Lord Kelvin's isotropic helicoid

TL;DR

This paper investigates Lord Kelvin's isotropic helicoid, demonstrating experimentally that it exhibits negligible translation-rotation coupling due to hydrodynamic interactions, confirming its existence as a weakly chiral particle in Stokes flow.

Contribution

The study provides experimental validation of Kelvin's isotropic helicoid and explains the weak coupling as arising from hydrodynamic interactions between non-chiral vanes.

Findings

No detectable translation-rotation coupling in fabricated particles.

Coupling arises only from hydrodynamic interactions between vanes.

Kelvin's isotropic helicoid exists as a weakly chiral particle.

Abstract

Nearly 150 years ago, Lord Kelvin proposed the isotropic helicoid, a particle with isotropic yet chiral interactions with a fluid, so that translation couples to rotation. An implementation of his design fabricated with a three-dimensional printer is found experimentally to have no detectable translation-rotation coupling, although the particle point-group symmetry allows this coupling. We explain these results by demonstrating that in Stokes flow, the chiral coupling of such isotropic helicoids made out of non-chiral vanes is due only to hydrodynamic interactions between these vanes. Therefore it is small. In summary, Kelvin's predicted isotropic helicoid exists, but only as a weak breaking of a symmetry of non-interacting vanes in Stokes flow.