Abstract
The electrohydrodynamic Kelvin-Helmholtz instability of the plane interface between two uniform superposed dielectric fluids of finite depths permeated with suspended particles through a porous medium is considered under the influence of general applied horizontal or vertical (in the absence and presence of surface charges) electric fields. Applying appropriate boundary conditions, the corresponding dispersion relations are obtained in these cases. Using a novel technique, the stability conditions are derived, separately, and some limiting cases are recovered. The maximum growth rates and corresponding critical dominant wavenumbers are discussed in detail if the two fluids are bounded or not, and also in the absence or presence of sutface charges. It is found that the horizontal electric field, porosity of a porous medium, and surface tensions have stabilizing effects, while the vertical electric fields and fluid velocities have destabilizing effects. Also, the fluid viscosities are found to have stabilizing as well as destabilizing effects, and the medium permeability has an opposite effect, while the number densities of suspended particles have no effect on the stability of the considered system.