John J. Molina, Yasuya Nakayama, Ryoichi Yamamoto
The hydrodynamic interactions of a suspension of self-propelled particles are studied using a direct numerical simulation method which simultaneously solves for the host fluid and the swimming particles. A modified version of the "Smoothed Profile" method (SPM) is developed to simulate microswimmers as squirmers, which are spherical particles with a specified surface-tangential slip velocity between the particles and the fluid. This simplified swimming model allows one to represent different types of propulsion (pullers and pushers) and is thus ideal to study the hydrodynamic interactions among swimmers. We use the SPM to study the diffusive behavior which arises due to the swimming motion of the particles, and show that there are two basic mechanisms responsible for this phenomena: the hydrodynamic interactions caused by the squirming motion of the particles, and the particle collisions. This dual nature gives rise to two distinct time and length scales, and thus to two diffusion coefficients, which we obtain by a suitable analysis of the swimming motion. The existence of these two diffusion coefficients, with their different scaling behaviors, has been observed in experiments (PRL, 103, 198103 (2009)) and simulations (PRE, 82, 021408 (2010)), but only if the diffusion of inert (non-swimming) tracer particles was considered, which significantly increases the complexity of the problem. Finally, we show that the collisions between swimmers can be interpreted in terms of hard-sphere collisions, in which the effective radius is reduced due to the collision dynamics. Our results, along with the simulation method we have introduced, will allow us to gain a better understanding of the complex hydrodynamic interactions in swimming suspensions.
View original:
http://arxiv.org/abs/1212.6133
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