# The role of correlations in the collective behaviour of microswimmer suspensions

## TL;DR

This paper investigates the collective behavior of microswimmers in fluid, revealing correlations below turbulence transition, developing a new kinetic theory, and validating it with large-scale simulations and tracer diffusivity measurements.

## Contribution

It introduces a novel kinetic theory capturing correlations in microswimmer suspensions, validated by large-scale simulations and experimental measures.

## Key findings

- Swimmers exhibit correlated motion below turbulence transition.
- The kinetic theory accurately predicts the asymmetry between pusher and puller swimmers.
- Tracer diffusivity shows non-trivial density dependence.

## Abstract

In this Letter, we study the collective behaviour of a large number of self-propelled microswimmers immersed in a fluid. Using unprecedently large-scale lattice Boltzmann simulations, we reproduce the transition to bacterial turbulence. We show that, even well below the transition, swimmers move in a correlated fashion that cannot be described by a mean-field approach. We develop a novel kinetic theory that captures these correlations and is non-perturbative in the swimmer density. To provide an experimentally accessible measure of correlations, we calculate the diffusivity of passive tracers and reveal its non-trivial density dependence. The theory is in quantitative agreement with the lattice Boltzmann simulations and captures the asymmetry between pusher and puller swimmers below the transition to turbulence.