Non-linear rheology of active particle suspensions: Insights from an analytical approach

TL;DR

This paper develops an analytical framework to understand the complex non-linear rheological behavior of active particle suspensions under shear flow, revealing shear thickening/thinning and sign-changing normal stress differences.

Contribution

It introduces an analytical approach to model active suspensions, predicting rheological behaviors consistent with experiments and numerical simulations.

Findings

Active suspensions exhibit shear thickening or thinning depending on particle activity type.

Normal stress differences can change sign, unlike passive suspensions.

Analytical results align with experimental and numerical data.

Abstract

We consider active suspensions in the isotropic phase subjected to a shear flow. Using a set of extended hydrodynamic equations we derive a variety of {\em analytical} expressions for rheological quantities such as shear viscosity and normal stress differences. In agreement to full-blown numerical calculations and experiments we find a shear thickening or -thinning behaviour depending on whether the particles are contractile or extensile. Moreover, our analytical approach predicts that the normal stress differences can change their sign in contrast to passive suspensions.