Rayleigh-Taylor instability with surface tension, porous media, rigid planes and exponential densities

The Rayleigh-Taylor instability of a slab of two exponential densities through porous media in the presence of surface tension is studied. The lower fluid is of decreasing exponential density while the upper fluid is of increasing density, A general dispersion relation is obtained and discussed analytically and numerically. Some special cases are recovered from the general dispersion relation. It is found that, the stratifications of the upper region as well as the permeabilities of the two regions have a destabilizing effect. It is also found that, the stratifications of the lower region, has a stabilizing effect. These conclusions with and without the stabilizing effect of surface tension are plotted.