Cluster volume and surface area in dispersions of penetrable particles or pores

The complete description of a homogeneous, multiphase dispersion is contained within the infinite set of n-body density distribution functions g(rn) which have been used to calculate macroscopic properties such as interfacial area and specific volume. Certain quantities of interest, however, must take the connectedness of the individual phases into account. This requires the introduction of a complete set of n-body connectedness functions g+n(rn). Until now, only the pair-connectedness function g+2(r2) has been computed. Here, a formalism for the estimation of higher-order connectedness functions from lower order ones is presented. Results are given for the average volume and interfacial area per cluster for a dispersion of randomly placed spheres.