Fluid mixing by curved trajectories of microswimmers

TL;DR

This paper derives an exact expression for tracer diffusion caused by run-and-tumble microswimmers, revealing its independence from run length and comparing it to entrainment effects in dilute suspensions.

Contribution

It provides the first exact formula for diffusion from dipolar microswimmers' run-and-tumble motion in three dimensions, clarifying the role of run length.

Findings

Tracer diffusion $D_{rr}$ is independent of run length $$ in dilute suspensions.

Derived an exact expression for $D_{rr}$ for dipolar swimmers in 3D.

Compared $D_{rr}$ to entrainment contributions, highlighting their relative significance.

Abstract

We consider the tracer diffusion $D_{rr}$ that arises from the run-and-tumble motion of low Reynolds number swimmers, such as bacteria. Assuming a dilute suspension, where the bacteria move in uncorrelated runs of length $\lambda$, we obtain an exact expression for $D_{rr}$ for dipolar swimmers in three dimensions, hence explaining the surprising result that this is independent of $\lambda$. We compare $D_{rr}$ to the contribution to tracer diffusion from entrainment.