Rayleigh–Taylor Instability of Superposed Dusty Jeffrey Fluids through Porous Medium with Interfacial Surface Tension

Abstract

The linear Rayleigh–Taylor instability of two immiscible superposed non-Newtonian fluids saturated by a porous medium in the simultaneous presence of interfacial surface tension and suspended dust particles is investigated. The non-Newtonian behavior of fluids is described by the Jeffrey model. The set of coupled partial differential equations satisfying the appropriate boundary conditions is solved by applying the linear theory and normal mode technique. The exact solutions are found for both regimes with constant density, and the dispersion relation (between the growth rate and the wave number) is obtained. The physical system is found to be stable for a bottom-heavy configuration density-wise, such as in the Newtonian viscous fluid using the Routh–Hurwitz criterion. However, for the unstable configuration, the surface tension, medium porosity, dynamic viscosity, and density of dust particles have a stabilizing impact on the growth rate of the unstable Rayleigh–Taylor mode; whereas the density difference between the fluids and the Jeffrey parameter has a destabilizing effect on the growth rate of the unstable Rayleigh–Taylor mode.