Influence of boundary roughness on the saturation of electrohydrodynamic Rayleigh-Taylor instability in two superposed fluids in the presence of nanostructured porous layer

Abstract

Using linear stability analysis, the influence of boundary roughness on electro-hydrodynamic Rayleigh-Taylor instability (EHRTI), in a poorly electrically conducting fluid film of finite thickness, is studied. It is a theoretical study, based on the assumption of densely packed porous lining, prepared with smart material of nanostructure, that permits the use of modified Darcy equation with Saffman-slip condition at the interface. Modify means the addition of Lorentz forces due to magnetic and electric fields. A dispersion that accounts for the growth rate of perturbed waves is derived and stability discussed theoretically. The effects of electromagnetic fields, surface tension, boundary roughness, and porous layer are demonstrated using Stokes and lubrication approximations and shown graphically for the above-said physical parameters on the stability of the system. The strength of electromagnetic fields, porous layer and boundary roughness decreases the unstable growth rate for finitely conducting fluids, while surface tension stabilizes the system for a lower Bond number.