Fluid entrainment by individual microswimmers

Stirring the surrounding fluid may be an evolutionary strategy of microscopic swimmers to ensuring continuous supply of nutrient and removal of waste products [1]. The possibility of a significant biogenic contribution to oceanic mixing is currently under intense debate [2]. However, different biomixing mechanisms, their effectiveness and universality remain poorly understood.

In this talk we focus on the Lagrangian transport of the surrounding fluid by microswimmers [3]. Fluid particles advected by swimmers move in loops that are, in general, almost closed. This observation is in apparent contradiction with the effectiveness of biomixing observed in experiments. We start with analyzing the fundamental reasons for closedness of the fluid particle trajectories. Building on the gained insight, we propose a classification of possible mixing mechanisms.

Next, we discuss the universal (common to all swimmers) and the swimmer-dependent features of the resulting fluid particle displacements and analyse the Darwin dift, the total fluid volume displaced by a swimmer passing from and to infinity. We show that the Darwin drift is finite for force-free swimmers and can be decomposed into a universal and a swimmer-dependent part. Results of detailed numerical simulations of Rhodobacter sphaeroides and simple models of microswimmers corroborate our considerations.

Finally, we discuss the effectiveness of stirring by entrainment in dilute random suspensions of swimmers and estimate the effective diffusivity in the kinetic theory spirit.[1] K. C. Leptos et al., PRL 103, 198103 (2009); H. Kurtuldu et al., PNAS 108, 10391 (2011).[2] E. Kunze et al., J. Marine Research 69, 591 (2011).[3] D. O. Pushkin, H. Shum and J. M. Yeomans, submitted to JFM, http://arxiv.org/abs/1209.3329 (2012).