A simple justification of effective models for conducting or fluid media with dilute spherical inclusions
David Gérard‐Varet · Asymptotic Analysis · 2021
We present a gentle approach to the justification of effective media approximations, for PDE’s set outside the union of [Formula: see text] spheres with low volume fraction. To illustrate our approach, we consider three classical examples: the derivation of the so-called strange term, made popular by Cioranescu and Murat, the derivation of the Brinkman term in the Stokes equation, and a scalar analogue of the effective viscosity problem. Under some separation assumption on the spheres, valid for periodic and random distributions of the centers, we recover effective models as [Formula: see text] by simple arguments.