Just how runny can a liquid get?

You’ve probably never wondered how runny a liquid can get, which is no bad thing because it’s not an easy question to answer.

There is a minimum level of viscosity – the point where a heated liquid transitions from a liquid-like to a gas-like state – but viscosity is considered impossible to calculate from theory because it strongly depends on liquid structure, composition and interactions as well as external conditions in a complicated way.

Scientists from Queen Mary University of London (QMU) and the Russian Academy of Sciences (RAS) think they’re onto something, however. But it, too, is complicated

In a paper published in the journal Science Advances, they suggest that two fundamental physical constants or constants of nature – measurable properties of the physical universe that do not change – govern how runny a liquid can be.

Their new equation, they say, relates the minimal value of elementary viscosity (the product of viscosity and volume per molecule) to the Planck constant, which governs the quantum world, and the dimensionless proton-to-electron mass ratio.

“This result is startling. Viscosity is a complicated property varying strongly for different liquids and external conditions, yet our results show that the minimal viscosity of all liquids turns out to be simple and universal,” says lead author Kostya Trachenko, from QMU.

There are practical implications of discovering this limit too, the researchers suggest.

It could be applied where a new fluid for a chemical, industrial or biological process with a low viscosity is required – a recent example being the use of supercritical fluids for green and environmentally clean ways of treating and dissolving complex waste products.

In this instance, the discovered fundamental limit provides a theoretical guide of what to aim for. It also tells us that we should not waste resources trying to beat the fundamental limit because the constants of nature will mould the viscosity at or above this point.

Fundamental physical constants and in particular dimensionless constants (fundamental constants that do not depend on the choice of physical units) are believed to define the Universe we live in, Trachenko and colleagues suggest.

A finely tuned balance between the proton-to-electron mass ratio and another dimensionless constant, the fine structure constant, governs nuclear reactions and nuclear synthesis in stars leading to essential biochemical elements including carbon.

This balance provides a narrow habitable zone where stars and planets can form, and life-supporting molecular structures can emerge. Change one of the dimensionless fundamental constants slightly, and the Universe becomes very different, with no stars, heavy elements, planets and life.

“There are indications that the fundamental lower limit of liquid viscosity may be related to very different areas of physics: black holes as well as the new state of matter, quark-gluon plasma, which appears at very high temperature and pressure,” suggests co-lead author Vadim Brazhkin, from the RAS.