Transport and Collective Dynamics in Suspensions of Confined Swimming Particles

Direct simulations of large populations of confined hydrodynamically interacting swimming particles at low Reynolds number are performed. Hydrodynamic coupling between the swimmers leads to large-scale coherent vortex motions in the flow and regimes of anomalous diffusion that are consistent with experimental observations. At low concentrations, swimmers propelled from behind (like spermatazoa) strongly migrate toward solid surfaces in agreement with simple theoretical considerations; at higher concentrations this localization is disrupted by the large-scale coherent motions.

Figure 1

Bead-rod-dumbbell model of a swimmer. The flagellum is represented by a force exerted on one of the beads of the dumbbell, and a force in the opposite direction exerted by the dumbbell on the fluid. The case $p=1$ is shown.

Figure 2

Mean-squared displacement vs time for non-Brownian swimmer and tracer particles in suspensions of swimmers at various concentrations. $L=15$ and $2H=5$.

Figure 3

Diffusion coefficient vs normalized concentration for the swimmer and tracer particles. $L=15$.

Figure 4

Snapshot of the velocity field at the midplane of the channel for ${\varphi }_e=0.56$, $L=15$, and $2H=5$. Two periods in the $x$ direction are shown, one in the $y$.

Figure 5

Concentration profile as a function of wall-normal position $z$ for different average concentrations. $L=15$ and $2H=5$.