Efficiency of Surface-Driven Motion: Nanoswimmers Beat Microswimmers

Surface interactions provide a class of mechanisms which can be employed for propulsion of micrometer and nanometer sized particles. We investigate the related efficiency of externally and self-propelled swimmers. A general scaling relation is derived showing that only swimmers whose size is comparable to, or smaller than, the interaction range can have appreciable efficiency. An upper bound for efficiency at maximum power is 1/2. Numerical calculations for the case of diffusiophoresis are found to be in good agreement with analytical expressions for the efficiency.