Theoretical framework for two-microswimmer hydrodynamic interactions

Hydrodynamic interactions are crucial for determining the cooperative behavior of microswimmers at low Reynolds numbers. Here we provide a comprehensive analysis of the scaling laws and the strength of the interactions in the case of a pair of three-sphere swimmers. Both stroke-based and force-based elastic microswimmers are analyzed using an analytic perturbative approach, focusing on passive and active interactions. The former are governed by the cycle-averaged flow field of a single swimmer, which is dipolar at long range. However, at intermediate distances, with a cross-over at the order of 10(2) swimmer lengths, the quadrupolar field dominates which, notably, yields an increase of the swimming velocity compared to individual swimmers, even when the swimmers are one behind another. Furthermore, we find that active rotations resulting from the interplay of the time-resolved swimming stroke and the ambient flow fields and, even more prominently, active translations are model-dependent. A mapping between the stroke-based and force-based swimmers is only possible for the low driving frequency regime where the characteristic time scale is smaller than the viscous one. Finally, we find that the long-term behavior of the swimmers, while sensitive to the initial relative positioning, does not depend on the pusher or puller nature of the swimmer. These results clearly indicate that the behavior of swarms will depend on the swimmer model, which was hitherto not well appreciated.

Automated summary

In this study, hydrodynamic interactions of a pair of three-sphere swimmers were comprehensively analyzed, revealing that quadrupolar field dominates at intermediate distances and increases swimming velocity. The rotations and translations behavior depend on the swimmer model and a mapping between stroke-based and force-based swimmers is possible only under low driving frequency. The long-term behavior of the swimmers is sensitive to initial relative positioning but independent of the pusher or puller nature of the swimmer.