Eur. Phys. J. E (2015) 38: 7
https://doi.org/10.1140/epje/i2015-15007-6

Regular Article

Autophoretic locomotion from geometric asymmetry

¹ LadHyX - Département de Mécanique, Ecole polytechnique - CNRS, 91128, Palaiseau Cedex, France
² Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Center for Mathematical Sciences, Wilberforce Road, CB3 OWA, Cambridge, UK

^* e-mail: sebastien.michelin@ladhyx.polytechnique.fr

Received: 14 November 2014
Revised: 16 January 2015
Accepted: 20 January 2015
Published online: 13 February 2015

Abstract

Among the few methods which have been proposed to create small-scale swimmers, those relying on self-phoretic mechanisms present an interesting design challenge in that chemical gradients are required to generate net propulsion. Building on recent work, we propose that asymmetries in geometry are sufficient to induce chemical gradients and swimming. We illustrate this idea using two different calculations. We first calculate exactly the self-propulsion speed of a system composed of two spheres of unequal sizes but identically chemically homogeneous. We then consider arbitrary, small-amplitude, shape deformations of a chemically homogeneous sphere, and calculate asymptotically the self-propulsion velocity induced by the shape asymmetries. Our results demonstrate how geometric asymmetries can be tuned to induce large locomotion speeds without the need of chemical patterning.