Abstract. The aim of the lecture is to demonstrate how the so-called factorial functional expansions can be applied to the solution of a wide class of transport problems in random particulate media. The solution is understood hereafter in statistical sense, i.e., one should evaluate all multipoint correlation functions for the needed random fields (temperature, defect concentration, displacement,etc.) making use of the given statistical description of the medium. In particular one would be thus able to interrelate rigorously the effective properties and the microstructural description. For simplicity we deal with a rigid random dispersion of non- overlapping spheres of radius a. We first recall (Sec. 2) the definition and the basic virial property of the factorial series [7]. In Sec. 3 the procedure of identification for the kernels is briefly discussed. In Sec. 4 we consider several examples (heat propagation, steady-state diffusion and an elastostatic counterpart of the sedimentation problem), and find the needed random fields to the order c^2 , where c is the volume fraction of the spheres.

[7]. Markov, K. Z., On the factorial functional series and their application to random media. SIAM J. Appl. Math., 51, 1991, No 1, 172-186.