Theory of the rate of wetting of a porous medium

Abstract

The classic equations of Washburn and Rideal for the rate of penetration of a fluid into a capillary due to surface tension are re-examined and time-dependent solutions are obtained for large times in both horizontal and vertical flow. By applying Darcy's law, a general theory of wetting of a porous medium is derived. The rate of fluid penetration is expressed in a form analogous to that for a capillary, in terms of fluid viscosity, surface tension, porosity and permeability. The permeability is calculated for the Happel–Kuwabara cell model of a porous medium, consisting of a swarm of identical spherical particles.