Rough wall effect on micro-swimmers

David Gérard-Varet (1) , Laetitia Giraldi (2)

1 UPD7 - Université Paris Diderot - Paris 7
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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. 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.

Mots clés: rough wall effect; Three-sphere swimmer; asymptotic expansion; Low-Reynolds number swimming; self-propulsion; Lie brackets; control theory; asymptotic expansion.

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

David Gérard-Varet, Laetitia Giraldi. Rough wall effect on micro-swimmers. 2013. ⟨hal-00867599v2⟩