The two-fluid theory and second sound in liquid helium

© 2009 American Institute of Physics, S-0031-9228-0910-020-0 Early research with liquid helium showed that it had remarkable new properties, especially below the so-called lambda transition near 2.2 K, where there is a sharp, narrow peak in the specific heat (see figure 1a). The liquid below the transition was named helium II to distinguish it from the liquid above the transition, called helium I. Three properties discovered in the late 1930s were particularly puzzling. First, a test tube lowered partly into a bath of helium II will gradually fill by means of a thin film of liquid helium that flows without friction up the tube’s outer wall. Second, in the thermomechanical effect, if two containers are connected by a very thin tube that can block any viscous fluid, an increase in temperature in one container will be accompanied by a rise in pressure, as seen by a higher liquid level in that container. Third is the viscosity paradox: The oscillations of a torsion pendulum in helium II will gradually decay with an apparent viscosity about one-tenth that of air, but if liquid helium is made to flow through a very fine tube, it will do so with no observable pressure drop—the apparent viscosity is not only small, it is zero! Laszlo Tisza was captivated by an idea being pushed in those days by Fritz London that the transition to helium II was a manifestation of Bose–Einstein condensation (BEC). In 1925 Albert Einstein had generalized a calculation for photons by Satyendra Nath Bose to massive particles, such as atoms; he found that for an ideal gas of identical, integer-spin particles below a certain temperature, a macroscopic fraction of the particles accumulates, or condenses, in the lowestenergy singleparticle state with zero momentum. After one of his discussions with London and inspired by the recently discovered effects, Tisza had the idea that the Bosecondensed fraction of helium II formed a superfluid that could pass through narrow tubes and thin films without dissipation. The uncondensed atoms, in contrast, constituted a normal fluid that was responsible for phenomena such as the damping of pendulums immersed in the fluid. That revolutionary idea demanded a “two-fluid” set of equations of motion and, among other things, predicted not only the existence of ordinary sound—that is, fluctuations in the density of the fluid—but also fluctuations in entropy or temperature, The two-fluid theory and second sound in liquid helium