Circularly confined microswimmers exhibit multiple global patterns

Geometric confinement plays an important role in the dynamics of natural and synthetic microswimmers from bacterial cells to self-propelled particles in high-throughput microfluidic devices. However, little is known about the effects of geometric confinement on the emergent global patterns in such self-propelled systems. Recent experiments on bacterial cells report that, depending on the cell concentration, cells either spontaneously organize into vortical motion in thin cylindrical and spherical droplets or aggregate at the inner boundary of the droplets. Our goal in this paper is to investigate, in the context of an idealized physical model, the interplay between geometric confinement and level of flagellar activity on the emergent collective patterns. We show that decreasing flagellar activity induces a hydrodynamically triggered transition in confined microswimmers from swirling to global circulation (vortex) to boundary aggregation and clustering. These results highlight that the complex interplay between confinement, flagellar activity, and hydrodynamic flows in concentrated suspensions of microswimmers could lead to a plethora of global patterns that are difficult to predict from geometric consideration alone.

Figure 1

Microswimmers in Hele-Shaw and circular confinement: (a) schematic of the set-up and the dipolar far-field flows created by a swimmer in Hele-Shaw confinement (inset); (b) Effect of the circular confinement is accounted for using an image system outside the circular domain as dictated by the Milne-Thompson circle theorem.

Figure 2

Snapshots for the emergence of three global modes: (a) chaotic swirling ($\nu =3$); (b) stable circulation ($\nu =0.5$); (c) boundary aggregation ($\nu =-0.5$). The corresponding flow fields are depicted at the bottom row. For all three simulations, $N=750$ and $R=50$.

Figure 3

Statistical data for the stable circulation mode shown in Fig. 2: (a) vortex order parameter $\Phi$; (b) mean tangential speed and probability distribution of the swimmers; (c) mean polarization field. The mean polarization field and tangential speed are computed based on the averaging of data over the shaded time range, which a stable vortex order has been developed.

Figure 4

(a) The time-averaged mean and standard deviation of long-time developed $\Phi$ over various initial conditions. The standard deviations are denoted by the errorbars. (b) Phase diagram showing the three different global modes: chaotic swirling, stable circulation and boundary aggregation, as a function of $\nu$ and $R$.