Effective Rheological Properties in Semidilute Bacterial Suspensions

TL;DR

This paper investigates how interactions among bacteria in suspensions lead to reduced viscosity, using a kinetic model and asymptotic analysis to derive explicit formulas and validate findings with simulations and experiments.

Contribution

It introduces an asymptotic analysis of a kinetic PDE model to explicitly compute the effective viscosity in bacterial suspensions, linking microscopic interactions to macroscopic properties.

Findings

Derived an explicit asymptotic formula for effective viscosity.

Showed qualitative agreement with experiments and simulations.

Proved existence, uniqueness, and regularity of the kinetic PDE model.

Abstract

Interactions between swimming bacteria have led to remarkable experimentally observable macroscopic properties such as the reduction of the effective viscosity, enhanced mixing, and diffusion. In this work, we study an individual based model for a suspension of interacting point dipoles representing bacteria in order to gain greater insight into the physical mechanisms responsible for the drastic reduction in the effective viscosity. In particular, asymptotic analysis is carried out on the corresponding kinetic equation governing the distribution of bacteria orientations. This allows one to derive an explicit asymptotic formula for the effective viscosity of the bacterial suspension in the limit of bacterium non-sphericity. The results show good qualitative agreement with numerical simulations and previous experimental observations. Finally, we justify our approach by proving existence, uniqueness, and regularity properties for this kinetic PDE model.