Electrohydrodynamic Kelvin - Helmholtz Instability of Cylindrical Interface through Porous Media

The effect of saturated porous bed structure on the linear analysis of Kelvin Helmholtz instability of cylindrical interface has been carried out, using viscous potential flow theory. The fluids are subjected to be uniform electric field which is acting in the axial direction. The fluids are considered to be viscous and incompressible with different kinematic viscosities. In viscous potential flow theory, viscosity enters through normal stress balance and tangential stresses are not considered. A dispersion relation that accounts for the axisymmetric waves has been obtained and stability criterion has been given in terms of relative velocity. Various graphs have been drawn to show the effect of various physical parameters such as porosity and permeability of medium, viscosity ratio, upper fluid fraction on the stability of the system. It is observed that axial electric field has stabilizing effect while porous media has destabilizing effect on the stability of the system.