Pressure Corrections in the Potential Flow Analysis of Electrohydrodynamics Kelvin-Helmholtz Instability of Cylindrical Interface through Porous Media

The effect of pressure correction on the linear analysis of Kelvin-Helmholtz instability of cylindrical interface in presence of saturated porous bed structure has been carried out, considering viscous potential flow theory. In the viscous potential flow theory, viscosity enters through normal stress balance and tangential stresses are not considered. The assume fluids in the system are considered to be viscous and incompressible with different kinematic viscosities. The fluids are subjected to be uniform electric field which is acting in the axial direction. A dispersion relation that accounts for the axisymmetric waves has been obtained and stability criterion has been given in terms of relative velocity. The viscous pressure is derived by mechanical energy equation and this pressure correction applied to compute the growth rate of Kelvin-Helmholtz instability. The difference 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. By the observation of the graphs, that axial electric field has stabilizing effect while porous media has destabilizing effect on the stability of the system.