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Every liquid you know resists flowing: honey a lot, water a little. In 1937 Pyotr Kapitsa found a liquid that, below a certain temperature, barely resisted at all. This post covers who Kapitsa was, how he found superfluidity, why earlier measurements had missed it, the physics of viscosity behind it, and what students can learn from his way of working.
Who was Pyotr Kapitsa?
The Nobel Prize biography describes a physicist who was also an engineer and inventor. Kapitsa was born in Kronstadt on 9 July 1894 and trained at the Petrograd Polytechnical Institute under A. F. Ioffe, finishing in 1918. With N. N. Semenov he proposed a method for measuring the magnetic moment of an atom in a non-uniform magnetic field, later used in the Stern-Gerlach experiments.
In 1921 he went to the Cavendish Laboratory in Cambridge to work with Rutherford. In 1924 he developed methods for producing very strong magnetic fields, up to 320 kilogauss in a volume of 2 cm³. He became director of the Royal Society Mond Laboratory, and in his last Cambridge years turned to low temperatures. In 1934 he returned to Moscow, where he organised the Institute for Physical Problems.
Why did he build a new helium liquefier?
In a 1934 Nature paper, Liquefaction of Helium by an Adiabatic Method without Pre-cooling with Liquid Hydrogen, Kapitsa explained the problem. The methods still in use were essentially those of Dewar and Kamerlingh Onnes, based on the Joule-Thomson effect, and they were very inefficient. He quoted an estimate that producing liquid helium this way took a hundred times more power than a reversible process would. His solution was to let compressed helium do work as it expanded in an engine, cooling it far more efficiently.
The Nobel facts page notes that this method produced liquid helium in large quantities and became very important for many experiments. Good tools come first; discoveries follow.
How did he discover superfluidity?
Below a temperature called the lambda point, liquid helium changes into a form known as helium II. Keesom had found that helium II conducts heat extraordinarily well. Kapitsa wondered whether this could be explained by convection, which would need the liquid to have an abnormally low viscosity.
In his Nature letter, Viscosity of Liquid Helium below the λ-Point (1938), he pointed to a weakness in earlier work. Measurements in Toronto had found a drop in viscosity below the lambda point, by a factor of 3 to 8 depending on the comparison, but "no check was made to ensure that the motion was laminar, and not turbulent." Kapitsa set out to measure the flow under conditions where it would stay laminar, and found that helium II flowed with almost no viscosity.
In the same issue, J. F. Allen and A. D. Misener reported their own flow measurements. They wrote that they "had reached the same conclusion as Kapitza": earlier oscillation measurements, which gave an upper limit of 10⁻⁵ CGS units for the viscosity, probably involved non-laminar flow. The effect became known as superfluidity. The Nobel facts page credits Kapitsa with discovering in 1937 "that at very low temperatures liquid helium flows without resistance".
Why did turbulence matter? A worked example
The Reynolds number tells you whether flow is smooth (laminar) or turbulent: Re = ρvd/η, where ρ is density, v speed, d the size of the channel and η viscosity. Turbulence sets in at high Re.
Suppose helium II really has a viscosity 1000 times smaller than you assumed. For the same density, speed and channel size, Re is 1000 times larger. A flow you expected to be smooth could easily be turbulent, and a viscosity calculated with a laminar formula would then be wrong. That was Kapitsa's objection. A careful experiment has to keep Re low, for example by using a very narrow channel, because a small d keeps the flow laminar and the measurement meaningful.
Two unit conversions you will need:
The CGS unit of viscosity is the poise: 1 P = 0.1 Pa s. So Allen and Misener's upper limit of 10⁻⁵ P is 10⁻⁶ Pa s.
1 tesla = 10⁴ gauss. So Kapitsa's 320 kilogauss is 3.2 × 10⁵ G = 32 T.
Common mistakes:
Applying Poiseuille's or Stokes' law to turbulent flow. Both assume laminar flow. Check Re first.
Converting poise the wrong way. 1 P is a tenth of a pascal second, not ten.
Thinking superfluid means "very runny". It means flow with no measurable viscosity through narrow channels, a quantum effect with no classical equivalent.
Our post on fluids and Bernoulli mistakes covers more on viscosity and flow. When flow patterns are hard to picture, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
How was he recognised?
Kapitsa shared the 1978 Nobel Prize in Physics "for his basic inventions and discoveries in the area of low-temperature physics", 41 years after the discovery. The other half went to Penzias and Wilson for the cosmic microwave background, a story told in our post on George Gamow. In his Nobel lecture he chose not to talk about helium at all, but about plasma and controlled thermonuclear reactions, his research of the time. The theory of superfluid helium was developed by Lev Landau, who received the 1962 Nobel Prize "for his pioneering theories for condensed matter, especially liquid helium".
What can a student take from Kapitsa's way of working?
Invent the equipment. His liquefier made the discovery possible.
Question the method behind a number. He did not accept the Toronto value until the flow conditions were checked.
Keep moving. He went from magnets to helium to oxygen production to plasma physics, and lectured on his newest work even when honoured for his old.
The earlier chapter is in our post on Kamerlingh Onnes and superconductivity.
Try this: find the Reynolds number for water flowing at 0.1 m/s through a 1 cm pipe (ρ = 1000 kg/m³, η = 0.001 Pa s), then decide whether the flow is laminar.
