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.