Modelling pore size distributions and water retention functions in dense polydisperse sphere packings

A probabilistic approach that determines the distribution of the volume of the voids (VSD) in packed spheres, given their size distribution (PSD), is proposed. The tetrahedron system of the dense random packing is adopted, but the probability of its formation is expressed in a new way, in terms of the radii, the PSD, and the pair formation probability of the spheres. The volume of the void within each tetrahedron is approximated by the volume of the osculatory sphere. This void is accessible through four openings, formed by the three touching spheres on each face of the tetrahedron. The size of these openings is assumed to be represented by the respective osculatory discs. Applying the law of capillarity to the voids and to their openings, the hysteretic water retention function characterizing the pack is defined. The approach is applied to spheres with power law, gaussian and log-normal distribution of sizes. The power law distribution generates a bell-shaped void size distribution. However, for the gaussian and the log-normal case, the type of the VSD is similar to that of the PSD through a non-linear transformation relating the sphere radius to the pore radius. The water retention function and the hysteretic domain depend upon the PSD and its standard deviation.