Pore-size distributions in filter media with graded densities

Many filter media, composed of a random array of solids, have larger pores on one face than on the other. The face receiving the feed stream is less densely packed than the bottom face. Explained here is a method of determining the differences in the pore-size distributions between the separate faces. The method starts from the knowledge that the most probable pore-size distribution in a thin plane of randomly-arrayed solids is such that the ratio of the standard deviation to the mean is fixed, no matter the value of the mean. In turn, the mean is a function of porosity (the ratio of void volume to bulk volume). Thus, with knowledge of the porosities of the two separate faces, we can deduce the differences between the mean pore sizes, and, thus, the distributions. Methods are suggested for determining the porosities of the separate faces.