Electrohydrodynamic instability of a suspended liquid film

Electrohydrodynamic instabilities at liquid-liquid interfaces are of high importance due to their relevance in various microfluidic applications. In this work, we analyze the stability of a system of three superposed layers of two immiscible liquids subject to a normal electric field. Following the leaky-dielectric model, the interfaces admit free charge while the bulk remains electroneutral. Interfacial charge dynamics is captured by a conservation equation accounting for Ohmic conduction, advection by the flow, and finite charge relaxation. We use this model to perform a linear stability analysis and uncover regimes of instability in terms of the relevant dimensionless groups of the problem.