Orbits of swimmers around obstacles

TL;DR

This paper models the hydrodynamic interactions of circular swimmers with obstacles at low Reynolds number, revealing stable bound orbits for contractile swimmers and unstable orbits for extensile swimmers, aligning with experimental data.

Contribution

It introduces a nonlinear dynamical system model for swimmer-obstacle interactions, highlighting the stability differences between contractile and extensile swimmers.

Findings

Contractile swimmers form stable bound orbits.

Extensile swimmers exhibit unstable orbits.

Model aligns with experimental observations.

Abstract

We present a two dimensional model of hydrodynamic interaction between a circular swimmer and a circular post at low Reynolds number, using a point singularity description of the swimming activity. We derive a nonlinear dynamical system fully describing the motion and discuss the generic features of the phase portrait and typical trajectories for a variety of squirmer modes. Contractile swimmers exhibit stable bound orbits arising from the contrasting nature of monopolar and dipolar squirmer modes, which are robust with respect to swimmer size and the inclusion of higher squirmer modes. The behaviour of extensile swimmers is related through time reversal and their orbits are unstable, in qualitative agreement with experimental observations.