Theoretical framework for pairwise microswimmer interactions

TL;DR

This paper develops a theoretical framework analyzing hydrodynamic interactions between pairwise three-sphere microswimmers with elasticity, revealing how these interactions influence collective behavior and propulsion efficiency at low Reynolds numbers.

Contribution

It introduces an analytic perturbative approach to compare stroke-based and force-based microswimmers, and characterizes their interaction scaling, strength, and long-term dynamics.

Findings

Swimmers separated by hundreds of lengths speed up propulsion.

Mapping between swimmer types is valid only at low frequencies.

Long-term behavior is independent of pusher or puller classification.

Abstract

Hydrodynamic interactions are crucial for determining the cooperative behavior of microswimmers at low Reynolds numbers. Here we provide a comprehensive analysis of the scaling and strength of the interactions in the case of a pair of three-sphere swimmers with intrinsic elasticity. Both stroke-based and force-based microswimmers are analyzed using an analytic perturbative approach. Following a detailed analysis of the passive interactions, as well as active translations and rotations, we find that the mapping between the stroke-based and force-based swimmers is only possible in a low driving frequency regime where the characteristic time scale is smaller than the viscous one. Furthermore, we find that for swimmers separated by up to hundreds of swimmer lengths, swimming in pairs speeds up the self propulsion, due to the dominant quadrupolar hydrodynamic interactions. Finally, we find that the long term behavior of the swimmers, while sensitive to initial relative positioning, does not depend on the pusher or puller nature of the swimmer.