Aline Lefebvre

Optimal strokes for axisymmetric microswimmers

We present a theory for low-Reynolds-number axisymmetric swimmers and a general strategy for the computation of strokes of maximal efficiency. An explicit equation characterizing optimal strokes is derived, and numerical strategies to obtain solutions are discussed. The merits of this approach are demonstrated by applying it to two concrete examples: the three linked spheres of Najafi and Golestanian and the pushmepullyou of Avron, Kenneth, and Oakmin.

Optimally swimming stokesian robots

We study self-propelled stokesian robots composed of assemblies of balls, in dimensions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability , and its proof relies on applying Chows theorem in an analytic framework, similar to what has been done in [4] for an axisymmetric system swimming along the axis of symmetry. We generalize the analyticity result given in [4] to the situation where the swimmers can move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.