Study of cavitation in superfluid helium-4 at low temperatures

We report studies of the negative pressure required to lead to the nucleation of bubbles in superfluid helium-4 in the temperature range down to 0.8 K. At the lowest temperatures studied, the tensile strength is found to be 3 bar. The results are compared with nucleation theory and the possible importance of nucleation on vortices is discussed.     

Critical behavior of liquid4He at negative pressures

We examine the equation of state of liquid⁴He at negative pressures close to the spinodal density _s where the hydrodynamic speed of sound vanishes. The non-analytic behavior of the equation of state and the speed of sound in the vicinity of the spinodal density are calculated in two and in three dimensions; we find for the speed of sound the non-analytic behavior mc _s ² ( — _s)^2/5 in three dimensions and mc _s ² [(-_s)/¦ln(-_s)¦]^1/2 in two dimensions.We then examine the low density regime numerically, using a semi-analytic microscopic theory. It is found that non-analytic exponents are visible only in a negligible density regime around the spinodal point. Estimates for the spinodal densities, and the range of critical fluctuations are provided.     

Elementary excitations and sound speed in liquid 4He at negative pressures

No Heading We present neutron scattering measurements of the phonon-roton excitations of superfluid ⁴He at negative pressures in the porous medium MCM-41. The phonon and maxon energies decrease systematically below bulk values as the density is decreased below the bulk value due to stretching of the liquid. The negative internal pressures are estimated by comparison of the observed maxon energies with extrapolation of positive pressure values and from the sound speed. The maximum negative pressure realized, about –5.5 bar, is consistent with surface tension arguments and the MCM-41 pore diameter of 47 Å. Slight broadening of the intrinsic lineshape is observed, suggesting shorter lifetimes of the excitations.PACS numbers: 61.12.Ex; 61.25.Bi; 62.60.+v; 68.03.Cd; 68.03.Kn; 67.40.Mj     

Noncompact groups and the excitation spectrum in superfluid helium-4

It has been shown that the underlying symmetry algebra in the superfluid ⁴He can be extended to the spectrum-generating noncompact groups. This method furnishes the excitation energy of this system, exact in the framework of the symmetry algebra.     

Liquid helium at negative pressures: Nucleation of bubbles and anomalous phonon dispersion

We calculate the rate at which bubbles nucleate in⁴He when the liquid is at negative pressure. Previous calculations have predicted that at low temperatures (T0.3 K) the nucleation rate remains low until a pressure of roughly –15 bar is reached. We show that this result is incorrect, and that at a critical pressure P_c (–9 bar) the liquid becomes macroscopically unstable. We have made a calculation of the nucleation rate allowing for this effect. It is shown that the effect of quantum nucleation is small and probably hard to observe experimentally. Finally, we demonstrate that one can understand the pressure dependence of the phonon dispersion relation by a simple model. This model uses a parameter which also enters into the nucleation calculation.     

Theory of quantum nucleation of bubbles in liquid helium

We calculate the rate at which bubbles form by quantum tunneling in liquid helium-3 and helium-4 at negative pressure. We find that quantum tunneling should be observable at temperatures below about 0.1 K in helium-3 and 0.2 K in helium-4, and at pressures close to the critical negative pressure at which the liquid becomes unstable against long wavelength density fluctuations.     

Creation of quantized vortices at the lambda transition in liquid helium-4

A fast ( 3 ms) adiabatic expansion of a volume of liquid ⁴ He through the lambda transition is being used to study the nature of the transition and to model the cosmological false vacuum to true vacuum phase transition of the early universe. Preliminary results are reported showing that, in accordance with theoretical predictions by W H Zurek (Nature 317, 505; 1985), there is copious production of quantized vortex lines, which represent the superfluid analogue of cosmic strings. The line density after the expansion appears to decay in two distinct stages, with a fast decay being followed by a much slower one, in agreement with earlier work on the decay of quantum turbulence created in thermal counterflow. Extrapolation of the initial fast decay suggests an initial line density, immediately following the expansion, of 10⁷ cm^–2 . Smaller, but still substantial, vortex densities are also found to occur when the system is expanded from below the lambda transition, and the physical implications are discussed.     

Boiling kinetics of superheated liquid helium-4

This paper studies the superheat of liquid helium⁴He by the method of measurement of mean lifetimes in a pure bubble chamber. The experimental setup and methods of measurements are described. This method allowed us to observe the temperature dependence of nucleation rate at a fixed pressure. Measurements were carried out in the pressure range from 0.50 to 1.20 atm. The temperatures of attainable superheat were compared with the Döring-Volmer homogeneous nucleation theory and with the experimental data obtained by the pulse method and the method of continuous isobaric heating by other investigators. Two peculiarities of boiling of superheated liquid helium have been revealed and interpreted. The influence of electron bubbles, the dependence of surface tension on the curvature of interface, and ionizing background radiation on nucleation kinetics are discussed.     

Acoustic attenuation in superfluid3He-B at low pressures

The attenuation of zero sound in superfluid³He-B has been measured up to 160 cm^–1, at pressures less than 4 bar and at frequencies 34.2, 44.2, and 54.0 MHz. The contribution of pair breaking to the attenuation has been measured for the first time. The gap (J=1 ^–) mode has been studied in magnetic fields up to 80 mT and the structure of its Zeeman components revealed. Coupling to the gap mode in the applied field allows a direct spectroscopic measurement of the energy gap. In zero magnetic field, the attenuation is well described by the theory of Wölfle, showing agreement with the magnitude of the attenuation and the frequency of the squashing mode resonance, for an appropriate choice of the parameterz=(c ₀–c₁)/c₁, wherec ₀, c₁ are the velocities of zero and first sound. This provides a determination of the Landau parameterF ₂ ^s and indicates that thef-wave interaction is negligible at these low pressures.     

Inhomogeneous nucleation of superfluid vorticity at a sharp edge

We report an experiment in which superfluid flow through a single 10-µm diameter orifice is examined at pressure heads as low as 0.03 dyne/cm². Accurate measurements of low pressure head are made possible by a recirculating flow cryostat, capable of generating a calibrated, continuous flow of superfluid helium. Current vs. potential data for temperatures between 1.46 and 2.14 K are analyzed according to the Iordanskii-Langer-Fisher thermal nucleation theory, modified to apply to a model in which vortex half-rings are inhomogeneously nucleated at the sharp-edged mouth of the orifice. We offer two possible interpretations of the results.Parts of this work were carried out with the support of National Science Foundation grants DMR-72-02971 and DMR-78-10778.     

Nucleation of negatively charged vortex rings in superfluid helium-4 near its solidification pressure

The rate at which negative ions nucleate vortex rings in He II has been measured at 25 bar for electric fields E up to 12 kV/cm and temperatures T down to 0.4 K. A strong temperature dependence of v observed for T 0.6K and E<5kV/cm is attributed to the influence of isotopic impurities. Although the temperature-independent behavior found for T 0.6K and 5<E< 12 kV/cm is consistent with a theoretical prediction by Bowley, the relatively very much larger values of measured near 1 K indicate a serious deficiency in the model on which the theory is based.Supported by the Science Research Council under grants GR/A/0388.3 and GR/A/4874.7.     

The nucleation of vortices in superfluid4He: Answers and questions

The velocity threshold for phase slips, v_c, has been measured in ultra-pure⁴He and ultra-dilute³He-⁴He mixtures, down to a temperature of 15 mK. These experiments have revealed a crossover from a temperature-dependent régime above 150 mK to a plateau of v _c below in ultra-pure⁴He. Concentrations of³He impurities as low as a few parts in 10^–9 greatly affect the plateau régime, causing v _c to decrease markedly at low temperature. These observations are interpreted in the framework of the nucleation, either thermally activated or by quantum tunnelling, of vortices in the approximate shape of half-rings. These vortices form on wall asperities at local velocities u_s estimated to be 22 m/s in these experiments. The half-ring model is shown to yield a critical velocity of the same magnitude but leaves many basic questions unanswered.     

Phase separation in solid mixtures of helium-3 and helium-4

Phase separation temperatures have been determined in bcc³He-⁴He mixtures as a function of³He concentration and melting pressure from measurements of changes in the X-ray lattice parameter and Bragg peak shape. A new rigid tail dilution refrigerator cryostat was used to study³He-⁴He crystals with³He concentrations of 0.10, 0.20, 0.30, 0.45, 0.60, and 0.70 and melting pressures between 3.0 and 4.3 MPa. The phase separation temperatures determined are in good agreement with regular solution theory and give little support for an asymmetry in the coexistence curve expected from a Nosanow-type model and reported from previous experiments using other signatures of phase separation. At a given concentration, differences in phase separation temperatures determined from slow cooling and warming data, respectively, are as much as 25 mdeg, but this is less than half the differences reported from previous experiments. A bcc-hcp transformation was seen in a crystal with 10%³He at aboutT=0.3 K for a melting pressure of3.7 MPa.     

A possible observation of quantum nucleation in superfluid He4 near crystallization

The overpressurization of superfluid He⁴ under crystallization is studied experimentally. The effect of a substrate and He³ impurities on the nucleation rate W is observed. The dependence of the metastable state lifetime versus the overpressurization and temperature is measured in the range 10^–7–1 s and 0.52–1.75 K. The results are compared with the theoretical predictions for the classic and quantum nucleation. The surface relief effect is considered. It is shown that relative to a flat surface, a cone-shaped pit is a site corresponding to a smaller nucleation energy. In this case a change of the nucleation rate versus the metastability degree and temperature in the classic region is analyzed. As a result, the most reliable qualitative manifestation of quantum nucleation is the independence of the metastable degree under the constant rate W upon temperature, which is observed below 1 K in the experiment.     

Experiments on Fermi liquid domains in normal and superfluid3He

We report on pulsed and CW NMR experiments in liquid³He at temperatures below 10 mK, when the Fermi liquid interaction gives rise to a nondissipative spin currents. Due to these currents, a coherently precessing spin state may be formed in NMR-experiments with Fermi liquids. The state consists of two domains. In one of the domains the magnetization is oriented along, and in the other opposite to the direction of the magnetic field. Hitherto such a state has only been observed in³He-⁴He solutions. We have found that the domains can also be formed in normal³He. Experimental results for normal³He are in a good agreement with theory and computer simulations. The conditions necessary for the formation of the state have been determined. We also have found that the two-domain state may be also created in the super fluid state (at least near T_c).     

Density of liquid 4-methylpentane-1 at high pressures and various temperatures

Using the hydrostatic weighing method the density of liquid 4-methylpentane-1 is determined over the temperature range 302.55–450.80°K and pressure range 0.098–68.6 MN/m².     

Dynamics of superfluid helium-3 in flow channels with restricted geometries

The dynamics of superfluid helium-3 in flow channels with transverse sizes smaller than the mean free path of quasiparticles with respect to collisions with each other is considered, taking into account the diffusive reflection of quasiparticles from the walls. For quasiclassical Green functions the boundary conditions obtained by Ovchinnikov for the similar problem in superconductors have been used. Equations are derived defining the behavior of the difference between chemical potentials of normal and superfluid components of helium-3. These equations describe a phenomenon similar to the branch imbalance (or charge imbalance) in superconductors, and determine the relaxation depth of the pressure gradient in superfluid helium-3. The time-dependent Ginzburg-Landau equations are also obtained for the order parameter in the case when the transverse size of the channel is close to the critical value when the superfluid transition temperature goes to zero. The approach makes it possible to study theoretically effects related to the overcritical flows of superfluid helium-3 through narrow channels under pressure.     

State equation of liquid helium-4 from 0.8 to 2.5 K

A state equation for liquid helium is constructed in the range from 0.8 K to about 2.5 K, based on density and temperature as independent parameters. The equation has been fitted to experimental PVT, specific heat,(P/T) _v, sound velocity, and lambda line properties from 14 different authors to an accuracy comparable with reasonable experimental errors in the measured quantities. Inclusion of logarithmic terms leads to agreement with experimental data as close as 100 µK from the lambda line. It is found that the logarithmic amplitude ratio is not constant as a function of distance along the lambda line. A new determination of lambda line density is also presented. The equation is available in computer form.     

Features of nucleation kinetics in vapor-gas mixtures at increased pressures of gas

The kinetics of nucleation in a vapor-gas mixture at increased pressures of the gas-ballast (at Knudsen numbers determined from the radius of a critical nucleus below unity) is theoretically investigated. Interpolation expressions for the nucleation rate at arbitrary Knudsen numbers are obtained.Academic Scientific Complex A. V. Luikov Institute of Heat and Mass Transfer of the Academy of Sciences Belarus, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 5, pp. 577–582, May, 1993.