# Enhanced velocity fluctuations in interacting swimmer suspensions

## TL;DR

This paper investigates how interactions among micro-swimmers affect velocity fluctuations, revealing divergence in variance and the impact of orientation decorrelation, with implications for passive tracer dynamics.

## Contribution

It introduces a theoretical framework for understanding velocity fluctuations in interacting swimmer suspensions, including run-and-tumble particles, and explains experimental observations.

## Key findings

- Velocity variance diverges logarithmically with system size in interacting suspensions.
- Inclusion of orientation decorrelation mechanisms arrests the divergence.
- Passive tracer dynamics exhibit a crossover between ballistic and diffusive regimes.

## Abstract

A dilute non-interacting suspension of micro-swimmers exhibits a finite velocity variance and short-ranged correlations that decay over a swimmer length. For a suspension of interacting straight swimmers, however, pair-interactions leads to a non-decaying velocity covariance, and a variance that diverges logarithmically with system size. The divergence is arrested on inclusion of orientation decorrelation mechanisms. Results for suspensions of run-and-tumble particles (RTPs) are presented, where the underlying straight-swimmer divergence leads to a broad cross-over between the ballistic and diffusive regimes, of immersed passive tracers, in the limit of long run lengths. Our analysis explains long-standing experimental observations of a volume-fraction dependent crossover time for passive tracer dynamics.