Modeling the relationships between particle and pore size distributions in multicomponent sphere packs: Application to the water retention curve

A probabilistic approach that computes the distribution of the volume of the voids in packed spheres given their size distribution is applied to determine the corresponding water retention curves. The assumption of dense random packing is adopted. The volume of the void determined by four spheres mutually in contact is approximated by the volume of the osculatory sphere. Every void is accessible through four openings. The size of these openings is assumed to be represented by the respective osculatory discs. Applying the law of capillarity to the radii of the voids and their openings, the hysteretic water retention function characterizing multicomponent sphere packs is defined. The approach is applied to power law, Gaussian and log-normal sphere size distributions. The water retention function and the hysteretic domain are found to depend upon the distribution type, the power exponent and the standard deviation. The power law distribution generates the narrowest hysteretic domain and the highest water capacity. The normally distributed sphere sizes generate the widest hysteretic domain and the lowest water capacity. Increasing the standard deviation of the sphere size distribution reduces the hysteretic domain for most of the effective saturation range, mainly because of the effect on the drying curve. (C) 1997 Elsevier Science B.V.