Heat conduction by liquid helium II in capillary tubes. IV. Mutual friction under pressure

Abstract

We report measurements of supercritical heat conduction in liquid helium II at pressures above the vapor pressure. The measurements were made in glass capillary tubes of diameter 50.5 and 366.8 Μm in the temperature range from 1.2 to 2.1 K. As in our previous results at the vapor pressure, a clear distinction can be made between two regimes in which the average separation of vortex lines is either comparable with or larger than the size of the flow channel. In the wider tube, at high relative velocities v between the superfluid and normal component, where the vortex spacing is small, a modified form of Gorter-Mellink mutual friction Fsn is observed which varies as Fsn=Aρsρnv(v−v0)2. The coefficient A increases with pressure, and its variation with T/Tλ(p) is in fairly good agreement with Schwarz ' microscopic theory of superfluid turbulence. However, the absolute magnitude of A is in general larger than in Schwarz ' theory and also larger than most other experimental values. In the narrower tube the measurements are all in the regime where the vortex spacing is comparable with the tube size, and they do not agree with the predictions of the Gorter-Mellink law. At present, the data cannot be analyzed quantitatively in the terms of the vortex line density, because B, the vortex line scattering coefficient, is not known at high pressures.