Existence of solitary travelling waves in interfacial electrohydrodynamics

Abstract

The propagation of waves on the surface of a fluid layer of finite depth is considered in the presence of a normal electric field, due to parallel electrodes at an arbitrary separation distance. The combined effect of electric field, gravity and surface tension is considered in the long-wavelength–small-amplitude limit. Travelling wave solutions are characterised in terms of the Froude number, an electric Weber number and a Bond number and conditions for the existence of solitary waves are determined in terms of these parameters.