Fundamental Aspects of Fluid Flow through Porous Materials

Abstract

An approach to the study of fluid flow through porous materials based on Darcy’s law and the continuity equation is introduced as a possible means of studying fluid uptake by paper. The approach leads to a flow equation that may be put in the form of a diffusion equation with a diffusivity dependent on the fluid content. Hence, with the boundary conditions imposed during one-dimensional fluid uptake by a porous material initially at a uniform fluid content, the uptake is proportional to the square root of time, which is the same result as given by the Green & Ampt equation and the Lucas-Washburn equation, both of which use the analogy of fluid flow through capillary tubes.