The share of the normal fluid phase is 100% at 2.17 K, and drops to almost 0% at 1 K as we cool the liquid.
This behavior is very different from, say, ice and liquid water. The phase transition happens to the whole body of water at a fixed temperature 0 C.
How can a phase change happen gradually as we lower the temperature?
If the different phases would exist as large 3-dimensional volumes of matter, and be separate from each other, then we should be able to separate the two phases and make 100% superfluid helium-4 at, e.g., 1.5 K.
Since that is not possible, the "structure" of helium-4 at 1.5 K has to contain matter from both phases. We cannot separate the phases if we keep the temperature constant.
Atoms in superfluid helium-4 probably are ordered in some way. That would explain the peak in the specific heat just below 2.17 K.
The plate-layered model of superfluid helium-4
o o o o o o o o plate of superfluid
o o o o o
o o o o o ordinary fluid
o o o o o
o o o o o o o o plate of superfluid
Let us introduce the plate model of superfluid helium-4. The superfluid component arranges itself into 2-dimensional plates of ordered helium atoms. Between the plates there is helium-4 in the normal fluid phase. Without the normal fluid layers, the plates would be broken apart by thermal vibrations.
It is a "lyotropic liquid crystal" where ordered structures of a superfluid are immersed into a normal fluid.
Thus, the microscopic structure of helium-4 under 2.17 K is a layered structure. Layers of the normal fluid phase may act as a some kind of a lubricant or a cushion between the more ordered structures of the superfluid phase.
When we lower the temperature to 0 K, the entropy of helium-4 drops to a very low level. There no longer can exist layers of the normal fluid phase. Apparently, the ordered structure of the superfluid phase cannot be broken apart by the zero-point fluctuation.
Why can the superfluid phase flow independent of the normal fluid phase? Why is the viscosity zero below 2.17 K?
If the superfluid phase exists as plates, those structures are able to move even though the normal fluid phase stays static. The two phases can move independently.
Why is the viscosity zero at a low temperature? Our hypothesis is that an ordered structure of helium atoms can slide through the normal fluid phase without friction. The atom lattice of the superfluid phase does not contain potential wells which would be able to capture atoms of the normal fluid phase, so that there would be an exchange of momentum.
Conclusions
The specific heat of helium-4 at less than 2.17 K suggests that the superfluid phase must be highly ordered.
The gradual phase change requires that the structure of helium-4 at less than 2.17 K must be layered at the atomary level. There must be layers of normal fluid between the highly ordered superfluid structures. The thickness of the superfluid structures is probably just one atom, while the layers of normal fluid may be up to tens of atoms thick.
Superfluidity requires that superfluid structures must be able to slide through the normal fluid without friction.
Could it be that the structure of helium-4 under 2.17 K is not as "classical" as we have presented? The disorder, or the normal fluid component, might be excitations, for example, phonons, which move in a highly ordered material. In semiconductors we have electrons and holes: it is like a two-fluid model.
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