Corrector equations in fluid mechanics: Effective viscosity of colloidal suspensions

Mitia Duerinckx, Antoine Gloria

Published 2019-09-20Version 1

Consider a colloidal suspension of rigid particles in a steady Stokes flow. In a celebrated contribution, Einstein argued that in the regime of dilute particles, the system behaves at leading order like a Stokes fluid with some explicit effective viscosity. In this contribution, we rigorously define a notion of effective viscosity, regardless of the dilute regime assumption. More precisely, we establish a homogenization result when particles are distributed according to a stationary and ergodic random point process. The main novelty is the introduction and analysis of suitable corrector equations.