AbstractA differential equation is derived which describes the pressure distribution during steady flow in a porous material occupied by two immiscible fluids such as air and water. It is assumed that Darcy's equation applies simultaneously to the wetting and the nonwetting phase. Each phase is assumed to be continuous, and therefore, any isolated portions of either phase must be regarded as part of the porous matrix. The equation may be applied to fluids flowing in any direction with respect to each other or in any direction with respect to the earth's gravitational field. In order to solve the equation, it is necessary to know the relationship between the pressure discontinuity across interfaces between the phases and the conductivity of the flowing phase or phases. The nature of this function and a method of obtaining it are discussed briefly.Experiments were conducted using a hydrocarbon liquid as the wetting fluid, air as the nonwetting fluid, and long columns of sand as porous media. Several cases were investigated, and results of two are presented: (1) downward flow through a uniform sand, and (2) downward flow through a sand into another sand of finer texture. Good agreement between experimental data and theory was obtained for all cases.

Scott, V. H., & Corey, A. T. (1961). Pressure Distribution During Steady Flow in Unsaturated Sands. Soil Science Society of America Journal, 25(4), 270–274. Portico.