Electrohydrodynamic Rayleigh - Taylor instability in a poorly conducting fluid layer bounded above by a nanostructured porous layer

Abstract

Electrohydrodynamic Rayleigh - Talyor instability (ERTI) at the interface region between a thin poorly conducting incompressible viscous fluid saturated nanostructured porous layer and a poorly conducting fluid layer in the presence of a non-uniform electric field is investigated using linear stability analysis. A simple theory based on electrohydrodynamic approximations and Saffman slip condition is proposed. An analytical expression for dispersion relation is derived in the form of n = n_b - β/v_a, where n is the growth rate and β/v_a, is the effect of compression. It is shown that the porous lining and transverse electric field control the growth rate of ERTI depending on whether the applied electric field is opposing or aligning the direction of gravity. In particular, we found that n tends to zero for equipartition of energy (i. e., Weber number We = 1).