โ Scribed by Robert B. Hallock
No coin nor oath required. For personal study only.
This appendix contains several comments relevant to the lectures of Roger Bowley. ! We begin with some introductory remarks on third sound and proceed to utilize third sound to study the stability of flow in helium films. We conclude with a remark about the effective thermal conductivity of a helium film.
Consider a helium film on a substrate and let the substrate be a smooth conductor. If we imagine the temperature is well below the bulk superfluid transition temperature and the film is not too thin, then the film will have superfluid properties. If we imagine bringing another small electrode in proximity to the first, then the application of an electric field will result in helium being drawn into the "capacitor" we have formed. So long as the capacitor gap is not too narrow (and we avoid capillary condensation) the region of the capacitor gap will hold helium film at a thickness which is enhanced relative to the film thickness away from the region of the electric field. If the field is removed abruptly, the helium will leave the region of the capacitor and move away from the gap as a wave. The wave is due to the motion of the superfluid and we call the wave third sound. 2 Accompanying the enhanced thickness of the film which constitutes the wave crest is a reduction of temperature; similarly, a wave trough is accompanied by an increase in temperature. This allows the detection 2 of third sound by either a sensitive capacitor or a sensitive thermometer. The restoring force is the Van der Waals attraction of the substrate and to first order the third sound velocity is given by C 2 = (ps/p)fd where f is the Van der Waals restoring force per unit mass and d is the thickness of the helium film. Here Ps/P is the superfluid fraction in the film. Over a modest region of film thickness it is observed that f-ot/d 3 where a characterizes the strength of the substrate-helium interaction. We have left out a number of details here, but these need not concern us. An important property of third sound is the fact
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