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 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 102 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.

Highlights

  • Locomotion of microscopic organisms such as bacteria or sperms is governed by laws which are different from those governing the world tangible by humans

  • 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

  • Hoping that similar universality of trends can be established for hydrodynamic interactions, we study microswimmer interactions in both the FB and the SB models using a recently developed perturbative approach [9]

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Summary

July 2021

Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Sebastian Ziegler1, Thomas Scheel1,2 , Maxime Hubert1 , Jens Harting2,3 and Ana-Suncana Smith1,4,∗ Keywords: microswimmers, collective behavior, low Reynolds number dynamics, active matter

Introduction
Force-based model of the three-bead swimmer
Results
Passive interaction
Active translation
Discussion and conclusions
Full Text
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