| Issue |
ESAIM: COCV
Volume 21, Number 3, July-September 2015
|
|
|---|---|---|
| Page(s) | 757 - 788 | |
| DOI | https://doi.org/10.1051/cocv/2014046 | |
| Published online | 13 May 2015 | |
Rough wall effect on micro-swimmers∗
1
Institut de Mathématiques de Jussieu et Université Paris
7, Bâtiment Sophie
Germain, 75205
Paris cedex 13,
France
2
Unité de Mathématiques Appliqueés (UMA), École Nationale
Supérieure de Techniques Avancées (ENSTA-Paristech), 828 Boulevard des Marchaux, 91762
Palaiseau,
France
laetitia.giraldi@polytechnique.edu
Received:
30
September
2013
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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