Homogenization of equations describing materials interacting with clouds of particles

Abstract

We shall describe the derivation of homogenized equations (in an asymp- totics of mean-field type) for systems consisting of a cloud of particles dispersed in a material enclosed in a bounded domain. We shall consider in particular the homoge- nization of the Stokes problem leading to the Brinkman force and the homogenization of a model describing the heat exchange between the material and the dispersed phase leading to a (time-dependent) two-temperature equation. In both cases, the homogenized equations can be rigorously derived using similar form for the correctors.