Hydrodynamic Synchronisation of Model Microswimmers

TL;DR

This paper models microswimmers with variable cycle times to study hydrodynamic phase locking, revealing conditions under which swimmers synchronize or not, and exploring collective behaviors like metachronal waves.

Contribution

Introduces a model allowing phase locking analysis of microswimmers with variable cycles, highlighting the role of hydrodynamics and symmetry in synchronization.

Findings

Phase locking occurs for extensile or contractile swimmers near 0 or pi phase difference.

Self T-dual swimmers do not exhibit phase locking.

Line of tethered swimmers shows oscillatory phase behavior similar to cilia waves.

Abstract

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.