Eur. Phys. J. E (2012) 35: 126
https://doi.org/10.1140/epje/i2012-12126-6

Regular Article

Translations and rotations at low Reynolds number: A study of simple model swimmers with finite amplitude strokes

Department of Mathematics, University of Bristol, Clifton, BS8 1TW, Bristol, UK

^* e-mail: t.liverpool@bristol.ac.uk

Received: 28 March 2012
Accepted: 31 October 2012
Published online: 6 December 2012

Abstract

We present a simple dynamical model of self-propeller at low Reynolds number in which self-propulsion is achieved via rotary elements (rotors). In this model by changing the sense of rotation of the rotors, the self-propeller can switch between a “linear swimming” phase where it swims in a straight line and a “tumbling” phase in which it can change direction in a controllable way via a global rotation of its body. We study the dynamics of this propeller in detail. To do this we provide an analytic framework within which the non-perturbative aspects of the internal dynamics can be treated allowing us to study the swimming process for arbitrary values of the swimmer deformations. Using it, we compute the averages (over a deformation cycle) of a number of characteristic properties of the swimmer such as its self-propulsion velocity, the dissipated power, its efficiency and the fluid flow patterns it generates. We compare these results to the corresponding average quantities for another class of model swimmers, where self-propulsion is achieved via periodic translations. Finally, we provide an explanation of why non-perturbative results can be obtained for these models using the geometrical language of gauge theory.