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Swimming and feeding : optimal strokes of model ciliates
To swim at low Reynolds numbers, micro-organisms undergo non time- reversible shape changes. Ciliated organism breaks the temporal symmetry by flapping many flexible cilia distributed on their surface. Previous studies have identified collective synchronization of neighboring cilia (metachronal waves), whose exact origin is still debated, and suggested that such coordinated swimming strokes allow to reduce the energy cost of locomotion. We are interested here in determining the properties of the optimal strokes of such ciliates, from both a swimming and a feeding point of view.
We consider here an axisymmetric envelope model of a ciliate, with prescribed tangential surface displacements. We show that the periodic strokes of this model swimmer, that maximize the distance travelled for a given energy cost, achieve symmetry-breaking at the organism level through the propagation of wave patterns similar to metachronal waves. The properties of these optimal strokes will be discussed, in particular the limitations on the swimming performance introduced by the finite cilia length.
Finally, the impact of the swimming stroke on the feeding ability of this model swimmer will be presented, considering a single organism in a continu- ous suspension of nutrients. The advection-diffusion problem for the nutrient is solved for different swimming (and non-swimming) strokes and the optimal feeding strokes (those maximizing the feeding rate for given energy cost) will be discussed.