Fluid transport and mixing by an unsteady microswimmer

We study the fluid drift due to a time-dependent dumbbell model of a microswimmer. The model captures important aspects of real microswimmers such as a time-dependent flagellar motion and a no-slip body. The model consists of a rigid sphere for the body and a time-dependent moving Stokeslet representing the flagella. We analyze the paths of idealized fluid particles displaced by the swimmer. The simplicity of the model allows some asymptotic calculations very near and far away from the swimmer. The displacements of particles near the swimmer diverge in a manner similar to an isolated no-slip sphere, but with a smaller coefficient due to the action of the flagellum. Far from the swimmer, the time dependence becomes negligible due to both being very fast and decaying with distance. Finally, we compute the probability distribution of particle displacements, and find that our model has fatter tails than previous steady models, due to the presence of a no-slip surface that drags particles along.