Elastic deformation instability in soft microfluidic configurations induced by non-uniform electro-osmotic flow*

We study theoretically and experimentally the deformation instability of an elastic sheet separated from a rigid surface by a thin liquid film subjected to non-uniform electro-osmotic flow. We first provide insight into the physical behavior of the system by considering a simplified model, inspired by electrostatic MEMS actuators, in which the elastic sheet is modeled as a rigid plate connected to a linear spring. Our theoretical analysis, supported by experimental observations, reveals an instability that is controlled by a non-dimensional parameter representing the ratio of electro-osmotic to elastic forces, and also indicates the existence of hysteresis for the onset of instability. We consider both a constant voltage and constant current actuation modes, and expand our analysis for the case of an elastic sheet that is free to deform under bending and tension conditions, providing approximate asymptotic solutions validated by numerical simulations.