Dynamical density functional theory for circle swimmers

Abstract

The majority of studies on self-propelled particles and microswimmers concentrates on objects that do not feature a deterministic bending of their trajectory. However, perfect axial symmetry is hardly found in reality, and shape-asymmetric active microswimmers tend to show a persistent curvature of their trajectories. Consequently, we here present a particle-scale statistical approach to circle-swimmer suspensions in terms of a dynamical density functional theory. It is based on a minimal microswimmer model and, particularly, includes hydrodynamic interactions between the swimmers. After deriving the theory, we numerically investigate a planar example situation of confining the swimmers in a circularly symmetric potential trap. There, we find that increasing curvature of the swimming trajectories can reverse the qualitative effect of active drive. More precisely, with increasing curvature, the swimmers less effectively push outwards against the confinement, but instead form high-density patches in the center of the trap. We conclude that the circular motion of the individual swimmers has a localizing effect, also in the presence of hydrodynamic interactions. Parts of our results could be confirmed experimentally, for instance, using suspensions of L-shaped circle swimmers of different aspect ratio.

Active particles in geometrically confined viscoelastic fluids

“…In such crowded systems, the interplay between confinement, specific swimming mechanisms, and the resulting hydrodynamic flows lead to a plethora of patterns that are difficult to predict from steric constraints and geometric considerations alone [59]. Furthermore, it would also be interesting to investigate the effect of other specific properties of circularly confined active systems, such as chirality [60], and the combination of detailed swimming patterns with the geometrical curvature [61], as they are also known to be responsible for strong localization of individual APs even in Newtonian fluids. ORCID iDs Figure A1.…”

Binary pusher–puller mixtures of active microswimmers and their collective behaviour

“…Hydrodynamic couplings between the swimmers are considered on the Rotne-Prager level [41,51,52]. Each swimmer consists of a spherical body of no-slip surface conditions for the surrounding fluid.…”

“…Here, we do not include this effect. That is, we only address the situation to lowest order in the length scale a/L [52].…”

“…(12), the sign of f determines whether the swimmer is a pusher or a puller, i.e., whether it pushes the fluid outward or pulls the fluid inward along the symmetry axis. To calculate the effect of the active forces of swimmer j on the motion of swimmer i, we use the mobility matrices of components [51,52] µ tt αβ (r) = 1 8πηr…”

“…We concentrate on the microscopic swimmer-scale level, explicitly taking into account the hydrodynamic interactions on this scale. The swimmers are resolved individually in a discretized description using a minimal swimmer model [51,52]. On this basis, we evaluate the global orientational behavior.…”