Volume 21, Number 3, July-September 2015
|Page(s)||757 - 788|
|Published online||13 May 2015|
Rough wall effect on micro-swimmers∗
Institut de Mathématiques de Jussieu et Université Paris
7, Bâtiment Sophie
Paris cedex 13,
2 Unité de Mathématiques Appliqueés (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA-Paristech), 828 Boulevard des Marchaux, 91762 Palaiseau, France
Revised: 8 April 2014
We study the effect of a rough wall on the controllability of micro-swimmers made of several balls linked by thin jacks: the so-called 3-sphere and 4-sphere swimmers. Our work completes the previous work [F. Alouges and L. Giraldi, Acta Applicandae Mathematicae 128 (2013) 153–179] dedicated to the effect of a flat wall. We show that a controllable swimmer (the 4-sphere swimmer) is not impacted by the roughness. On the contrary, we show that the roughness changes the dynamics of the 3-sphere swimmer, so that it can reach any direction almost everywhere.
Mathematics Subject Classification: 93B05
Key words: Low-Reynolds number swimming / self-propulsion / three-sphere swimmer / rough wall effect / Lie brackets / control theory / asymptotic expansion
© EDP Sciences, SMAI, 2015
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