Quasi-isothermal superfluid-film flow: Oscillations between two reservoirs

We have carried out a detailed study of the frequency and damping of the oscillations in levels of two reservoirs of HeII which are coupled only via the mobile superfluid film. Our experiments cover the temperature range 1.2 & T ( 2.13 K and utilize several geometries under quasi-isothermal conditions. Below 2 K our results for the damping are in quantitative agreement with predictions based on a theory first proposed by Robinson. This indicates that the damping mechanisms proposed by Allen and by Calvani, Greulich, and Maraviglia are of minor importance under our experimental conditions. It is argued that the Robinson theory can explain the previous general agreement with the Allen theory. Consider a reservoir containing He II which is coupled only by the superfluid film to a second reservoir also containing He Ii. As is well known, the application of a chemical-potential difference between the two reservoirs will result in mass transport via the film which will serve to reduce the applied chemical-potential difference. Various methods, for example, the imposition of a temperature difference or a level difference may be used to create a difference in chemical potential. At the end of the flow which acts to remove the relative potential difference, the level in each reservoir will oscillate about its new equilibrium value. The damping constant and frequency of these oecillations form the subject of the present study. These oscillations were first studied in detail by Atkins. ' He derived an expression for the oscillation frequency valid under isothermal conditions and carried out an experimental study of the oscillation frequency as a function of temperature. Since that early work by Atkins, a number of in