软机器人应用的基于不稳定性的软执行器。