Effective Viscosity of Dilute Bacterial Suspensions: A Two-Dimensional Model

TL;DR

This paper derives a formula for the effective viscosity of dilute 2D bacterial suspensions, incorporating self-propulsion effects, which explains observed decreases in viscosity in active suspensions.

Contribution

It introduces a novel term in the viscosity formula accounting for self-propulsion, extending classical passive suspension models to active systems.

Findings

Effective viscosity decreases due to self-propulsion.

Derived formula includes classical and active terms.

Explains experimental observations of active suspensions.

Abstract

Suspensions of self-propelled particles are studied in the framework of two-dimensional (2D) Stokesean hydrodynamics. A formula is obtained for the effective viscosity of such suspensions in the limit of small concentrations. This formula includes the two terms that are found in the 2D version of Einstein's classical result for passive suspensions. To this, the main result of the paper is added, an additional term due to self-propulsion which depends on the physical and geometric properties of the active suspension. This term explains the experimental observation of a decrease in effective viscosity in active suspensions.