Viscous corrections for the viscous potential flow analysis of electrohydrodynamic Kelvin-Helmholtz instability with heat and mass transfer

The linear analysis of Kelvin-Helmholtz instability of the interface between two viscous fluids in the presence of horizontal electric field has been carried out when there is heat and mass transfer across the interface. The viscous correction for the viscous potential flow theory has been used for the investigation. Both fluids are taken as incompressible, viscous and dielectric with different kinematic viscosities and different permittivities. In the viscous potential flow theory, viscosity enters through normal stress balance and effect of shearing stresses is completely neglected. We include the viscous pressure in the normal stress balance along with irrotational pressure and it is assumed that this viscous pressure will resolve the discontinuity of the tangential stresses at the interface of two fluids. A dispersion relation has been derived and stability is discussed theoretically as well as numerically. Stability criterion is given in terms of a critical value of relative velocity of two fluids as well as critical value of the applied electric field. It has been observed that tangential electric field and vapor fraction both have stabilizing effect on the stability of the system while heat and mass transfer destabilizes the interface. Also, it has been found that the effect of irrotational shearing stresses stabilizes the system.