Effective viscosity of semi-dilute suspensions

This review is devoted to the large-scale rheology of suspensions rigid particles in Stokes fluid. After describing recent results on definition effective viscosity such systems framework homogenization theory, we turn our new asymptotic expansion dilute regime. includes a optimal proof Einstein’s formula for first-order expansion, as well continuation this higher orders. The essential difficulty originates long-range nature hydrodynamic interactions: suitable renormalizations are needed and captured by means diagrammatic expansions.