An approach based on the porous media model for multilayered flow in the presence of interfacial surfactants

Abstract

The current study deals with the linear stability of a fluid multilayered system in the presence of porous media. Fluids are subject to normal electric field, where there are insoluble surfactants contaminating the interfaces. The physical model consists of an inner layer sandwiched between two semi-infinite fluids. A single surface between two different fluid layers is studied as a limiting case, in which a small Reynolds number is covered. The objective of this work is to investigate the impact of viscosity and porosity properties on the linear growth rate and the sheet behaviour as a result of the interfacial surfactants. In the light of boundary constraints and geometry of the imposed system, the solutions of the hydrodynamic equations of motion lead to an implicit dispersion equation that basically depends on the growth rate along with the wave number. The physical parameters that control the fluid sheet strongly and significantly affect the shape of the waves, their amplitude and thus the stability profile of the liquid layers. Through the theoretical and analytical study, in addition to the numerical visualisations, the stability pictures are plotted and investigated. It is observed that both Marangoni and electric Weber numbers play opposite roles on the stability of the fluid sheet. This means that Marangoni number works to inhibit the growth rate while, the electric number encourages a stretching in the wave amplitude.