The role of symmetry in driven propulsion at low Reynolds number

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Abstract
We theoretically and experimentally investigate low-Reynolds-number propulsion of achiral planar shapes that possess a dipole moment and that are driven externally by a rotating magnetic field. Symmetry considerations (involving parity, P, and charge conjugation, C) establish correspondence between propulsive states depending on orientation of the dipolar moment. Highly symmetrical (P-even) objects exhibit no net propulsion. Individual less symmetrical (CP-even) propellers can efficiently propel due to spontaneous symmetry breaking, while a large ensemble of such motors would not propel on average. Particular magnetization orientation, rendering the shape CP-odd, yields unidirectional motion typically associated with chiral structures, such as helices.

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