Understanding the stochastic dynamics of tracer particles in active fluids is important for identifying the physical properties of flow generating objects such as colloids, bacteria or algae. Here, we study both analytically and numerically the scattering of a tracer particle in different types of time-dependent, hydrodynamic flow fields. Specifically, we compare the tracer motion induced by an externally driven colloid with the one generated by various self-motile, multi-sphere swimmers. Our results suggest that force-free swimmers generically induce loop-shaped tracer trajectories. The specific topological structure of these loops is determined by the hydrodynamic properties of the microswimmer. Quantitative estimates for typical experimental conditions imply that the loops survive on average even if Brownian motion effects are taken into account.

We describe and analyze CUDA simulations of hydrodynamic interactions in active dumbbell suspensions. GPU-based parallel computing enables us not only to study the time-resolved collective dynamics of up to a several hundred active dumbbell swimmers but also to test the accuracy of effective time-averaged models. Our numerical results suggest that the stroke-averaged model yields a relatively accurate description down to distances of only a few times the dumbbell's length. This is remarkable in view of the fact that the stroke-averaged model is based on a far-field expansion. Thus, our analysis confirms that stroke-averaged far-field equations of motion may provide a useful starting point for the derivation of hydrodynamic field equations.

We define a model microswimmer with a variable cycle time, thus allowing the possibility of phase locking driven by hydrodynamic interactions between swimmers. We find that, for extensile or contractile swimmers, phase locking does occur, with the relative phase of the two swimmers being, in general, close to 0 or pi, depending on their relative position and orientation. We show that, as expected on grounds of symmetry, self T-dual swimmers, which are time-reversal covariant, do not phase-lock. We also discuss the phase behaviour of a line of tethered swimmers, or pumps. These show oscillations in their relative phases reminiscent of the metachronal waves of cilia.Comment: 17 pages, 8 figure

Active dumbbell suspensions constitute one of the simplest model system for collective swimming at low Reynolds number. Generalizing recent work, we derive and analyze stroke-averaged equations of motion that capture the effective hydrodynamic far-field interaction between two oscillating, asymmetric dumbbells in three space dimensions. Time-averaged equations of motion, as those presented in this paper, not only yield a considerable speed-up in numerical simulations, they may also serve as a starting point when deriving continuum equations for the macroscopic dynamics of multi-swimmer suspensions. The specific model discussed here appears to be particularly useful in this context, since it allows one to investigate how the collective macroscopic behavior is affected by changes in the microscopic symmetry of individual swimmers.