Nonlinear analysis of capillary instability with mass transfer through porous media

In this paper, we investigate the nonlinear capillary 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, leads to imposing a first-order nonlinear partial differential 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 the heat and mass transfer and porous medium both stabilize the interface while porosity supports the growth of disturbance waves.