A circle swimmer at low Reynolds number

TL;DR

This paper introduces a simple three-sphere model for low Reynolds number swimmers that move in circles, analyzing how their motion depends on geometric parameters and flow field decay.

Contribution

It generalizes the linear swimmer model to include circular motion by using a triangular configuration of spheres with time-dependent link lengths.

Findings

Swimmers exhibit clockwise or anticlockwise circular motion based on tilt angle.

Flow field decays quadrupolarly at large distances.

Model potential for experimental realization.

Abstract

Swimming in circles occurs in a variety of situations at low Reynolds number. Here we propose a simple model for a swimmer that undergoes circular motion, generalising the model of a linear swimmer proposed by Najafi and Golestanian (Phys. Rev. E 69, 062901 (2004)). Our model consists of three solid spheres arranged in a triangular configuration, joined by two links of time-dependent length. For small strokes, we discuss the motion of the swimmer as a function of the separation angle between its links. We find that swimmers describe either clockwise or anticlockwise circular motion depending on the tilting angle in a non-trivial manner. The symmetry of the swimmer leads to a quadrupolar decay of the far flow field. We discuss the potential extensions and experimental realisation of our model.