Density of He II in Superfluid Flow

Abstract

The density of He II in supercritical, superfluid flow has been measured by a sensitive capacitance technique in the temperature range from 1.3 to 1.8 K. The average density of the liquid decreased with increasing superfluid velocity. The largest fractional density change observed was Ap/p = -9 x 10" 6 at a velocity of 7.75 cm/sec. The results can be accounted for adequately by the two-fluid, thermohydrodynamic equations of motion utilizing the expressions for the nonlinear, superfluid dissipation force and the mutual friction force.The effect of the presence of quantized vorticity on the bulk or average density of He II has been the concern of a number of experiments. Andronikashvili and Tsakadze 1 (AT) reported that the density of He II in rotation was greater than the density at rest. The fractional change in the density, Ap/p, which was observed upon rotation of the helium was as large as 4 parts in 10 4 at 1.42 K and an angular velocity of 30 sec" 1 . Subsequent measurements of the density of rotating helium by others 2 " 4 did not reveal any change within the error of the measurements. The most precise measurements 4 indicated that any fractional change in the density of He II upon rotation was not greater than 5 parts in 10 7 under conditions similar to those reported by AT. Further experiments 5 suggested that the anomalous increase in density observed by AT arose from thermal effects caused by dissipation during rotation.Erben and Pobell 6 (EP) have measured the density of He II in turbulent thermal counterflow. Under these conditions vortex lines are also present, 7 and any change in the density due to the structure of the vortices would be expected to occur there as well as in rotating helium. The results presented by EP show that there is an anomalous increase in the density of He II when it is set into turbulent counterflow. The largest fractional increase in the density was reported to be about 2 to 3 parts in 10 4 which is the same order of magnitude as the largest change reported by AT. In addition EP found that the state of increased density was metastable and could be suppressed by mechanical disturbances such as vibration. Their observations of the metastability of the density change provided an explanation of the contradictory results obtained in measurements of the density of rotating He II.The work presented here was undertaken in order to examine any change in the density of He II which could be attributed to the structure of vortex lines under conditions of supercritical superfluid flow. The results of our experiment, in which the normal fluid remains essentially at rest, can be compared with the results of AT and EP in thermal counterflow and rotation. If the anomalous increase in the density of the liquid observed by AT and EP were associated with the vortex structure and not with an effect incidental to the presence of vortices, then the effect should have been quite readily observable with the resolution and concentration of vortex lines attainable in our experiment. We found, however,...