Electrohydrodynamic instability of two superposed viscous miscible streaming fluids

The linear stability of two dielectric viscous fluids separated by a horizontal interface is investigated. The interface admits heat and mass transfer. The system is stressed by a normal periodic electric field producing surface charges at the interface. The effect of surface tension, small viscosity, velocity streaming and gravity on the critical surface charges density and on corresponding electric field are analyzed. The contribution of viscosity with the existence of surface charges and streaming are discussed. The investigation includes the stability analysis of the presence of the periodic electric field as well as the constant one. It is found that the presence of the surface charges made by the normal electric field play a dual role in the stability criterion, which shows some analogy with the nonlinear theory of stability. Some previous studies are compared using appropriate data. The marginal state of stability is also considered. It is found that the surface charges vanish under certain conditions. This study shows that the mass and heat transfer parameter has a destabilizing effect whether the electric field is static or periodic. Parametric excitation of the electrohydrodynamic (EHD) surface waves is analyzed in the case of Rayleigh–Taylor (R–T) instability. The transition curves are obtained by means of Whittaker's technique. The analytical results are numerically confirmed.