Mild assumptions for the derivation of Einstein's effective viscosity\n formula

Abstract

We provide a rigorous derivation of Einstein's formula for the effective\nviscosity of dilute suspensions of $n$ rigid balls, $n \\gg 1$, set in a volume\nof size $1$. So far, most justifications were carried under a strong assumption\non the minimal distance between the balls: $d_{min} \\ge c n^{-\\frac{1}{3}}$, $c\n> 0$. We relax this assumption into a set of two much weaker conditions: one\nexpresses essentially that the balls do not overlap, while the other one gives\na control of the number of balls that are close to one another. In particular,\nour analysis covers the case of suspensions modelled by standard Poisson\nprocesses with almost minimal hardcore condition.\n