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 λ, we obtain an exact expression for D(rr) for dipolar swimmers in three dimensions, hence explaining the surprising result that this is independent of λ. We compare D(rr) to the contribution to tracer diffusion from entrainment.