Interfacial instability of thin films in soft microfluidic configurations actuated by electro-osmotic flow

We analyze the interfacial instability of a thin film confined between a rigid surface and a prestretched elastic sheet, triggered by nonuniform 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 nondimensional 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.