Hydrodynamics with spin in bacterial suspensions

TL;DR

This paper introduces a hydrodynamic model incorporating spin to explain the self-propelling motion of bacteria with rotating flagella, providing quantitative estimates that align with experimental observations.

Contribution

It generalizes the reciprocal theorem of Stokesian hydrodynamics to include spin, modeling bacterial propulsion through rotating flagella.

Findings

High bacterial velocities explained by cooperative flagella action

Quantitative estimates of torque match experimental data

Model extends hydrodynamics with spin to biological systems

Abstract

We describe a new kind of self-propelling motion of bacteria based on the cooperative action of rotating flagella on the surface of bacteria. Describing the ensemble of rotating flagella in the framework of the hydrodynamics with spin the reciprocal theorem of Stokesian hydrodynamics is generalized accordingly. The velocity of the self-propulsion is expressed in terms of the characteristics of the vector field of flagella orientation and it is shown that unusually high velocities of \textit{Thiovulum majus} bacteria may be explained by the cooperative action of the rotating flagella. The expressions obtained enable us to estimate the torque created by the rotary motors of the bacterium and show quantitative agreement with the existing experimental data.