Instability in a non-ohmic/ohmic fluid interface under a perpendicular electric field and unipolar injection

Abstract

We set the equations for the linear electrohydrodynamic instability of an interface between two fluids, subjected to a perpendicular field and a unipolar charge injection. One of the fluids is modeled as being in non-ohmic regime (insulating), whereas the other is ohmic. A new interfacial instability mechanism is described, which may account for the Rose-window instability. The equations are analytically solved in the limit of long wavelength and neglecting the fluid motion. We show that this limit applies well to the case of an air-ohmic liquid interface. The applicability to a liquid-liquid interface is also analyzed.