How runny a liquid can be?

Study shows that two fundamental physical constants govern how runny a liquid can be.


Viscosity (η) is the resistance of a liquid to flow. Liquids get thicker when cooled and runnier when heated, but how runny can a liquid ever get if we keep heating it?

At a point, the liquid reaches a specific temperature; it transitions between the liquid-like and gas-like state and has a minimum value of viscosity.

The higher the viscosity, the slower the liquid flows. Likewise, the lower the viscosity, the faster the liquid flows.

Although, it is quite difficult to calculate viscosity from theory because it strongly depends on liquid structure, composition, and interactions as well as external conditions in a complicated way. This difficulty has been compared with the difficulty of calculating fundamental physical constants, the constants which shape the fabric of our Universe.

Despite this difficulty, scientists from the Queen Mary University of London and the Russian Academy of Sciences have developed an equation to calculate the viscosity of the liquid.

They show that two fundamental physical constants govern how runny a liquid can be. Physical constants, or constants of Nature, are measurable properties of the physical universe that do not change.

The equation relates the minimal value of elementary viscosity to the Planck constant, which governs the quantum world, and the dimensionless proton-to-electron mass ratio.

Professor Kostya Trachenko, lead author of the paper from the Queen Mary University of London, said: “This result is startling. Viscosity is a complicated property varying strongly for different liquids and external conditions. Yet our results show that the minimum viscosity of all liquids turns out to be simple and universal.”

There are practical implications of discovering this limit too. It could be applied where a new fluid for a chemical, industrial, or biological process with a low viscosity is required. One example where this is important is the recent 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 useful theoretical guide of what to aim for. It also tells us that we should not waste resources trying to beat the central limit because the constants of Nature will mould the viscosity at or above this point.

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

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.

Professor Trachenko said: “The lower fundamental limit reminds us how fundamental constants of Nature affect us daily, starting from making a morning cup of tea by extending their overarching rule to specific, yet complex, properties such as liquid viscosity.”

Vadim Brazhkin, a co-lead author from the Russian Academy of Sciences, added“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. Exploring and appreciating these and other connections is what makes science ever so exciting.”

Journal Reference:
  1. Minimal quantum viscosity from fundamental physical constants. DOI: 10.1126/sciadv.aba3747


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