Damped Oscillation in the Surface Film of Liquid Helium II

Abstract

There are many ex:perimental data on the flow phenomena of liquid helium II. The most of them are classified in one of the three categories; the heat conduction and mass transfer through narrow slits, and the surface flow. Several parameters have been introduced to account for the experimental results. The systematic analysis of them, however, is not yet complete. Among those parameters, the critical yelocity and the mutual friction seem to be most essential, because both of these, in a sense, imply the break down of ideal two fluidity of liquid helium; In the present and following letters we shall clarify their interrelation. We first take up the oscillation of the surface film observed by Atkins!). He has succeeded in ex:plaining the period of oscillation by means of the two fluid theory. Here we concern ourselves with the damping. Simple estimation shows that the normal viscosity is too small and Gorter's cubic mutual friction is too large to account for the observed logarithmic decrement. Gorter's mutual friction contradicts also the fact that the observed decrement has the constant value 1.9 x 102. As for a linear mutual friction, its existence is rather doubtful. Even if we assume its existence and adjust its magnitude to explain some data of heat conduction through slies, the damping arising from this friction is too large. Consequently we are forced to assume that there exists no friction in the equation of motion for the superfluid, at least, below a certain critical velocity. In fact, as we shall see below, we can .explain the observed damping without introducing any kind of friction in the equation of motion. A part of the superfluid flowing in over the wall of the capillary must transform itself into the normal fluid. This transformation requires an amount of energy, which has to be supplied from the outer bath to the reservoir attached to the capillary. On account of the well-known Kapitza resistance at the boundary, a small but finite temperature difference ,d T is established between the reservoir and the bath. As the period of oscillation is fairly long (27.8 sec.) and thermal conductivity of the copper boundary is very high, we can assume that ,dT is given by