Effective viscosity of random suspensions without uniform separation

Abstract

This work is devoted to the definition and the analysis of the effective viscosity associated with a random suspension of small rigid particles in a steady Stokes fluid. While previous works on the topic have been conveniently assuming that particles are uniformly separated, we show how some ideas due to Jikov can be adapted to relax this unphysical assumption, in particular allowing for contacts in dimension $d>3$ and for almost contacts in dimension $d=3$, provided that some geometric non-degeneracy condition is satisfied.