Abstract
The linear stability analysis of a two-dimensional incompressible leaky dielectric viscous liquid sheet, saturating porous medium of the Brinkman (or Darcy) types, surrounded by a hydrodynamically passive conducting medium when an electric field is applied parallel to the initially flat bounding fluid interfaces and admitting surface charges has been investigated. The dispersion relation is derived in each case, and the stability discussion, based numerically on the root-finding solution of the dispersion equation, has been achieved. For the Brinkman model, we found that the electric Weber number and conductivity ratio have destabilizing effects, and both the permittivity ratio and medium permeability have dual roles on the stability of the system, while the Reynolds number and porosity of porous medium have stabilizing effects. It is found also that the system is more unstable in the presence of a porous medium than in its absence. For the Darcy model, we found that the electric Weber number, permittivity ratio, and Reynolds number have stabilizing effects, and the conductivity ratio has a destabilizing effect, while both the porosity and permeability have usually stabilizing effects that decrease (or increase) by increasing the porosity (or permeability), respectively.