Strange 3D-printed shapes check 150-year-old mathematical concept

By Leah Crane

An odd form described by mathematician Lord Kelvin in 1871 and predicted to behave unusually in a fluid has lastly been totally studied in the true world because of 3D printing – and it appears Kelvin could have been fallacious. The behaviour of the form, referred to as an isotropic helicoid, has been described in fluid dynamics textbooks, but it surely hadn’t been straight measured till now.

An isotropic helicoid should expertise the identical quantity of drag from a fluid no matter its orientation, like a sphere, but additionally rotate because it strikes by way of the fluid. So for those who dropped an isotropic helicoid right into a tank of a viscous liquid, it ought to spin because it sinks, just like the way in which a propeller turns.

Greg Voth at Wesleyan University in Middletown, Connecticut, and his colleagues 3D printed 5 totally different shapes that must be isotropic helicoids, every slightly greater than a centimetre throughout, and dropped them right into a tank of silicon oil. They had been unable to detect rotation in any of them, that means the predictions for an isotropic helicoid could also be fallacious.

“You’ve got to guess that somebody else has tried this in 150 years – in Kelvin’s original paper, it even sounds like he tried it,” says Voth. “I suspect that people have tried to fabricate these particles, but they were limited by defects in the fabrication so they simply didn’t publish, so the hypothesis of this behaviour has stayed with us.”

Upon delving into the hydrodynamic results in play, the researchers calculated that there was virtually definitely a hyperlink, or coupling, between the movement and rotation of their particles, that means they fulfilled Kelvin’s standards. But this was far too small to have any detectable impact.

“The coupling is tiny, but it still exists,” says Voth. He and his crew are actually engaged on constructing an isotropic helicoid the place that coupling could possibly be measurable, which might lastly vindicate Lord Kelvin’s concept.

Journal reference: Physical Review Fluids, DOI: 10.1103/PhysRevFluids.6.074302