Homogenization of active suspensions and reduction of effective viscosity

TL;DR

This paper studies the homogenization of active suspensions of swimmers in a steady Stokes flow, revealing how their activity can alter the effective viscosity, either increasing or decreasing it depending on the swimming mechanism.

Contribution

It introduces a novel nonlinear homogenization approach with new correctors to analyze active suspensions and their impact on effective viscosity.

Findings

Active particle activity can reduce or increase effective viscosity.

The model accounts for adaptive swimming forces based on fluid deformation.

A semi-quantitative two-scale analysis is used for qualitative homogenization.

Abstract

We consider a suspension of active rigid particles (swimmers) in a steady Stokes flow, where particles are distributed according to a stationary ergodic random process, and we study its homogenization in the macroscopic limit. A key point in the model is that swimmers are allowed to adapt their propulsion to the surrounding fluid deformation: swimming forces are not prescribed a priori, but are rather obtained through the retroaction of the fluid. Qualitative homogenization of this nonlinear model requires an unusual proof that crucially relies on a semi-quantitative two-scale analysis. After introducing new correctors that accurately capture spatial oscillations created by swimming forces, we identify the contribution of the activity to the effective viscosity. In agreement with the physics literature, an analysis in the dilute regime shows that the activity of the particles can either increase or decrease the effective viscosity (depending on the swimming mechanism), which differs from the well-known case of passive suspensions.