A model of two viscoelastic liquid films traveling down in an inclined electrified channel

Abstract

This study addresses the stability of two immiscible, viscoelastic electrified fluids for two films, each has a finite depth in porous media. The system is subjected to both an interfacial insoluble surfactant and surface charge accumulated at the interface. We study both the cases of small Reynolds and wave numbers, where stability process and numerical calculations are performed to describe the linear stage of the interface evolution. The surface tension is allowed to vary linearly with surfactants and temperature. The governing equations and the corresponding conditions led to three evaluation equations for the stream function, temperature, and the electric potential. In dealing with this system we assumed two cases of both small Reynolds and wave numbers. The stability pictures are illustrated, in which regions of stability and instability are identified. For small Reynolds number, numerical computations show that the surfactants through the elasticity number can be used to either suppress or enhance the interface stability depending on the thickness ratio of the channel. Weber number can be either stabilizing or destabilizing depending on the selected parameters, in particular, the viscosity ratio. Comparing the present results with that available in the literature, our results are in good agreement. In the long-wave limit, both the Darcy number and permeability ratio have a stabilizing influence on the movement of the interface.