Interfacial surface statistics arising in diffusion and flow problems in porous media

A study is made of the surface-void, surface-surface, and surface-particle correlation functions that arise in expressions for transport properties associated with diffusion-controlled reactions and flow in porous media consisting of impenetrable spherical particles distributed randomly throughout void. The relationship between these three different correlation functions is noted for this model. We present an exact low-density expansion of the surface-particle correlation for such a distribution. All of the two-point correlation functions are computed, for the first time, from integral relations that we derived elsewhere, as a function of the distance between the two points for various sphere volume fractions up to 94% of the random close-packing value.