Fluid mixing by curved trajectories of microswimmers

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.