Pressure Corrections for the Potential Flow Analysis of Electrohydrodynamic Kelvin-Helmholtz Instability

The present paper deals with the study of the pressure corrections to the viscous potential flow analysis of Kelvin-Helmholtz instability with tangential electric field at the interface of two viscous fluids. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses for two fluids are not continuous at the interface. Here we have considered viscous pressure in the normal stress balance along with the irrotational pressure and it is assumed that the addition of this viscous pressure will resolve the discontinuity between the tangential stresses and the tangential velocities at the interface of two fluids. The viscous pressure is derived by mechanical energy balance equation and this pressure correction applied to compute the growth rate of electrohydrodynamic Kelvin-Helmholtz instability. A dispersion relation is obtained and stability criterion is given in the terms of critical value of relative velocity. It has been observed that the inclusion of irrotational shearing stresses have stabilizing effect on the stability of the system.