How measuring Reynolds similarity in superfluids could help demonstrate the existence of quantum viscosity

Every fluid, from Earth’s atmosphere to the blood pumped through the human body, has viscosity, a quantifiable characteristic describing how the fluid deforms when it encounters other matter. If the viscosity is higher, the fluid flows calmly, a so-called laminar state. If the viscosity decreases, the fluid changes from laminar flow to turbulent flow.

The degree of laminar or turbulent flow is called the Reynolds number, which is inversely proportional to viscosity. Reynolds’ law of dynamic similarity, also known as Reynolds similarity, states that if two fluids flow around similar structures with different length scales, they are hydrodynamically identical, provided they exhibit the same Reynolds number.

However, this Reynolds similarity does not apply to quantum superfluids, because they have no viscosity – or so researchers believe. Now, a researcher at the Nambu Yoichiro Institute for Theoretical and Experimental Physics at Osaka Metropolitan University in Japan has theorized a way to examine Reynolds similarity in superfluids, which could demonstrate the existence of quantum viscosity in superfluids.

Dr. Hiromitsu Takeuchi, a lecturer at the Graduate School of Science at Osaka Metropolitan University, published his approach in Physical examination B.

“Superfluids have long been considered an obvious exception to Reynolds similarity,” said Dr. Takeuchi, explaining that Reynolds’ law of similarity states that if two flows have the same Reynolds number, then they are physically identical. “The concept of quantum viscosity overturns the common sense of superfluid theory, which has a long history of more than half a century. Establishing similarity in superfluids is an essential step in unifying classical and quantum hydrodynamics.”

However, quantum superfluids can have turbulence, leading to a quantum dilemma: turbulence in fluids requires dissipation, so how can superfluid turbulence undergo dissipation without viscosity? They must be dissipated and can follow Reynolds similarity, but the right approach to examine it has not yet been developed.

These characteristics could be examined, Dr. Takeuchi theorizes, by analyzing how a solid sphere transforms into a superfluid. By combining the terminal falling velocity of the sphere with the resistance the sphere encounters from the fluid as it falls, researchers can determine an analogue of the Reynolds similarity. This means that the effective viscosity, called quantum viscosity, can be measured.

“This study focuses on a theoretical question related to understanding quantum turbulence in superfluids and shows that Reynolds similarity in superfluids can be verified by measuring the terminal velocity of an object falling in a superfluid,” said Dr. Takeuchi.

“If this verification can be performed, it suggests that quantum viscosity exists even in pure superfluids at absolute zero. I look forward to seeing it verified experimentally.”