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We combine a general formulation of microswimmmer equations of motion with anumerical bead-shell model to calculate the hydrodynamic interactions with thefluid, from which the swimming speed, power and efficiency are extracted. Fromthis framework, a generalized Scallop Theorem emerges. The applicability toarbitrary shapes allows for the optimization of the efficiency with respect tothe swimmer geometry. We apply this scheme to `three-body swimmers' of variousshapes and find that the efficiency is characterized by the single bodyfriction coefficient in the long-arm regime, while in the short-arm regime theminimal approachable distance becomes the determining factor. Next, we applythis scheme to a biologically inspired swimmer that propels itself using arotating helical flagellum. Interestingly, we find two distinct optimal shapes,one of which is fundamentally different from the shapes observed in nature(e.g. bacteria).

Efficient shapes for microswimming: from three-body swimmers to helical flagella