Motion of the Interface between Two Immiscible Liquids of Unequal Density in a Porous Solid

Abstract

A general solution is obtained to a two-dimensional problem of the movement of the interface between two immiscible liquids of unequal density in a porous solid, the interface motion being the result of the force of gravity acting on the two liquids. The solution is obtained by direct potential theory methods and employs a method of approximation similar to that used in the linear theory of water waves. It is shown that the elevation of the interface above its equilibrium position satisfies a ``nonoscillatory'' wave equation, i.e., the classical wave equation in which the wave velocity is pure imaginary. The solution of the special case of an initially plane tilted interface is included.