  Electrohydrodynamic instabilities of fluid-fluid interfaces can be exploited
in various microfluidic applications in order to enhance mixing, replicate
well-controlled patterns or generate drops of a particular size. In this work,
we study the stability and dynamics of a system of three superimposed layers of
two immiscible fluids subject to a normal electric field. Following the
Taylor-Melcher leaky dielectric model, the bulk remains electroneutral while a
net charge accumulates on the interfaces. The interfacial charge dynamics is
captured by a conservation equation accounting for Ohmic conduction, advection
by the flow and finite charge relaxation. Using this model, we perform a linear
stability analysis and identify different modes of instability, and we
characterize the behavior of the system as a function of the relevant
dimensionless groups in each mode. Further, we perform numerical simulations
using the boundary element method in order to study the effect of
nonlinearities on long-time interfacial dynamics. We demonstrate how the
coupling of flow and surface charge transport in different modes of instability
can give rise to nonlinear phenomena such as tip streaming or pinching of the
film into droplets.
