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Optimal translational swimming of a sphere at low Reynolds number

Swimming velocity and rate of dissipation of a sphere with surface distortions are discussed on the basis of the Stokes equations of low Reynolds number hydrodynamics. At first the surface distortions are assumed to cause an irrotational axisymmetric flow pattern. The efficiency of swimming is optimized within this class of flows. Subsequently more general axisymmetric polar flows with vorticity are considered. This leads to a considerably higher maximum efficiency. An additional measure of swimming performance is proposed based on the energy consumption for given amplitude of stroke.