Efficient shapes for microswimming: from three-body swimmers to helical   flagella
  We combine a general formulation of microswimmmer equations of motion with a numerical bead-shell model to calculate the hydrodynamic interactions with the fluid, from which the swimming speed, power and efficiency are extracted. From this framework, a generalized Scallop Theorem emerges. The applicability to arbitrary shapes allows for the optimization of the efficiency with respect to the swimmer geometry. We apply this scheme to `three-body swimmers' of various shapes and find that the efficiency is characterized by the single body friction coefficient in the long-arm regime, while in the short-arm regime the minimal approachable distance becomes the determining factor. Next, we apply this scheme to a biologically inspired swimmer that propels itself using a rotating helical flagellum. Interestingly, we find two distinct optimal shapes, one of which is fundamentally different from the shapes observed in nature (e.g. bacteria). 
Bram Bet, Gijs Boosten, Marjolein Dijkstra, Ren\'e van Roij
cond-mat.soft