Rheology of active suspensions with hydrodynamic interactions

TL;DR

This paper models the shear viscosity of dilute active suspensions considering hydrodynamic interactions, rotary diffusion, and external flow, providing analytical expressions that reveal how swimming mechanisms influence viscosity.

Contribution

It introduces a kinetic framework using a non-linear Fokker-Planck equation to analytically derive shear viscosity dependence on swimming details and interactions.

Findings

Analytical expressions for stress tensor at small Peclet numbers.

Explicit dependence of shear viscosity on swimming mechanisms.

Second-order volume fraction effects on viscosity.

Abstract

Using a simple model of self-propelled particle, the effective shear viscosity of a dilute, spatially homogeneous suspension of active particles is studied. We use formulation of non-linear Fokker-Planck equation to drive a kinetic description, including the effect of external flow field, rotary diffusion, and particle-particle hydrodynamic interactions in two dimensions. Analytical expressions are obtained for the stress tensor at small Peclet numbers, in a simple shear flow, up to second order of volume fraction of the swimmers, which shows the explicit dependence of shear viscosity on the details of the swimming mechanism.