Does Lord Kelvin’s Isotropic Helicoid Exist?

In 1871, Lord Kelvin hypothesized the existence of a particle he called an isotropic helicoid which is chiral so that it couples translation and rotation but is isotropic in both drag and translation-rotation coupling. Since then, several textbooks and theoretical papers have considered isotropic helicoids. We recently fabricated particles with a 3D printer following the isotropic helicoid design that Lord Kelvin proposed, dropped them in a quiescent fluid, and were surprised to find that they showed no rotation-translation coupling. We then calculated the translation-rotation coupling for an isotropic helicoid made of 12 oblate ellipsoids configured according to Lord Kelvin’s design. This calculation is done in Stokes flow, ignoring inter-particle interactions. Again we found precisely zero rotation-translation coupling. Numerical simulations agree with the experiments and theory. We conclude that Lord Kelvin’s particle is isotropic but does not couple translation and rotation. We conjecture that it is not possible to fabricate a particle that has isotropic but non-zero translation-rotation coupling and isotropic drag.