On the Irreducible Tensors Method in the Theory of Diffusive Interaction between Particles

Abstract

In the papers by Elperin and Krasovitov ^1–3 the authors claim that they have suggested a new method called “modified method of irreducible multipoles” in order to solve the quasi steady state heat and mass transfer equations for systems with many interacting burning particles. “A method of solution of the Laplace equation in a region exterior to N arbitrarily located spheres of different radii is suggested. The method is based on the expansion of the solution into irreducible multipoles.” (p. 79) ¹. “The present study extends the modified method of irreducible multipoles expansion, suggested by Elperin and Krasovitov (1994) to combustion of random char/carbon particles of different radii.” (p. 167) ². “The method of expansion into irreducible multipoles which was developed in our previous works (Elperin and Krasovitov, 1994a, 1994b) is applicable to more realistic problems and is particularly suitable for dense random clusters of droplets (particles).” (p. 288) ³. It is important to note here that mathematically the irreducible tensors approach gives the possibility of finding the solution of linear boundary-value problems (BVP) for the Laplace equation in a three-dimensional multi-connected domain.