Rotation-translation coupling in a highly symmetric propeller at low Reynolds number*

Nature has developed several strategies to generate locomotion at low Reynolds (Re) numbers. Ciliates and sperm cells beat cilia in a non-reciprocal way to overcome the scallop-theorem. Bacteria use the inherently symmetry-broken shape of a rotating helical flagellum to create translational motion. Artificial corkscrew propellers were successfully employed to mimic the rotation-translation coupling of the latter [Nanoscale, 3, 557-563 (2011)]. A long time ago Purcell stated: “Turn anything - if it isn't perfectly symmetrical, you'll swim.” [Am. J. Phys. 45, 3 (1977)]. All these examples inevitably indicate the close connection between an objects’ symmetry and its propulsion dynamics at low Re. In turn, this raises the question if all propellers have to be chiral to be propulsive? Can highly symmetrical, achiral shapes be propulsive too? We provide a rigorous symmetry analysis of an achiral, planar V-shaped object and experimentally prove that this shape can be indeed propulsive when driven by an external field. This is, to our knowledge, the first demonstration of a truly achiral micro-object that propels; showing that chirality is not prerequisite for propulsion at low Reynolds number.