NONLINEAR ELECTROVISCOUS POTENTIAL FLOW INSTABILITY OF TWO SUPERPOSED COUPLE-STRESS FLUIDS STREAMING THROUGH POROUS MEDIUM

Abstract

Nonlinear Kelvin–Helmholtz instability of two supersposed couple-stress fluids saturating a porous medium in the presence of nor mal electric fields when there are no sur face charges at the interface is investigated in three dimensions via the viscous potential flow analysis. The multiple time scales method is used to obtain a dispersion relation for the linear problem and a Ginzburg–Landau equation with complex coef ficients for the nonlinear problem, describing the behavior of the system. The stability conditions are obtained and discused both analytically and numerically in both linear and nonlinear cases in two- and three-dimensional disturbances. It is found, in the linear case, that the sur face tension, porosity of the porous medium, kinematic viscosities, and kinematic viscoelasticities have stabilizing ef fects, while the fluid velocities and applied electric fields have destabilizing ef fects. In the nonlinear analysis, it is found that the medium per meability, porosity of porous medium, and sur face tension have destabilizing ef fects, while the fluid velocities, electric fields, and kinematic viscoelasticities have stabilizing ef fects, and the kinematic viscosities have slightly stabilizing ef fects only af ter a critical wavenumber value. The stability of the system has been compared in twoand three-dimensional disturbances