A stokesian submarine

Free access article

Issue		ESAIM: Proc. Volume 28, 2009 CEMRACS 2008 - Modelling and Numerical Simulation of Complex Fluids


Page(s)		150 - 161
DOI		http://dx.doi.org/10.1051/proc/2009044
Published online		23 November 2009

ESAIM: Proc., 2009, Vol. 28, pp. 150-161
DOI: 10.1051/proc/2009044

Aline Lefebvre-Lepot¹ and Benoît Merlet²

¹ CMAP (Centre de Mathématiques Appliquées) Ecole Polytechnique, route de Saclay 91128 Palaiseau Cedex, France, aline.lefebvre@polytechnique.edu
² Université Paris Nord - Institut Galilée LAGA (Laboratoire d'Analyse, Géométrie et Applications) Avenue J.B. Clément 93430 Villetaneuse, France, merlet@math.univ-paris13.fr

Published online: 23 November 2009

Abstract
We consider the problem of swimming at low Reynolds numbers. This is the relevant asymptotic for micro- and nano-robots needing to navigate in an aqueous medium. As a model, we propose a robot composed of three balls. The relative positions of these balls can change according to three degrees of freedom. We prove that this robot is able to navigate in a plane by modifying the conformation of its shape.

Résumé
Nous considérons le problème de la nage à faible nombre de Reynolds. C'est l'asymptotique pertinente pour les micro- et nano-robots devant se déplacer dans un milieu aqueux. Nous proposons comme modèle un robot formé de trois boules qui peuvent se déplacer les unes par rapport aux autres selon trois degrés de liberté. Nous démontrons qu'en changeant sa conformation, ce robot peut effectivement naviguer dans un plan.

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