Effective properties of heterogeneous materials: Proper application of the non-interaction and the “dilute limit” approximations

The paper addresses common misunderstanding of the non-interaction approximation (NIA) – its incorrect identification with “dilute limit”, occurring in the context of transport, elastic, viscous etc. properties of heterogeneous materials. It is rooted in incorrect implicit assumption that physically weak interaction necessarily imply large spacing between inhomogeneities. This may lead to violation of rigorous bounds for the effective properties as well as drastic reduction of the concentration range where the NIA remains sufficiently accurate. We clarify the proper use of various formulations of NIA and their limitations.