A frictionless microswimmer

We investigate the self-locomotion of an elongated microswimmer by virtue of unidirectional tangential surface treadmilling. We show that the propulsion could be almost frictionless, as the microswimmer is propelled forward with the speed of the backward surface motion, i.e. it moves through an almost quiescent fluid. We investigate this swimming technique using the special spheroidal coordinates and also find an explicit closed-form optimal solution for a two-dimensional treadmiller via complex-variable techniques. Slender-object surface treadmilling is a particularly efficient mode of locomotion because the viscous drag is determined by the smallest length scale of the object rather than by the largest scale, as is the usual case for low Reynolds number flow.