Hydrodynamic length-scale selection and effective viscosity in microswimmer suspensions

TL;DR

This paper develops a theoretical framework to predict vortex size and effective viscosity in microswimmer suspensions, explaining the physical origins of mesoscale turbulence and matching experimental observations.

Contribution

It introduces a fourth-order field theory derived from microscopic models to explain vortex length-scale selection and viscosity changes in active suspensions.

Findings

Vortex size is determined by local alignment and hydrodynamic interactions.

Simulation results agree with experimental vortex measurements in bacteria.

The theory predicts viscosity enhancement or reduction depending on microorganism type.

Abstract

A universal characteristic of mesoscale turbulence in active suspensions is the emergence of a typical vortex length scale, distinctly different from the scale-invariance of turbulent high-Reynolds number flows. Collective length-scale selection has been observed in bacterial fluids, endothelial tissue and active colloides, yet the physical origins of this phenomenon remain elusive. Here, we systematically derive an effective fourth-order field theory from a generic microscopic model that allows us to predict the typical vortex size in microswimmer suspensions. Building on a self-consistent closure condition, the derivation shows that the vortex length scale is determined by the competition between local alignment forces and intermediate-range hydrodynamic interactions. Vortex structures found in simulations of the theory agree with recent measurements in Bacillus subtilis suspensions. Moreover, our approach correctly predicts an effective viscosity enhancement (reduction), as reported experimentally for puller (pusher) microorganisms.