Linear stability of a thin film flow along permeable wall under alternating electric field

Abstract

This study considers the linear stability of two‐layer films of immiscible liquids confined between an upper impermeable solid plate and a lower porous rigid substrate. The fluids are subjected to a periodic electric field. Based on the von Kármán‐Pohlhausen method an integral boundary‐layer model for the film thickness, surface charge and the flow rate is derived. The dynamics of the liquid‐liquid interface is described for arbitrary amplitudes by evolution equations derived from the basic hydrodynamic equations using long wave approximation. The parameters governing the film flow system and the permeable substrate strongly effect the wave forms and their amplitudes and hence the stability of the fluid. Analytical and numerical simulations of this system of linear evolution equations are performed. The case of uniform electric field is considered as special case, it is found that, the permeability of the porous medium promotes the oscillatory behavior. While a stabilizing influence is observed for increasing of both the non‐dimensional conductivity and the electric conductivity ratio. When the case of alternating electric field is taken into account, the method of multiple scales is applied to obtain approximate solutions and analyze the stability picture. Stability behavior is noticed for the decreasing of the permeability parameter and the dielectric constant ratio of the fluids.