Stability of Liquid Interfaces in Porous Media

Abstract

An analysis is presented for the stability of liquid interfaces moving with uniform velocities in homogeneous isotropic porous media. The effects of viscosity, surface tension, and body forces are taken into account. The first part of this investigation concerns the linear stability of a finite depth liquid layer bounded by two semi-infinite liquids. It is found that the critical conditions separating stable from unstable disturbances are independent of the depth of the liquid layer. For a sufficiently large flow velocity, the system is stable if, across each interface, the viscosity decreases in the direction of flow, and it is unstable if viscosity increases in the direction of flow across at least one interface. The second part treats the nonlinear frontal stability of two semi-infinite liquids. The results show that the nonlinearity is destabilizing owing to the decrease of the surface tension force. Deviations from Darcy's law are found to be stabilizing when the flow is from the denser to the lighter fluid and vice versa.