The role of symmetry in driven propulsion at low Reynolds number

TL;DR

This study combines theory and experiments to explore how symmetry influences propulsion of achiral objects at low Reynolds number, revealing that non-chiral shapes can propel through rotation-translation coupling without requiring chirality.

Contribution

It demonstrates that achiral, symmetric objects can achieve propulsion via induced dipoles, challenging the notion that chirality is necessary for propulsion at low Reynolds numbers.

Findings

Symmetry considerations determine propulsive states of driven objects.

Achiral objects with induced dipoles can propel without chirality.

Propulsion is possible through rotation-translation coupling in symmetric shapes.

Abstract

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, $\widehat{P}$, and charge conjugation, $\widehat{C}$) 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 ($\widehat{P}$-even) objects exhibit no net propulsion while individual less symmetrical ($\widehat{C}\widehat{P}$-even) propellers do propel. Particular magnetization orientation, rendering the shape $\widehat{C}\widehat{P}$-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 ($\widehat{P}$- and $\widehat{C}\widehat{P}$-even) planar shape with an induced electric dipole that can propel by electro-rotation. We thereby show that chirality is not essential for propulsion due to rotation-translation coupling at low Reynolds number.