Self-organized vortices of circling self-propelled particles and curved active flagella

Abstract

Self-propelled pointlike particles move along circular trajectories when their translocation velocity is constant and the angular velocity related to their orientation vector is also constant. We investigate the collective behavior of ensembles of such circle swimmers by Brownian dynamics simulations. If the particles interact via a "velocity-trajectory coordination" rule within neighboring particles, a self-organized vortex pattern emerges. This vortex pattern is characterized by its particle-density correlation function Gρ, the density correlation function Gc of trajectory centers, and an order parameter S representing the degree of the aggregation of the particles. Here we systematically vary the system parameters, such as the particle density and the interaction range, in order to reveal the transition of the system from a light-vortex-dominated to heavy-vortex-dominated state, where vortices contain mainly a single and many self-propelled particles, respectively. We also study a semidilute solution of curved, sinusoidal-beating flagella, as an example of circling self-propelled particles with explicit propulsion mechanism and excluded-volume interactions. Our simulation results are compared with previous experimental results for the vortices in sea-urchin sperm solutions near a wall. The properties of the vortices in simulations and experiments are found to agree quantitatively.

Microswimmers near surfaces

“…The circular motion of sperm near surfaces also gives rise to an interesting collective behaviour at higher densities -where sperm form quite regular arrays of vortices in which several sperm swim together in tight circles [49,50] -and in shear flowwhere sperm align against the flow direction and can swim upstream with a fixed deviation angle (rheotaxis) [51][52][53]. A discussion of more generic aspects of circle swimmers is given in the minireview [54] by H. Löwen in this issue; an overview of the behaviour of microswimmers in external (flow) fields is provided in the minireview [55] by H. Stark.…”

Dynamical density functional theory for circle swimmers

“…Apart from that, near surfaces bent self-propelled objects tend to follow circular trajectories [42,43]. In modeling approaches, circle swimmers are often realized by simply imposing an effective torque or rotational drive in addition to the self-propulsion mechanism [15,31,35,[44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59].…”

Transport Powered by Bacterial Turbulence

“…Introduction. Suspensions of bacteria or synthetic microswimmers show fascinating collective behavior emerging from their self-propulsion [1][2][3][4] which results in many novel active states such as swarming [5][6][7][8] and "active turbulence" [9][10][11][12][13][14]. In contrast to hydrodynamic turbulence, the apparent turbulent (or swirling) state occurs at exceedingly low Reynolds numbers but at relatively large bacterial concentrations.…”