Interfacial EHD instability of a liquid of finite conductivity under unipolar charge injection

Low conducting liquids exhibit the so-called rose-window instability. This instability appears when charge is injected in an air-liquid interface. It seems to be associated to the destabilizing role of the electric pressure onto the surface. Depending on the liquid conductivity the charge on the interface is of the same sign (low conductivity) or opposite sign (high conductivity) to that of the injected charge. Both situations have different instability thresholds. In this paper we write down and solve numerically the linearized equations of motion of the liquid, assuming that it behaves as an ohmic conductor.