EHD instability of two rigid rotating dielectric columns in porous media

Abstract

The present work analyses the linear azimuthal stability of a single interface between two cylindrical dielectric fluids. The theoretical model consists of two incompressible rotating electrified fluids throughout the porous media. The system is influenced by a uniform azimuthal electric field. The inner cylinder is filled with a viscous liquid. The outer one is occupied by an inviscid gas. The problem meets its motivation from a geophysics point of view. Therefore, for more convenience, the problem is considered in a planar configuration. Typically, the normal mode analysis is used to facilitate the stability approach. The examination resulted in a stream function, which is governed by a fourth-order ordinary differential equation with complicated variable coefficients. By means of the Mathematica software along with the special functions, the distribution of the stream function is written in terms of the modified Bessel functions. A non-dimensional procedure exposes some non-dimensional numbers, for instance, Weber, Ohnesorg, Taylor, Rossby and Darcy numbers. These numbers are considered with regard to the temporal and spatial increase of both frequency and modulation. The linear stability theory generated a very complicated transcendental dispersion equation. The influences of various physical parameters in the stability profile were studied as well.