# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1701.08691