Electroviscous potential flow analysis for two bounded fluids streaming with mass and heat transfer in a porous medium

Using viscous potential flow theory, the linear stability analysis of two superposed dielectric fluids streaming with interfacial transfer of mass and heat through porous media is studied for two layers of finite thickness. The system is influenced by general applied horizontal or vertical (in absence or presence surface charges) electric fields. The method of multiple scales with appropriate boundary conditions are used to derive a quadratic dispersion relation in frequency with complex coefficients, separately. The stability of the system is conferred in detail and some limiting cases are recovered. It is observed that the horizontal electric field, porosity of a porous medium, fluid viscosities and surface tensions, increase the stability of the system while the vertical electric field, medium permeability, fluid velocities and fluid depths reduce the stability of the system. Lately the instability in the presence of surface charges at the interface occurs faster than the case of the absence of surface charges. Finally, the mass and heat transfer play a dual role on the stability of the system for vertical (in presence of surface charges) electric fields, while it increase the stability of the system for other cases.