Nonlinear Rayleigh–Taylor instability of cylindrical flow with mass transfer through porous media

The work discusses nonlinear Rayleigh–Taylor instability of the interface between two viscous, incompressible and thermally conducting fluids in a fully saturated porous medium, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. We use viscous potential flow theory in which the flow is assumed to be irrotational and viscosity enters through normal viscous stresses at the interface. The perturbation analysis, in the light of the multiple expansions in both space and time, leads to imposing the well-known Ginzburg–Landau equation. The various stability conditions are discussed both analytically and numerically. The results are displayed in many plots showing the stability criteria in various parameter planes. It is observed that heat and mass transfer has stabilizing effect on the stability of the considered system while medium porosity destabilizes the interface. The flow through porous media is more stable than the pure flow.