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.     

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.     

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.     

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.     

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 hard-sphere model of the helium film

A quantum hard-sphere system bounded by two parallel rigid walls is studied at absolute zero as a model of a helium film. A variational wave function is constructed which is of the Bijl-Dingle-Jastrow type modified by a one-body term which vanishes at the walls; Monte Carlo quadrature is used. We focus our attention particularly on the behavior of the single-particle density function and the condensed-state wave function, i.e., the order parameter. Both show significantly different behavior from that predicted by the Hartree theory. The healing length is calculated, we believe for the first time, and is rather small. The average condensate as a function of distance between two walls is also investigated. The calculation serves as a special probe for approximations to the ground-state wave function in a uniform system.This work has been supported by the U.S. Atomic Energy Commission under contract # AT(11-1)-3077 and Grant No. GH-36457 with National Science Foundation.     

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.     

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.     

Porous plug and superfluid helium film flow suppressor for the soft X-ray spectrometer onboard Astro-H

Suppression of superfluid helium flow is critical for the Soft X-ray Spectrometer (SXS) onboard Astro-H, to achieve a life time of the liquid helium over 5 years. The superfluid film flow must be sufficiently small, compared to a nominal helium gas flow rate of the SXS . For this purpose, four devices composed of a porous plug, an orifice, a heat exchanger, and knife edge devices will be employed based on the experience of the X-ray microcalorimeter (XRS for X-Ray Spectrometer) onboard Suzaku. The porous plug is a phase separator of the liquid and gas helium. A potential film flow leaking from the porous plug is suppressed by the orifice. Almost all the remaining film flow evaporates at the heat exchanger. The knife edge devices stop the remaining film flow by using atomically sharp edges. In this paper, we describe the principle and design of these four devices.     

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.     

The drag-out problem in film coating theory

Summary An important step towards the understanding of many industrial coating processes is a solution of the dragout problem, which is to determine the thickness of the film of liquid which clings to a plate when it is drawn steadily out of a bath of the liquid. An approximate solution, valid for small capillary numbers, was given by Landau and Levich, and considerable effort has been exerted to extend or refine this work. In this paper we show that the Landau-Levich result is an asymptotic solution valid as the capillary number tends to zero, a fact not properly appreciated hitherto, and show how correction terms may be obtained by the method of matched expansions. We also show how the results may be applied to the coating of a horizontal roller.     

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.     

The appearance of vortices in the flow of helium II between rotating cylinders

We argue that the appearance of quantized vortices in laminar Taylor-Couette flow of helium II is a problem for which free energy minimization should give valid results even in the presence of dissipation. We (approximately) reduce the problem to an equivalent problem in solid-body rotation, for which the solution for the low-lying states has been obtained by Fetter. We then use approximations to the solution for solid-body rotation to predict the appearance of vortices for the general Taylor-Couette problem. These results compare moderately well with the existing data, which now seem relatively incomplete.     

Towards a quantum field theory of defects and stresses—quantum vortex dynamics in a film of superfluid helium

With the goal of developing a quantum field theory of defects under stress we first solve this problem for the simpler case of vortices in a thin film of superfluid ⁴He. The theory we obtain, to be called quantum vortex dynamics (QVD), turns out to be what is known in quantum field theory as scalar quantum electrodynamics in 2 + 1 dimensions (also called scalar Abelian Higgs model).