Dynamical density functional theory for circle swimmers

TL;DR

This paper develops a dynamical density functional theory for circle swimmers, revealing how trajectory curvature influences their collective behavior and spatial distribution within confining potentials.

Contribution

It introduces a minimal microswimmer model incorporating hydrodynamic interactions and demonstrates how curvature affects swimmer localization and density distribution.

Findings

Increased curvature leads to central clustering of swimmers.

Hydrodynamic interactions influence the collective dynamics.

The theory aligns with experimental observations of L-shaped 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 of 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.