Role of symmetry in driven propulsion at low Reynolds number

We theoretically and experimentally investigate low-Reynolds-number propulsion of geometrically achiral planar objects that possess a dipole moment and that are driven by a rotating magnetic field. Symmetry considerations (involving parity (P) over cap and charge conjugation (C) over cap) establish correspondence between propulsive states depending on orientation of the dipolar moment. Although basic symmetry arguments do not forbid individual symmetric objects to efficiently propel due to spontaneous symmetry breaking, they suggest that the average ensemble velocity vanishes. Some additional arguments show, however, that highly symmetrical ((P) over cap -even) objects exhibit no net propulsion while individual less symmetrical ((C) over cap(P) over cap -even) propellers do propel. Particular magnetization orientation, rendering the shape (C) over cap(P) over cap -odd, yields unidirectional motion typically associated with chiral structures, such as helices. If instead of a structure with a permanent dipole we consider a polarizable object, some of the arguments have to be modified. For instance, we demonstrate a truly achiral ((P) over cap- and (C) over cap(P) over cap -even) planar shape with an induced electric dipole that can propel by electrorotation. We thereby show that chirality is not essential for propulsion due to rotation-translation coupling at low Reynolds number.