The stability and mixing of a density-stratified horizontal flow in a saturated porous medium

Abstract

The mixing of two miscible fluids in motion in a saturated isotropic porous medium and the stability of the density interface between them has been studied. The density interface was formed by a line source introducing a denser fluid into a uniform confined horizontal flow. It was shown that the half-body thus formed may be approximated to within the density difference by the shape when the densities are equal. The mixing of the two fluids by lateral dispersion along such an interface was investigated experimentally and it was found that up to density differences of at least 1 per cent there was no observable effect on the lateral dispersion coefficient. A theoretical investigation has been made of the stability of the uniform two-dimensional horizontal motion of two miscible fluids of different density in a saturated, isotropic, homogeneous porous medium. The fluid of higher density overlay the lower density fluid and both were moving with the same seepage velocity in the same direction. The analytical solution for the stability was obtained from the continuity equation, Darcy's law and the dispersion equation by investigating the stability of arbitrary sinusoidal perturbations to the velocity vector and the density profile prescribed by the lateral dispersion of one fluid into the other. A stability equation similar to the Orr-Sommerfeld equation was obtained and a neutral stability curve in a wave number - Rayleigh number plane was found by two approximate methods. The growth rates of instabilities were investigated for a linear density profile and it has been found that although the flow was always unstable the growth rates of unstable waves could be so low as to form a quasi-stable flow; examples of such flows have been demonstrated experimentally.