# Pair Dispersion in Dilute Suspension of Active Swimmers

## TL;DR

This paper analytically investigates pair dispersion of passive tracers in dilute active swimmer suspensions, revealing how swimmer reorientation influences microscale mixing efficiency.

## Contribution

It provides a scale-dependent analytical model of relative diffusivity of tracers in active suspensions, emphasizing the role of swimmer reorientation in mixing.

## Key findings

- Small-scale relative dispersion is suppressed due to velocity correlations.
- Reorientation of swimmers significantly impacts mixing efficiency.
- Analytical expressions for scale-dependent diffusivity are derived.

## Abstract

Ensembles of biological and artificial microswimmers produce long-range velocity fields with strong nonequilibrium fluctuations, which result in dramatic increase diffusivity of embedded particles (tracers). While such enhanced diffusivity may point to enhanced mixing of the fluid, a rigorous quantification of the mixing efficiency requires analysis of pair dispersion of tracers, rather than simple one-particle diffusivity. Here, we calculate analytically the scale-dependent coefficient of relative diffusivity of passive tracers embedded in a dilute suspension of run-and-tumble microswimmers. Although each tracer is subject to strong fluctuations resulting in large absolute diffusivity, the small-scale relative dispersion is suppressed due to the correlations in fluid velocity which are relevant when the inter-tracers separation is below the persistence length of the swimmers motion. Our results suggest that the reorientation of swimming direction plays an important role in biological mixing and should be accounted in design of potential active matter devices capable of effective fluid mixing at microscale.