M.F. El-Sayed

Effect of normal electric fields on Kelvin–Helmholtz instability for porous media with Darcian and Forchheimer flows

The linear electrohydrodynamic Kelvin–Helmholtz instability of the interface between two dielectric fully saturated porous media under the effect of normal electric fields is considered. The lighter fluid is above the heavier one so that in the absence of both motion and electric fields, the arrangement is stable and the interface is flat. It is shown that when the fluids are moving parallel to each other at different velocities, the interface may become unstable, and the normal electric fields have usually destabilizing effect. The corresponding conditions for marginal stability are derived for Darcian and Forchheimer flows. In both the cases, the velocities, and the electric fields should exceed some critical values in order for the instability to manifest itself. In the case of Darcy’s flow, however, an additional condition, involving the fluids viscosities, their density ratios and the electric field values is required.

Effect of general applied electric field on conducting liquid jets instabilities in the presence of heat and mass transfer

A novel system to study the effect of general applied electric field on the stability of a cylindrical interface between the vapor and liquid phases of conducting fluids in the presence of heat and mass transfer is investigated. The vapor is hotter than the liquid and the two phases are enclosed between two cylindrical surfaces coaxial with the interface. The linear dispersion relations are obtained and discussed, for both cases of axial and radial constant electric fields, and the stability of the system is analyzed theoretically and numerically for both cases. Some limiting cases in the literature and discussed and recovered. In the former case of axial electric field, both axisymmetric and asymmetric disturbances are considered. It is found, in this case, that the heat and mass transfer, revealed through a single parameter, has no influence on the stability of the system, which is contrary to the stabilizing result obtained earlier for plane geometry. In the later case of radial electric field, it is found that each of the heat and mass transfer, the azimuthal wavenumber, and the dimensions of the system has a stabilizing effect; while the electrical conductivity has a destabilizing influence on the considered system.

NONLINEAR KELVIN-HELMHOLTZ INSTABILITY OF TWO SUPERPOSED DIELECTRIC FINITE FLUIDS IN POROUS MEDIUM UNDER VERTICAL ELECTRIC FIELDS

A weakly nonlinear theory of wave propagation in two superposed dielectric fluids streaming through porous media in the presence of vertical electric field and in the absence of surface charges at their interface 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 with complex coefficients for the nonlinear problem, describing the behavior of the system. The stability of the system is discussed both analytically and numerically in both cases, and the corresponding stability conditions are obtained. It is found, in the linear case, that the stability criterion is independent of the medium permeability and that the medium porosity, surface tension, and dimension all have stabilizing effects the fluid viscosities, velocities, and depths have destabilizing effects, and the electric field has a dual role in the stability of the system. In the nonlinear analysis, it is found that the electric field has a stabilizing effect in two-dimensional disturbances and destabilizing effect in three-dimensional disturbances cases. The surface tension, fluid depths, and medium porosity have stabilizing effects in both two- and three-dimensional disturbance cases and the fluid viscosities, velocities, and medium permeability have destabilizing effects in both cases, and this stability or instability occurs faster for three-dimensional disturbance cases. It is found also that the system is unstable in the absence of fluid velocities or for nonporous media. Finally, the dimension was found to have a dual role (stabilizing as well as destabilizing) in the considered system, while it has a destabilizing effect in the case of nonporous media.