EHD KELVIN-HELMHOLTZ INSTABILITY OF TWO SUPERPOSED BOUNDED VISCOUS DIELECTRIC FLUIDS WITH SUSPENDED PARTICLES IN POROUS MEDIUM

The linear electrohydrodynamic Kelvin-Helmholtz instability of the plane interface between two uniform superposed viscous dielectric fluids of finite depths permeated with suspended dust particles streaming through porous ninth' m has been investigated in three-dimensional configuration. The perturbed equations of motion and the appropriate boundary and interfacial conditions are combined to obtain a dispersion relation in a complicated form, which can not be solved in a closed form. We solve the dispersion relation numerically via a novel technique using Muller's method and Gaster's theorem to tabulate the growth rates in terms of wave numbers for various values of the other physical parameters. It is found that the electric field, fluid velocities, and number densities of the particles have stabilizing effects on the system. It is shown also that the medium permeability, dynamic viscosities, dielectric constants, and porosity of porous medium have a destabilizing effect. Finally, fluid densities are found to have dual roles on the stability of the system separated by a constant wave number value. A comparison between these results and the corresponding results obtained earlier for ideal fluids has been achieved for the parameters. It is noted that the suspended dust particles have a stabilizing effect, while they have no effect on the stability of the system in absence of fluid viscosities.