Capillary Conduction of Liquids Through Porous Mediums

The flow of liquids in unsaturated porous mediums follows the ordinary laws of hydrodynamics, the motion being produced by gravity and the pressure gradient force acting in the liquid. By making use of Darcey's law, that flow is proportional to the forces producing flow, the equation K∇2ψ+∇K·∇ψ+g∂K/∂z=−ρsA∂ψ/∂t may be derived for the capillary conduction of liquids in porous mediums. It is possible experimentally to determine the capillary potential ψ=∫dp/ρ, the capillary conductivity K, which is defined by the flow equation q=K(g−▿ψ), and the capillary capacity A, which is the rate of change of the liquid content of the medium with respect to ψ. These variables are analogous, respectively, to the temperature, thermal conductivity, and thermal capacity in the case of heat flow. Data are presented and application of the equations is made for the capillary conduction of water through soil and clay but the mathematical formulations and the experimental methods developed may be used to express capillary flow for other liquids and mediums. The possible existance of a hysteresis effect between the capillary potential and moisture content of a porous medium is considered.