M511

This talk is devoted to the large-scale rheology of systems of suspended particles in a Stokes fluid. After reviewing recent results on the definition of the effective viscosity of such systems in terms of homogenization theory, I will focus on its asymptotic expansion in dilute regime. I will present a new, optimal proof of Einstein's viscosity formula for the first-order expansion and show how to pursue the asymptotic expansion to higher orders. The essential difficulty originates in the long-range nature of hydrodynamic interactions: these require suitable renormalizations, which will be systematically captured by means diagrammatic expansions. This is based on joint work with A.Gloria.

Mitia Duerinckx