The Zero-Viscosity Climb of Helium-II

Place liquid helium-4 inside a vacuum flask and pump away the vapor to lower the temperature. At 2.17 Kelvin, the bubbling liquid suddenly goes quiet. The boiling stops entirely. The liquid remains cold, but its physical behavior undergoes a transition. If the vessel has a flat bottom, the liquid begins to climb.

A micro-thick film of the fluid crawls up the inner wall of the container, travels over the rim, and starts dripping from the outer bottom edge. It does not stop until the beaker is empty.

This is not a capillary trick. The fluid is moving against gravity, driven by a macroscopic quantum state that eliminates internal friction.

In classical fluid mechanics, every liquid has viscosity. Viscosity is the internal friction that resists flow, dragging molecules against one another and against the container walls. When water flows through a pipe, the layer of water touching the metal is stationary, while the center moves fastest. This velocity gradient requires energy to maintain.

At 2.17 Kelvin—a boundary known as the lambda point—helium-4 undergoes a transition from a normal fluid, Helium-I, to a superfluid state known as Helium-II. This transition was first observed in detail by Pyotr Kapitsa, John Allen, and Don Misener in 1937. They discovered that Helium-II flows through microscopic cracks with no measurable resistance.

Its viscosity is zero. Measured.

To understand why the liquid climbs, look at the Rollin film. Named after Bernard Rollin, who first detected its thermodynamic anomalies in 1936, this film is a thin layer of helium, roughly 30 nanometers thick, that coats any solid surface it touches.

Normally, surface tension draws a thin layer of liquid up a container wall until gravity balances the upward pull. For ordinary liquids, viscosity prevents this film from moving rapidly or far. For Helium-II, the absence of viscosity means the film behaves like a frictionless conveyor belt.

The driving force is van der Waals attraction. The atoms of the glass container exert an attractive electromagnetic force on the helium atoms. Because there is no viscosity to resist the motion, the helium atoms slide over one another to cover the dry glass surface, seeking a lower energy state.

As the helium atoms at the front of the film advance up the wall, they pull the liquid behind them. Once the film crosses the rim of the beaker and descends the outer wall, gravity assists the flow. The film acts as a siphon. It drains the beaker, drop by drop, from the bottom of the vessel. If you lift the beaker higher above the reservoir, the rate of dripping remains constant.

László Tisza proposed the two-fluid model in 1938 to explain this behavior. He suggested that Helium-II is a mixture of two components: a normal fluid component that retains viscosity and carries heat, and a superfluid component with zero viscosity and zero entropy.

The two components interpenetrate without interacting. As the temperature approaches absolute zero, the fraction of the superfluid component approaches 100 percent.

This model explains the fountain effect, first demonstrated by John Allen and Harry Jones in 1938. They packed a tube with fine powder, immersed it in Helium-II, and shone a light on the lower part of the tube to heat it.

Because the superfluid component has zero entropy, it flows toward warmer regions to dilute the heat, moving through the tiny gaps in the powder without friction. The normal component, which has viscosity, cannot escape back through the powder quickly enough. The resulting pressure buildup forces a dramatic jet of liquid helium out of the top of the tube.

The underlying physics relies on Bose-Einstein condensation. Helium-4 atoms are bosons; they have an even number of constituent particles (two protons, two neutrons, and two electrons), giving them an integer spin.

Below 2.17 Kelvin, a significant fraction of these bosons occupy the lowest possible quantum energy state. In this ground state, the wave functions of the individual atoms overlap and merge. Instead of behaving as a collection of billiard-ball particles colliding and scattering, the atoms behave as a single, coherent quantum object.

Because the entire condensate shares one quantum wave function, an individual helium atom cannot scatter off the wall of the container or another atom unless the collision has enough energy to excite the entire condensate at once. At low velocities, the energy of the flow is too low to create these excitations, which Lev Landau identified as rotons and phonons.

Without scattering, there is no resistance. Without resistance, there is no viscosity. The liquid climbs. Measured.

---

This article is AI-generated (synthetic) content, produced by an automated editorial system with human direction and review. Every claim is traced to published, peer-reviewed sources.