Three-dimensional pattern formation in suspensions of swimming micro-organisms

Suspensions of self-propelled particles, such as swimming micro-organisms, are known to undergo complex dynamics as a result of hydrodynamic interactions. This fluid dynamics video presents a numerical simulation of such a suspension, based on a kinetic theory recently developed by Saintillan and Shelley (Physics of Fluids, 20, 123403, 2008). Starting from a nearly uniform and isotropic initial distribution, our simulations show the formation of strong density fluctuations, which merge and break up in time in a quasiperiodic fashion. These fluctuations are found to occur on the size of the simulation box, in agreement with a prediction from a linear stability analysis. In addition, the dynamics are characterized by complex chaotic flow fields, which result in efficient fluid mixing.