What Is a Superfluid, and Why Does Helium Climb Walls?

Most liquids get thicker and more sluggish as they cool. Liquid helium does the opposite. Below about two kelvin it becomes a superfluid, a liquid that flows with no measurable internal friction, squeezes through cracks that stop ordinary liquids, and climbs up and over the walls of its container. Our Superfluid tee is that strange liquid in pixels. This post builds on our explainer What Happens at Absolute Zero?

What is a superfluid?

A superfluid is a liquid that flows without viscosity. Viscosity is the internal friction that makes honey slow and keeps any ordinary liquid from sliding through very narrow channels. In the Nobel Committee’s summary, the superfluid phase of helium “is freely flowing (without viscosity), can penetrate fine pores that are closed for ordinary liquids and for many gases, can creep upwards along walls and is an excellent heat conductor” (NobelPrize.org, 1996 advanced information^[1]).

In ordinary helium-4 this phase appears at a phase transition about 2.17 K above absolute zero (NobelPrize.org, 1996 press release^[2]). The temperature of that transition is called the lambda point (λ-point), and the liquid below it is called helium II. One kelvin (K) is the same size step as one degree Celsius, but counted up from absolute zero.

Who discovered superfluidity?

Two short letters printed one after the other in Nature in January 1938 announced it. Pyotr Kapitza in Moscow started from a puzzle: helium II conducts heat abnormally well, as Willem Keesom had found, and Kapitza suspected convection currents, which would require “an abnormally low viscosity” (Kapitza 1938^[3]). His letter, titled “Viscosity of Liquid Helium below the λ-Point,” reported that the viscosity of helium II was extraordinarily small. On the next page, J. F. Allen and A. D. Misener in Cambridge reported their own flow measurements on helium II, noting they had reached the same conclusion as Kapitza about earlier viscosity measurements (Allen & Misener 1938^[4]).

The Nobel Foundation credits Kapitsa with the discovery: “Kapitsa discovered in 1937 that at very low temperatures liquid helium flows without resistance. The phenomenon became known as superfluidity” (NobelPrize.org^[5]). He shared the 1978 Nobel Prize in Physics for his low-temperature work. Allen and Misener’s simultaneous paper is why historians of the subject usually name all three.

Why does superfluid helium climb walls?

Liquid helium wets almost any surface it touches, so the walls of its container are coated by a very thin film of liquid. In an ordinary liquid that film would be held in place by its own viscosity. In helium II the film can flow freely, so it creeps up the inside wall, over the rim and down the outside. The Nobel Committee lists this “creep upwards along walls” as one of the signature properties of the superfluid (NobelPrize.org^[1]). Our earlier post The Cool Science of Superfluidity has more on what it looks like in the lab.

What is the fountain effect?

Weeks later, in March 1938, Allen and H. Jones reported “new phenomena connected with heat flow in helium II” (Allen & Jones 1938^[6]). In what became known as the fountain effect, gently heating superfluid helium on one side of a fine porous plug drives liquid through the plug towards the heat, strongly enough to spout a jet above the surface. Heat and flow are tied together in helium II in a way they are not in any ordinary liquid.

Why does it happen? Bosons and the two-fluid picture

The explanation is quantum. A helium-4 atom contains an even number of particles (two protons, two neutrons, two electrons), which makes it a boson. Bosons can pile into the same lowest-energy quantum state, a process called Bose–Einstein condensation. The 1996 Nobel press release sums up the accepted picture: the superfluid “is a kind of Bose-Einstein condensate of helium atoms,” an idea “first explained schematically by Fritz London and then in detail by Lev Landau” (NobelPrize.org^[2]).

In 1938 László Tisza took London’s idea, in which one fraction of the atoms sits in the lowest energy level while the rest are spread over excited states, and used it to explain transport in helium II (Tisza 1938^[7]). This grew into the two-fluid model: helium II behaves as if it were a mixture of a frictionless superfluid component and an ordinary “normal” component that carries heat. Lev Landau published his theory of the superfluidity of helium II in 1941 (Landau 1941^[8]) and received the 1962 Nobel Prize in Physics “for his pioneering theories for condensed matter, especially liquid helium” (NobelPrize.org^[9]).

The quantum nature shows up most clearly in rotation. A superfluid cannot spin like an ordinary liquid. Above a critical rotation speed, microscopic vortices appear, and the circulation around each one “cannot take on any arbitrary value, but is quantized” (NobelPrize.org^[1]). Here a quantum rule is visible in the motion of a whole bucket of liquid.

Can helium-3 be a superfluid too?

Helium-3 has one neutron fewer, so its atoms contain an odd number of particles. That makes each atom a fermion, and fermions obey the exclusion principle, which forbids two of them from sharing a state (see Why Can’t Two Electrons Share a State?). Fermions cannot condense on their own. They can, however, pair up, as electrons do in superconductors, and pairs behave like bosons.

David Lee, Douglas Osheroff and Robert Richardson found exactly this at Cornell in the early 1970s. Helium-3 becomes superfluid only about two thousandths of a degree above absolute zero, roughly a thousand times colder than helium-4, and it has at least three different superfluid phases (NobelPrize.org^[2]). They shared the 1996 Nobel Prize in Physics.

How is a superfluid related to a Bose–Einstein condensate?

Both rest on bosons crowding into a single quantum state. Superfluid helium is a dense, strongly interacting liquid, while the first Bose–Einstein condensate of a dilute atomic gas was made only in 1995, by cooling rubidium atoms to less than 170 billionths of a degree above absolute zero (NIST^[10]). Our Condensa sticker stands for that condensed state, and our Thermodynamics collection covers the temperature floor all of this approaches but never reaches.

FAQ

At what temperature does helium become superfluid?

Helium-4 becomes superfluid at about 2.17 K, the lambda point. Helium-3 does so only at about 0.002 K.

Is superfluid helium really frictionless?

Its superfluid component flows without measurable viscosity through narrow channels, but helium II also contains a normal component that does carry viscosity and heat. That is the core of the two-fluid picture.

Why does superfluid helium escape from containers?

A thin film of liquid coats the walls and, with no viscosity to hold it back, flows up and over the rim. The bulk liquid follows through the film.

Who won Nobel Prizes for superfluidity?

Lev Landau (1962) for the theory of liquid helium, Pyotr Kapitsa (1978) for low-temperature physics including superfluidity, and Lee, Osheroff and Richardson (1996) for superfluid helium-3.

References

1. NobelPrize.org, Advanced information: The Nobel Prize in Physics 1996 (superfluid helium-3). https://www.nobelprize.org/prizes/physics/1996/advanced-information/
2. NobelPrize.org, Press release: The Nobel Prize in Physics 1996 (Lee, Osheroff, Richardson). https://www.nobelprize.org/prizes/physics/1996/press-release/
3. P. Kapitza (1938), “Viscosity of Liquid Helium below the λ-Point,” Nature 141, 74 (DOI 10.1038/141074a0). https://www.nature.com/articles/141074a0
4. J. F. Allen & A. D. Misener (1938), “Flow of Liquid Helium II,” Nature 141, 75 (DOI 10.1038/141075a0). https://www.nature.com/articles/141075a0
5. NobelPrize.org, Pyotr Kapitsa – Facts (Nobel Prize in Physics 1978). https://www.nobelprize.org/prizes/physics/1978/kapitsa/facts/
6. J. F. Allen & H. Jones (1938), “New Phenomena Connected with Heat Flow in Helium II,” Nature 141, 243–244 (DOI 10.1038/141243a0). https://www.nature.com/articles/141243a0
7. L. Tisza (1938), “Transport Phenomena in Helium II,” Nature 141, 913 (DOI 10.1038/141913a0). https://www.nature.com/articles/141913a0
8. L. Landau (1941), “Theory of the Superfluidity of Helium II,” Phys. Rev. 60, 356–358 (DOI 10.1103/PhysRev.60.356). https://journals.aps.org/pr/abstract/10.1103/PhysRev.60.356
9. NobelPrize.org, The Nobel Prize in Physics 1962 (Lev Landau). https://www.nobelprize.org/prizes/physics/1962/summary/
10. NIST News (13 July 1995), “Physicists Create New State of Matter at Record Low Temperature”. https://www.nist.gov/news-events/news/1995/07/physicists-create-new-state-matter-record-low-temperature

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.