Analysis of the Viscosity of Dilute Suspensions Beyond Einstein's Formula

We provide a mathematical analysis of the effective viscosity of suspensions of spherical particles in a Stokes flow, at low solid volume fraction phi. Our objective is to go beyond Einstein's approximation mu(eff) = (1+ 5/2 phi)mu. Assuming a lower bound on the minimal distance between the N particles, we are able to identify the O(phi(2)) correction to the effective viscosity, which involves pairwise particle interactions. Applying the methodology developped over the last years on Coulomb gases, we are able to tackle the limit N -> +infinity of the O(phi(2))-correction, and provide an explicit formula for this limit when the particles centers can be described by either periodic or stationary ergodic point processes.