Instability of an interface between air and a low conducting liquid subjected to charge injection

Abstract

We study the linear stability of an interface between air and a low conducting liquid in the presence of unipolar injection of charge. As a consequence of charge injection, a volume charge density builds up in the air gap and a surface charge density on the interface. Above a certain voltage threshold the electrical stresses may destabilize the interface, giving rise to a characteristic cell pattern known as rose-window instability. Contrary to what occurs in the classical volume electrohydrodynamic instability in insulating liquids, the typical cell size is several times larger than the liquid depth. We analyze the linear stability through the usual procedure of decomposing an arbitrary perturbation into normal modes. The resulting homogeneous linear system of ordinary differential equations is solved using a commercial software package. Finally, an analytical method is developed that provides a solution valid in the limit of small wavenumbers