Below about 0.87 kelvin, a mixture of the two stable isotopes of helium does something no ordinary liquid does: it refuses to finish mixing. Helium-3 and helium-4 are chemically identical — both noble, both inert, differing only in one missing neutron — and at higher temperatures they dissolve into each other completely, one liquid, no seam. Cool the mixture past that threshold and it spontaneously separates into two liquid phases stacked by density: a light phase on top, almost pure helium-3, and a dense phase below, mostly helium-4 with a small, fixed, temperature-dependent fraction of helium-3 dissolved in it — roughly 6.6% at absolute zero, a number fixed by quantum statistics rather than anything you can tune.
This phase separation, which sounds like a nuisance, is the entire mechanism of a dilution refrigerator, one of the few technologies that reaches continuous cooling below 10 millikelvin without any moving parts doing the cooling — no compressor, no piston, nothing mechanical straining against the cold. The trick is to force helium-3 to keep crossing that phase boundary against its will, from the concentrated side into the dilute side, over and over, forever, by pumping helium-3 vapor away from the dilute phase in a separate chamber (the "still") and letting osmotic pressure across the phase boundary pull more helium-3 through to replace it. Crossing from concentrated to dilute costs energy — it's endothermic, the mixing-enthalpy equivalent of evaporative cooling, except the "evaporation" here is one isotope dissolving reluctantly into a solvent it would rather not be in — and that latent heat is drawn from the refrigerator's coldest point, the mixing chamber, continuously, as long as the circulation keeps running.
Every joint in the plumbing that carries this circulating helium-3 pays a tax that only matters at these temperatures: Kapitza resistance, the thermal boundary resistance between a solid wall and liquid helium, which arises because phonons — the sound-like lattice vibrations that carry heat through a solid — struggle to transmit their energy across an interface into a liquid whose own excitations look completely different. At room temperature this resistance is invisible, swamped by everything else. At millikelvin temperatures it can dominate the entire thermal budget, meaning the engineering of a working dilution unit is as much about surface area and interface geometry — sintered silver heat exchangers with enormous internal surface, to buy back what Kapitza resistance takes away — as it is about the isotope chemistry underneath.
The helium-4 solvent itself isn't inert scenery, either. Below 2.17 K it becomes a superfluid, and superfluid helium-4 does something no classical fluid can: it carries heat not by ordinary conduction but by counterflow, described by Landau's two-fluid model as a superfluid component with zero viscosity and zero entropy flowing one way while a normal component carrying the entropy flows the other, the two interpenetrating without friction. This is why superfluid helium-4 can exhibit the fountain effect — heat one end of a superfluid-filled tube and liquid literally fountains out the other, driven by a thermally generated pressure difference that has no ordinary hydraulic explanation, only a quantum one. The two-fluid picture isn't a metaphor for how superfluid helium behaves; it's the closest thing to a literal description physics has for a liquid that is, at every point, secretly two liquids at once.
And underneath all of it, phonon transport in the metal and dielectric components of the refrigerator itself changes character. At these temperatures the mean free path of a phonon — how far it travels before scattering off an impurity, a boundary, another phonon — can exceed the physical size of the component carrying it. Heat stops diffusing and starts moving ballistically, like light through clear glass rather than like heat through a wall, and the engineering problem of getting heat OUT of the coldest stage becomes a problem of geometry and surface finish as much as of material choice, because the phonons, like the isotopes above them, are traveling in straight lines through a machine built specifically to interrupt them as gently as possible.
Seed: Dilution refrigeration — helium-3/helium-4 phase separation, Kapitza resistance, superfluid counterflow.