Abstract : In 1905, Albert Einstein published two papers that led to an experiment to measure the Avogadro number. The first paper studies the Brownian motion and establishes the Einstein relation in kinetic theory. The second paper studies a Stokes fluid with a suspension of rigid particles, and establishes the Einstein formula for the effective viscosity of this 'complex fluid'. The Avogadro number, which appears in both relations, can then be deduced from two measurements of fluid mechanics. Performed by Jean Perrin in 1907-1909, these experiments confirmed the atomistic nature of matter (for which he was awarded a Nobel prize in 1926) using classical fluid mechanics!
The aim of the talk is to give an elementary and robust proof of Einstein's effective viscosity formula, and to discuss higher-order expansions.
This is a joint work with Mitia Duerinckx (ULB).

Keywords : effective viscosity; homogenization; dilute regime