Electrohydrodynamic Kelvin-Helmholtz Instability of Two Bounded Superposed Viscous Fluids Streaming with Fine Dust in Porous Medium

Abstract

The electrohydrodynamic Kelvin Helmholtz instability of the plane interface between two uniform superposed viscous dielectric fluids of finite depths permeated with suspended dust particles through a porous medium has been considered in three-dimensional configuration. Applying appropriate boundary conditions, the corresponding dispersion relations has been obtained in a complicated form. Using a novel numerical technique. The effect of various parameters on the stability have been discussed in detail, according to the behavior of growth rates against the wave number, where the maximum growth rates and corresponding dominant as well as the critical wave numbers have been used to show these effects. This problem has been solved once again in two-dimensional case via the viscous potential flow analysis method, and the corresponding dispersion relation has been obtained. The stability discussion has been carried out via a critical value of the relation velocity of the two fluids as well as the growth rate. Some limiting cases are considered and recovered previous works in the literature. Conclusions for both problems are summarized at the end of each chapter, with one appendix.