Electrohydrodynamic interfacial instability at a stagnation point

A wide variety of physical systems and engineering applications involve the deformation of fluid interfaces under the combined effects of an applied electric field and an external fluid flow. Here, we present analytic and numerical approaches to study the stability of a planar interface separating two immiscible fluids subject to an imposed stagnation point flow and a tangential electric field. The interfacial charge dynamics is modeled by accounting for Ohmic conduction, advection by the flow and finite charge relaxation. Using this model, we perform a local linear stability analysis in the vicinity of the stagnation point to study the behavior of the system in terms of the relevant dimensionless groups of the system. Further, we present a numerical normal-mode linear stability analysis based on the full system of equations and boundary conditions using the boundary element method. This allows us to uncover the most unstable eigenmodes directly. Our analysis demonstrates how the interplay between charge convection and conduction in the dominant mode of instability leads to a stabilizing effect. Finally, using numerical simulations of the full nonlinear problem, we demonstrate how the coupling of flow and interfacial charge dynamics gives rise to nonlinear phenomena such as tip formation and the development of charge density shocks.