Ions in the helium film

The existence of a small negative ion current flow in a saturated helium film has been inferred from the current collected at electrodes situated in the vapor above a surface of liquid helium in diode and triode cells. Currents to a disk collector in the vapor and a ring collector in the helium film on the walls were measured as a function of temperature between 0.9 and 4.2 K and of applied field up to 200 V cm^–1. A current of 10^–13 A attributed to an ion flow in the film was detected in a temperature range 1.2–1.6 K and at low fields <70 V cm^–1 under conditions where the current to the collector in the vapor was much smaller than the current to the collector in the film. A positive current which appeared to reach the collector in the vapor was attributed to a negative current of photoelectrons emitted from the collector into the vapor.     

Dissipation in the superfluid helium film

We have measured the rate of energy dissipation in superfluid helium film flow in an attempt to test a recent theory due to Harris-Lowe, which predicts that for superfluid stream velocitiesv _sthat just exceed the critical velocityv _c0, the rate of dissipation is given by an equation of the form Q=C(v_s–v_c0)^3/2. Our experiments at 1.33 K show that the exponent, predicted to be 3/2, is 1.491±0.021.The research for this paper was supported by the Defence Research Board of Canada, Grant number 9550-57.     

A rough hard-sphere model for the thermal conductivity of molten salts

A new model based on the rough hard-sphere theory is proposed for the correlation and prediction of the thermal conductivity of molten salts. The model is capable of predicting the thermal conductivity of all the members of a family of molten salts characterized by a common anion if the behavior of any single member of the family of salts is known. Only the molar volumes of the molten salt and the solid salt at the melting temperature are required in the calculations. In addition, the model is easily extended to mixtures with a simple mixing rule.     

Analysis of helium II film boiling

The heat flux removed in the boundary transition from a vapour film to helium II is studied. It was found that the properties of the heat flux can be essentially explained physically by non-equilibrium molecular-kinetic effects at the vaporization condensation interface. A method of calculating the value of the heat flux is proposed.     

Superfluid helium film in zero gravity

The behaviour of nearly-saturated superfluid helium films, several hundred Angstroms thick was investigated under zero gravity conditions in a small cryostat carried on a 0.3 m diameter, 3 m long sounding rocket, using a quartz microbalance technique^1,2. The flight provided 30 s of high acceleration, about 5 min. of zero gravity, and 90 s of mg acceleration. The temperature of the experiment ranged from 1.67 to 2.15 K. In contrast to ground test results, thick films uniformly distributed on all surfaces were observed in zero gravity.     

Distribution of flow rates in the helium II film

New rate measurements of the flow of the saturated helium film out of a Pyrex beaker, employing a capacitance depth gauge technique, have been obtained. The high resolution has allowed us to observe the occurrence of transitions as small as1 1/2% of the flow rate. Such transitions are much smaller than any previously observed or expected from earlier measurements, which resulted in a preferred flow-rate hypothesis. Even so, the results do establish that some form of a preferred flow-rate structure is a fundamental feature of helium-film transport.The research for this paper was supported by the Defence Research Board of Canada, Grant No. 9510–23.     

The theory of nondissipative flow in the helium film

The necessary conditions are examined for a film in contact with its own vapor to flow without dissipation. When the local gas is in equilibrium with the vapor of a bulk reservoir, the equilibrium thickness of the flowing film is the same as that of the film at rest. For nonsteady flow, the predicted thickness depends on a nonequilibrium condition that cannot be deduced from thermodynamic arguments. A plausible form is proposed for the needed condition. It is shown that the film may be thinner than the rest value for times large compared with apparent relaxation times of the system. The results reconcile a number of experiments which had previously appeared contradictory. In addition, the theory is consistent with measurements of the convection speed of third sound and shows why previous efforts to explain the attenuation of third sound have failed.Work supported in part by NSF Grant No. GH34682.     

The superfluid transition of a helium film according to the Landau-Ginzburg-Pitaevskii theory of helium II

The superfluid transition of a helium film is discussed in the framework of the phenomenological Landau-Ginzburg-Pitaevskii theory. In order to obtain agreement with experiments, it turns out to be essential to check the film solutions of the Ginzburg-Pitaevskii differential equation for stability.     

A dilute hard-sphere bose-gas model calculation of low-density atomic hydrogen gas properties

The isolated pair wave equation is solved for two isolated hydrogen atoms interacting via the ³ _u ⁺ potential, from which a scattering length a = 0.72 » is determined and used as an effective hard-core diameter in a dilute hard-sphere Bose-gas model calculation. In the low-density limit, these results for the ground state energy compare closely with earlier Monte Carlo data. Using established criteria for the values of density and temperature over which the hard-sphere model is valid, we have calculated the energy, first- and secondsound velocities, depletion factor, and superfluid transition temperature, and expressions are given for the specific heat and normal fluid fraction. The scattering length of atomic hydrogen interacting via the singlet potential is found to be 0.12 » and similar calculations for helium give a scattering length much too large to justify application of the hard-sphere model.Work supported by NASA Grant No. NGR 06-002-159.     

Dissipation by pinned vortex lines in the superfluid helium film

The status of theoretical and experimental work on dissipation in the helium film is reviewed, and it is concluded that there does not yet exist a satisfactory theoretical interpretation of dissipation in the film which can account for the complete range of observed phenomena below the superfluid transition temperature T. Although the most recent theory, which accounts for dissipation in terms of intrinsic fluctuations in the flow, has been successful in a temperature interval just below T, attempts to extend the theory to include all temperatures below T have not met with the same degree of success. A new model is proposed which accounts for dissipation in superfluid helium film transport in terms of the continuous generation of pinned vortex lines. In principle, this model is similar to one advanced by Vinen, involving the growth and decay of a tangled array of vortex lines. Qualitatively, it is shown that the present mechanism can account for many of the phenomena observed in helium film transport experiments at temperatures well below the transition. For example, sharp changes in the flow rate are associated with changes in the number of pinned vortex lines. In addition, the theory predicts that at superfluid stream velocitiesv _sthat just barely exceed the critical velocityv _c0for the appearance of dissipation, the rate of dissipation Q is given by Q=AN(v_s–v_c0)^3/2 whereN is the number of pinned vortex lines, andA is a constant determined by the vortex line parameters. The value of 3/2 for the exponent is a clear prediction of the theory, and it represents the first precise, numerical prediction by any theory of a physical quantity which is associated with dissipation in the helium film, and which can be measured experimentally.The research for this paper was supported by the Defence Research Board of Canada, Grant number 9550-57.     

An experiment on dissipation in helium film flow

Experiments are reported in a double-bucket system with a view to examining the application to helium film flow of recent predictions regarding the exponential relationship between the superflow speed and the chemical potential gradient driving force. The theory is found to be generally commensurate with our experimental results with a notable exception. One of the parameters, which is predicted to be constant, is experimentally found to have a definite temperature dependence which we give in detail. We report also our evidence with regard to the height dependence of film thickness in the dissipative regime. We find that this thickness appears to be determined by the mean distance to the two bath levels.     

Transfer of the helium film between 0.3 K and the λ point

A high-accuracy method for measuring helium-level changes was developed. Measurements made above 1 K were in agreement with the generally accepted behavior of the helium film. A very slight dependence of the transfer rateR on the level difference was observed atall level differences. Below 1 K the transfer shows an entirely new pattern;R increases and becomes strongly dependent on the level difference. The transfer also displays some metastability, two distinct rates being possible at the same temperature, level difference, and barrier height. Measurements of the inertial oscillations indicate that there is no increase in the film thickness at low temperatures.     

Review paper: The hydrodynamics of helium II film

After an introduction to the hydrodynamical properties of He II, a survey is given of the flow properties of superfluid helium in the film. Special attention is given to some unsolved problems, such as: has rotating He II (ω<ω _c1 ) a shrunken temperature-dependent parabolic meniscus and is a stationary moving He II film thinner than a static film? A review will be given of the present state of affairs both from an experimental and theoretical point of view.     

A more accurate model of wetting transitions with liquid helium

Up to now the analysis of the liquid helium prewetting line on alkali metal substrates have been made using the simple model proposed by Saam et al.¹ Some improvements on this model are considered within a mean field, sharp kink model. The temperature variations of the substrate-liquid interface energy and that of the liquid density are considered, as well as a more realistic effective potential for the film-substrate interaction. A comparison is made with the experimental data on rubidium and cesium.     

Ionic currents modulated by film flow in superfluid helium

The oscillations of two helium baths coupled by the saturated film have been studied with a new method employing positive ions. The sensitivity of such a method for the variation of liquid-level height is found to be of the order of 10^–6 cm. The film current was observed to be modulated with a frequency double that of the level oscillations. This interesting new feature is discussed in the framework of the present theory of liquid helium.     

Transition to film boiling of helium under stepped thermal loading

The results of an experimental investigation of the transition to film boiling of helium under stepped thermal loading, obtained in a wide range of pressures, are presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 4, pp. 551–554, April, 1985.     

Potential probe dissipation measurements in a flowing superfluid helium film

Dissipation along a thermally driven, flowing, superfluid helium film has been measured using an adaptation of the Keller-Hammel potential probes. These data are described by Langer-Fisher fluctuation theory, provided the velocity dependence is characteristic of vortex ring generation.Work performed under the auspices of the U.S. Atomic Energy Commission.