Electrohydrodynamic Kelvin–Helmholtz instability with heat and mass transfer: Effect of perpendicular electric field

In this paper, we investigate the effect of perpendicular electric field on the linear analysis of Kelvin–Helmholtz instability of a plane interface between two viscous and dielectric fluids, when the fluids are subjected to constant normal electric field and, when there is heat and mass transfer across the interface. We use viscous correction for the viscous potential flow theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by taking viscous contributions to the irrotational pressure. A quadratic dispersion relation that accounts for the growth of disturbance waves is obtained and stability criterion is given in terms of a critical value of relative velocity as well as applied electric field. It is observed that heat transfer and perpendicular electric field both have destabilizing effect while vapor fraction stabilizes the interface.