Eur. Phys. J. E (2015) 38: 42
https://doi.org/10.1140/epje/i2015-15042-3

Regular Article

Three-sphere low-Reynolds-number swimmer with a passive elastic arm

¹ GSSI - Gran Sasso Science Institute, viale Francesco Crispi 7, 67100, L’Aquila, Italy
² SISSA - International School for Advanced Studies, via Bonomea 265, 34136, Trieste, Italy

^* e-mail: desimone@sissa.it

Received: 24 September 2014
Revised: 29 January 2015
Accepted: 26 March 2015
Published online: 22 May 2015

Abstract

One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer’s geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers.