Thermoviscous Effects in Steady and Oscillating Flow of Superfluid 4He: Experiments

The correct interpretation of superfluid flow experiments relies on the knowledge of thermal and viscous effects that can cause deviations from ideal behavior. The previous paper presented a theoretical study of dissipative and reactive(nondissipative) thermoviscous effects in both steady and oscillating flow of an isotropic superfluid through small apertures and channels. Here, a detailed comparison is made between the theory and a wide array of experimental data. First, the calculated resistance to steady superflow is compared with measurements taken in a constant pressure-head flow cell. Second, the resonant frequency and Q of three different helmholtz oscillators are compared with predictions based on the calculated frequency response. The resonant frequency and Q are extracted numerically from the frequency response, and analytical results are given in experimentally important limits. Finally, the measured and calculated frequency response are compared at a temperature where the Helmholtz oscillator differs significantly from a simple harmonic oscillator. This difference is used to explain how the thermal properties of the oscillator affect its response. The quantitative agreement between the theory and experiment provide an excellent check of the previously derived equations. Also, the limiting expressions shown in this paper provide simple analytical expressions for calculating the effects of the various physical phenomena in a particular experimental situation.     

Turbulent Flow Around an Oscillating Body in Superfluid Helium: Dissipation Characteristics of the Nonlinear Regime

By examining the resonance curves of an oscillator submerged in superfluid liquid helium, it is found that their shape is affected by two distinct dissipation regimes when the amplitude is large enough to generate turbulence in the liquid. In a resonance curve, the central part close to resonance, may be in a turbulent regime, but the response is of much lower amplitude away from the resonance frequency, so that the oscillation can still be in the linear regime for frequencies not exactly at resonance. This introduces an ambiguity in estimating the inverse quality factor Q ^?1 of the oscillator. By analyzing experimental data we consider a way of matching the two ways of estimating Q ^?1 and use the information to evaluate the frictional force as a function of velocity in a silicon paddle oscillator generating turbulence in the superfluid.     

Novel Oscillating Aerogel Experiments in Superfluid 3He at Ultralow Temperatures

We present novel experiments on a disk of 98% aerogel oscillating in superfluid ³ He at ultralow temperatures. The aerogel dik is attached to a goal post shaped vibrating wire resonator and immersed in liquid ³ He cooled by a Lancaster style nuclear cooling stage. At low pressures we see no evidence for superfluidity within the aerogel down to our base temperature of below <0.11T_c. At higher pressures we observe large temperature dependent frequency shifts, reminiscent of torsional oscillator experiments. We find the transition temperature at 5 bar to be around 600K. The response of the resonator is highly non linear when the helium in the aerogel is superfluid. The resonant frequency decreases strongly with increasing wire amplitude. This offers an exciting new technique for measuring the superfluid properties of ³ He in aerogel in the ultralow temperature regime.     

Thermoviscous Effects in Steady and Oscillating Flow of an Isotropic Superfluid: Theory

A calculation is presented of thermoviscous effects in both steady and oscillating flow of an isotropic superfluid through small apertures and channels. These calculations, which are based on the two-fluid model, are motivated by the work of Robinson and Atkins which included only the thermal effects of flow through a superleak. This paper extends these calculations to include the effects of normal fluid flow, compressibility, and thermal expansion. These effects are found to be both dissipative and reactive(nondissipative). The motivation for the extension is to provide a clear understanding of the reactive and dissipative forces at work in superfluid flow experiments. In the paper which immediately follows this one, predictions based on the results of this paper are compared with a wide array of experimental data. This work takes on importance due to the recent discovery of gyroscopic effects, and the possible development of sensitive gyroscopes in experimental cells whose geometry is similar to the one considered in this paper.     

Particle Image Velocimetry Studies of Counterflow Heat Transport in Superfluid Helium II

Heat is transported in helium II by a mechanism known as thermal counterflow where the liquid behaves as if it consists of two fluid components: the viscous normal fluid that carries the entropy and the inviscid superfluid that flows in opposition to conserve mass and momentum. Although the two fluid model has been successful at interpreting a number of unique transport processes in helium II, only recently has there been a significant effort to actually observe the associated fluid component motion. We have previously shown that Particle Image Velocimetry (PIV) can be used to visualize the motion of micron scale particles in helium II in response to thermal counterflow. These studies have led to some exceptional observations. The present paper summarizes our recent PIV experimental results on counterflow in helium II including the observed flow patterns around a cylinder and through a rectangular channel with backward facing step change in cross section, configurations which have been studied extensively in classical fluid mechanics. In addition to contributing to the fundamental understanding of helium II turbulence, as is discussed in the last section of the article, we show how this work also has a potential application in micron-scale particle classification and separation.     

Interaction of Helium Rydberg State Atoms with Superfluid Helium

The pair potentials between ground state helium and Rydberg He $^*(2s,2p,3s)$ atoms are calculated by the full configuration interaction electronic structure method for both the electronic singlet and the triplet manifolds. The obtained pair potentials are validated against existing experimental molecular and atomic data. Most states show remarkable energy barriers at long distances ( $R > 5$ Å), which can effectively stabilize He $^*$ against the formation of He $_2^*$ at low nuclear kinetic energies. Bosonic density functional theory calculations, based on the calculated pair potential data, indicate that the triplet ground state He $^*$ reside in spherical bubbles in superfluid helium with a barycenter radius of 6.1 Å at the liquid saturated vapor pressure. The pressure dependency of the relative He $^*$ $2s$ $^3S$ $\rightarrow $ $2p$ $^3P$ absorption line blue shift in the liquid was obtained through both the statistical line broadening theory as well as the dynamic adiabatic following method. The pronounced difference between the results from the static and dynamic models is attributed to the dynamic Jahn–Teller effect that takes places in the electronically excited state within the dephasing time of 150 fs. Transient non-thermalized liquid surroundings near He $^*$ may contribute to an artificial reduction in the absorption line blue shift by up to 30 cm $^{-1}$ .     

Intermittent Switching Between Potential Flow and Turbulence in Superfluid Helium at mK Temperatures

Superfluid flow around an oscillating microsphere is investigated at temperatures down to 25 mK. Stable laminar flow below a critical velocity and turbulence at large drives are found to be separated below 0.5 K by an intermediate range of driving forces where the flow is unstable, intermittently switching between laminar and turbulent phases. We have recorded time series of this switching phenomenon and have made a statistical analysis of the switching probability. The mean lifetime of the turbulent phases grows with increasing drive and becomes infinite at a critical value. Stability of the laminar phases above the critical velocity is limited by natural background radioactivity or cosmic rays.     

Hysteretic Behavior of Superfluid Helium in Anopore

Superfluid ⁴He exhibits hysteretic behavior due to capillary condensation in Anopore, a porous membrane containing mostly non-intersecting cylindrical pores. Because the pores are non-intersecting, we expect the system may behave similarly to a system of nearly non-interacting spins, where spinup is equivalent to a filled pore and a spin-down is equivalent to an empty pore. We show the global hysteresis loop as well as subloops, and compare the results to those predicted for a system of non-interacting spins.     

Modeling Kelvin Wave Cascades in Superfluid Helium

We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the later and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in k-space via using a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and closeness of numerics for the higher-order DAM to the analytical predictions for the lower-order DAM.     

An Interpretation of Dispersionless Modes in Neutron Diffraction Experiments on Helium Films

We analyze the dynamic structure function S(q, ) for neutron scattering off helium films in the direction perpendicular to the substrate. Dispersionlessmodes that have been found in neutron diffraction experiments on helium films adsorbed on graphite powder (H. J. Lauter, H. Godfrin, and H. Wiechert, Excitations in ⁴ He films, in Proceedings of the Second International Conference on Phonon Physics, World Scientific, 1985) are interpreted as standing waves or resonances of the helium liquid perpendicular to the substrate. Our interpretation is supported by microscopic calculations of the ⁴He dynamic structure function.     

More about Rotons in Superfluid Helium 4

In a recent paper¹ it was argued that rotons in superfluid helium 4 are the soft modes announcing a charge density wave that leads to the crystal: rotons are a normal state property. A small superfluid condensate acts to hybridize quasiparticles and soft density fluctuations - hence a level repulsion that lowers the energy: superfluidity is energetically favourable. A shallow roton implies a very small condensate density, as found in He4: what we need is a saturation mechanism. The clue is depletion due to quantum fluctuations. In (1) we assumed that such a depletion was drawn from the condensate itself: superfluidity then disappears in the liquid if the roton gap is too small. Here we explore an alternate possibility: quantum fluctuations are drawn from the normal fluid. We reach the opposite conclusion: superfluidity persists down to the spinodal limit where the roton gap vanishes, with an unusual power law dependence. We briefly mention the possible extension of that argument to a frozen charge density wave: in a toy 1d model it might shed light on the features that favour supersolids.     

Capture of Superfluid Helium by Porous Structures

We have studied superfluid helium capture in a sample of silica aerogel of 98.2% porosity in the temperature range from 1.22 K up to 1.89 K. The high retention of He in the aerogel sample corresponds to a similar phenomenon in impurity-helium condensates, in which very high values of the ratio of helium atoms to impurity atoms (up to 60) have been seen. We have observed that removing the aerogel sample from superfluid helium in a cylindrical glass beaker caused a decrease of the helium level corresponding to the geometrical volume of the sample (≈1 cm³). This observation has allowed us to conclude that superfluid helium is completely captured by the porous sample. Superfluid helium filling aerogel and impurity-helium samples (porous structures) serves as a dispersive medium of gel-like samples which interacts strongly with impurity nanoclusters forming the dispersing system.      

New Results for the Realization of the Superfluid Transition Temperature of Helium

A two-chamber sealed cell has been developed to realize the superfluid transition temperature of helium. A series of temperature plateaus are obtained while a series of small heat flows are applied to the capillary connecting the two chambers. The plateau temperatures are extrapolated to determine the transition temperature at zero heat flow. This paper reports the new results for the realization of the transition temperature of helium using seven cells. More than 30 measurements have been made in two laboratories since 2002, as five cells sealed in 2000 and two cells sealed in 2009 are used. The standard deviation of the measurements is ~0.02 mK.     

Relaxation of Anisotropic Systems of Quasi-particles in Superfluid Helium

We investigate the relaxation of boundless and anisotropic quasiparticle systems, in liquid ⁴He, with given initial values of momentum and energy densities. The evolution is governed by the dispersion curve which determines the interactions between quasi-particles. The first stage of the relaxation is the rapid creation of a quasistationary low-energy phonon system. This system transforms to another quasistationary system which contains high-energy phonons as well as low energy-phonons. Finally the system evolves to a stationary system of phonons and rotons. The temperature T and the drift velocity u are found for the closed quasi-particle system during its relaxation. This allows us to study the quasi-particle energy and the angular distribution of momentum, and the thermodynamic functions of the quasi-particles system, at each of stage of its evolution.      

The Creation of Long-Lived Multielectron Bubbles in Superfluid Helium

Multielectron bubbles (MEBs) in liquid helium were first observed in the late 1970s, but their properties have never been explored experimentally due to their short lifetimes. MEBs in liquid helium are predicted to have dynamic instabilities for zero or positive pressures, and stability for negative pressures. We report the production of long-lived MEBs in a novel cell filled with helium at static negative pressures. MEBs were extracted from the vapor sheath of a heated filament loop embedded in the superfluid helium and were observed by high-speed photography as they rose in the helium under buoyant forces. In earlier studies we found that MEBs created in this way had large amplitude oscillations and were unstable to decay. By creating MEBs at temperatures just under the lambda point, these oscillations are rapidly damped and the MEBs relax toward a spherical shape and stability as they rise in the helium.     

Experimental Investigation of Exotic Negative Ions in Superfluid Helium

We have constructed a new apparatus designed to study the exotic negative ions in superfluid helium-4 previously observed. Our apparatus is similar to that used by Ihas and Sanders, and by Eden and McClintock. The ions are generated from an electrical discharge in the vapor above the surface of the liquid and the mobility is measured by the time-of-flight method. We have detected eleven exotic ions with distinct mobility, and have measured their mobility as a function of temperature. In addition to the peaks in the time-of-flight signal due to the different exotic ions, there is a smoothly varying and continuous background signal. The variation of the background with field and temperature appears to be inconsistent with any explanation invoking the decay of one exotic ion into another, and supports the idea it arises from negative ions with a continuous distribution of mobility. This is a striking result because it would indicate that these ions have a continuous size distribution.     

Vortex-Ring Specific Heat of Superfluid Helium in Porous Materials

The specific heat of superfluid ⁴ He in a porous material is calculated using a vortex-ring renormalization theory, both for completely filled pores and for thin films. The porous medium introduces a new length scale L into the problem which is of the order of the pore size of the material, and which becomes the starting vortex-ring size of the recursion relations (the T=0 correlation length). The specific heat displays a lambda-like critical peak, but the amplitude of the peak is suppressed by a very large factor (L/a _o ) ³ compared to the bulk, where a _o 2.5 Å is the starting ring size for the bulk liquid calculation. This is in agreement with scaling theories invoking two-scale-factor universality, and provides a simple picture of the superfluid transition in porous materials, where the vortex cores of the rings are the material itself.