2020/04/12 by Gérard-Varet, David, Mecherbet, Amina
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2004.05601
This paper is a follow-up of article [6], on the derivation of accurate effective models for viscous dilute suspensions. The goal is to identify an effective Stokes equation providing a o(λ2) approximation of the exact fluid-particle system, with λ the solid volume fraction of the particles. This means that we look for an improvement of Einstein's formula for the effective viscosity in the form μeff(x) = μ+ (5)/(2) μρ(x) λ+ μ2(x) λ2. Under a separation assumption on the particles, we proved in [6] that if a o(λ)2 Stokes effective approximation exists, the correction μ2 is necessarily given by a mean field limit, that can then be studied and computed under further assumptions on the particle configurations. Roughly, we go here from the conditional result of [6] to an unconditional result: we show that such a o(λ2) Stokes approximation indeed exists, as soon as the mean field limit exists. This includes the case of periodic and random stationary particle configurations.