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.