A general analysis for the electrohydrodynamic instability of stratified immiscible fluids

Abstract

A general solution approach for the electrohydrodynamic instability of stratified immiscible fluids is presented. The problems of two and three fluid layers subject to normal electric fields are analysed. Analytical solutions are obtained by employing the transfer relations (Melcher 1981 Continuum Electromechanics. MIT Press) relating the disturbance stresses to the flow variables at the interface(s). This approach provides a convenient alternative to the direct solution of the linearized problem. The results assume a general format. Both new dispersion relations and those from various previous works are shown to be special cases when proper simplifications are considered. As a specific example, the instability behaviour of a three-layer channel flow is investigated in detail using this framework. This work provides a unifying method to treat a generic class of instability problems.