Heat Transfer in Superfluid Helium

Abstract

The superfluidity phenomenon of helium, which was discovered in the 1930s by Kapitza (Nature 141:74, 1938) [1], is about 100 years old. The superfluidity, which a macroscopic quantum phenomenon, is related to the formation (“condensation”) of a finite number of particles in one quantum state. This condensate of particles features some properties of the dissipation-free motion, which are responsible for the superfluidity phenomenon (Schmitt in Introduction to superfluidity: field-theoretical approach and applications. Springer, 2004) [2]. Below we shall be concerned only with superfluidity of Helium-4, which is the most common of the two isotopes of helium in nature. The superfluidity of the second isotope (Helium-3), which is a much more involved insufficiently known problem (Audi et al. in Nucl Phys A 729:3–128, 2003) [3], is beyond the scope of this book. So, below by “helium” we shall mean Helium-4. Helium is an extremely unusual system. This inert gas condenses only at a few degrees Kelvin and only helium remains a fluid down to absolute zero \( T = 0 \). Solidification of helium requires pressure about 30 atm. Because of this, the phase diagram for helium does not contain the triple point, which is standard for all other substances. At normal pressure helium boils at 4.2 K, the thermodynamic critical point corresponds to 5.19 K at pressure 2.24 atm. The “reluctance” of helium to form crystals can be explained by quantum effects—because of small mass of atoms and weakness of their interactions, their deflections from the equilibrium position in helium crystal are comparable with the interatomic distance, which leads to the “delocalization” of atoms in the crystal. To a certain extent, the smallness of the amplitude of the zero-point vibrations of atoms in the crystal lattice is analogous to the behavior of electrons in an ordinary metal. A remarkable property of quantum crystals of helium is their ability to generate crystallization waves, which can be looked upon as a dissipationless recrystallization of the surface.