On the properties of helium films and superleaks

Abstract

The properties of liquid helium in very narrow channels and in the Rollin film are investigated theoretically, using as a model Landau's ideal gas of elementary excitations. Besides roton and phonon excitations, surface waves and quantized vortex lines must be considered; moreover the energy of a roton is reduced by the proximity of a solid wall. The order of magnitude of the critical velocity and the dependence of the critical velocity on film thickness can be explained in terms of the surface excitations, but in “superleaks” (e.g. Vycor glass) this mechanism is inoperative. Apart from a contribution to the specific heat at low temperatures, the surface excitations will affect the thermal properties very little. The reduction of the roton energy near a wall will produce bigger effects in the thermal properties (affecting both films and superleaks). For a sattsrated film, the effects are still slight, but in a thinner film (or narrow enough channel) the onset temperature for superflow will be reduced considerably; the specific heat will have a broad maximum instead of a λ-anomaly. Both these predictions agree with experiment.