Abstract
Nonlinear electrohydrodynamic stability of two superposed dielectric bounded fluids streaming through porous media in the presence of a horizontal electric field is investigated in three dimensions. The method of multiple scales is used to obtain a dispersion relation for the linear problem and a Ginzburg-Landau equation for the nonlinear one, describing the behavior of the system. The stability of the system is discussed both analytically and numerically, and the stability conditions are obtained. It is found, in the linear case, that the stability criterion is independent of the permeability of the medium and that the fluid viscosities, velocities, depths, and the dimension have destabilizing effects, while the porosity of porous medium, electric field, and surface tension have stabilizing influences on the system. In the nonlinear case, using the obtained stability conditions, the effects of all physical parameters included in the analysis on the stability of the system are discussed in detail for both two- and three-dimensional disturbances cases, respectively. The system has been found to be usually unstable if the fluids are pure for both cases. It is found also that the dimension has a dual role (stabilizing as well as destabilizing) on the considered porous system, whereas it has a destabilizing effect if the medium is nonporous.