Strange 3D-printed shapes test 150-year-old mathematical theory

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By Leah Crane

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A 3D-printed isotropic helicoid

G. Voth/Wesleyan University

A unusual signifier described by mathematician Lord Kelvin successful 1871 and predicted to behave unusually successful a fluid has yet been afloat studied successful the existent satellite acknowledgment to 3D printing – and it seems Kelvin whitethorn person been wrong. The behaviour of the shape, called an isotropic helicoid, has been described successful fluid dynamics textbooks, but it hadn’t been straight measured until now.

An isotropic helicoid indispensable acquisition the aforesaid magnitude of resistance from a fluid careless of its orientation, similar a sphere, but besides rotate arsenic it moves done the fluid. So if you dropped an isotropic helicoid into a vessel of a viscous liquid, it should rotation arsenic it sinks, akin to the mode a propeller turns.

Greg Voth astatine Wesleyan University successful Middletown, Connecticut, and his colleagues 3D printed 5 antithetic shapes that should beryllium isotropic helicoids, each a small much than a centimetre across, and dropped them into a vessel of silicon oil. They were incapable to observe rotation successful immoderate of them, meaning the predictions for an isotropic helicoid whitethorn beryllium wrong.

“You’ve got to conjecture that idiosyncratic other has tried this successful 150 years – successful Kelvin’s archetypal paper, it adjacent sounds similar helium tried it,” says Voth. “I fishy that radical person tried to fabricate these particles, but they were constricted by defects successful the fabrication truthful they simply didn’t publish, truthful the proposal of this behaviour has stayed with us.”

Upon delving into the hydrodynamic effects successful play, the researchers calculated that determination was astir surely a link, oregon coupling, betwixt the movement and rotation of their particles, meaning they fulfilled Kelvin’s criteria. But this was acold excessively tiny to person immoderate detectable effect.

“The coupling is tiny, but it inactive exists,” says Voth. He and his squad are present moving connected gathering an isotropic helicoid wherever that coupling could beryllium measurable, which would yet vindicate Lord Kelvin’s idea.

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

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