Switching Phenomena between Laminar and Turbulent Flows of Superfluid 4He Generated by a Vibrating Wire

We have investigated the turbulence transition of the superfluid ⁴He flow generated by a vibrating wire. For a 1.2-kHz vibrating wire, we observed intermittent switchings between laminar and turbulent flows. The switching rate decreases with increasing temperature above 100 mK, until no occurrence of the switchings at 350 mK. For a 2.4-kHz vibrating wire, we find that the switching rate is much lower than that of the 1.2-kHz vibrating wire even at low temperatures. This result indicates that a mechanism causing the switchings is influenced by the temperature and the oscillation frequency of the superfluid flow.     

Vibrating Wire Thermometry in Superfluid 3He

We report systematic measurements of the response of a Vibrating Wire Resonator (VWR) in normal and superfluid liquid ³He. Special attention has been paid to the hydrodynamic regime of the superfluid B-phase, where the response parameters of the VWR do not follow a simple law. We show that a simple interpolation between the region where first order slip-corrections can be applied and the ballistic regime is insufficient. Measuring an empirical effective viscosity, we propose a temperature calibration method which allows the use of VWRs as a secondary thermometer at intermediate and high pressures in the temperature range 0.2 T _c < T < 50 mK.     

Stability of Laminar and Turbulent Flow of Superfluid 4He at mK Temperatures Around an Oscillating Microsphere

The flow of superfluid helium around a vibrating microsphere is investigated at temperatures between 1 K and 25 mK. At small oscillation amplitudes pure potential flow is observed, the linear drag force on the sphere being determined only by ballistic quasiparticle scattering below 0.7 K with phonons contributing exclusively below 0.5 K. At larger oscillation amplitudes a strongly nonlinear drag force gives evidence of stable turbulent flow if at least 0.6 pW are transferred from the sphere to the turbulent superfluid. In an intermediate range of amplitudes (or driving forces) both flow patterns are unstable and intermittent switching between both is observed below 0.5 K. We have recorded time series of this switching phenomenon at constant drives and temperatures lasting up to 36 hours. We have made a statistical analysis of the times series by means of reliability theory. The lifetime of the turbulent phases grows with increasing drive and diverges at a critical value (or at least becomes unmeasurably long). Stability of the laminar phases in the intermediate regime depends on the excess velocity of the sphere above the critical velocity. Metastable laminar phases are observed above the critical velocity having a mean lifetime limited to 25 minutes by natural background radioactivity which occasionally produces local vorticity due to ionization of the liquid. Finally, it is suggested that the breakdown of potential flow belongs to the class of “system failure” experiments which is well known in reliability testing and whose statistical properties are described by extreme-value theory. PACS numbers: 67.40.Vs, 47.27.Cn.     

Vibrating Wire Measurements in Superfluid 3He at the Melting Curve Down to 0.53 mK

Measurements of the vibrating wire spectrum have been carried out in superfluid ³ He along the melting curve down to 0.53mK. We have observed that at temperatures below 0.3 T_c the width of the mechanical resonance of the wire decreases exponentially with 1/T, indicating the ballistic regime of collisions with quasiparticles. The value of the superfluid energy gap was found to be (1.99±0.05)T_c, in good agreement with the values obtained from heat capacity measurements. The vibrating wire was thereby calibrated for further experiments at temperatures below 0.5mK, where the sensitivity of the melting curve thermometry becomes rather poor.     

Kelvin-Wave Cascades in Turbulent Superfluid 4He at Very Low Temperatures

There has been much interest recently in the mechanism by which superfluid (quantum) turbulence can decay in liquid ⁴He at very low temperatures, where mutual friction has a negligible effect. As in classical turbulence, energy must probably flow from larger to smaller length scales, and it has been suggested that on the smallest scales the relevant motion is a Kelvin wave on a quantized vortex with wave number greater than the inverse vortex spacing. By considering the behaviour of a simple model it is shown by computer simulations how energy can flow to shorter length scales (higher wave numbers) in a system of Kelvin waves, and how this process can lead to a remarkably simple Kelvin-wave energy spectrum. A discussion is included of the relevance of this model to the decay of superfluid grid turbulence at a very low temperature.     

Vortex Generation in Superfluid 3He by a Vibrating Grid

Recently we have found that a vibrating wire resonator produces turbulence in superfluid ³He-B at low temperatures when driven above its pair-breaking critical velocity. The vorticity is produced along with a beam of excitations from pair breaking. Here, we discuss preliminary measurements of turbulence generated from an oscillating grid at low temperatures. The grid oscillator is made from a goal-post shaped vibrating wire resonator supporting a fine copper mesh. While the dissipation by a conventional wire resonator is dominated by pair-breaking at the velocities required for turbulence generation, the dissipation of the grid oscillator appears to be dominated by turbulence. This allows us to generate turbulence without the unwanted effects of a quasiparticle beam. Preliminary measurements suggest that the grid turbulence has a rather different behaviour from that generated by conventional wire resonators.     

Observation of Superfluid 4He Adsorbed in One-Dimensional Mesopores

To study one-dimensional (1D) quantum liquid of ⁴ He, we measured the heat capacity and performed a torsional oscillator experiment for ⁴ He adsorbed on a new mesoporous substrate whose adsorption area consists of walls of straight one-dimensional 18Å diameter tunnels. The presence of adsorbed quantum liquid was examined by the isotope effect on the heat capacity for ³ He and ⁴ He adatoms. Above a coverage n _o , the heat capacity isotherms are completely different because of the Fermi and the Bose fluids, respectively. In the torsional oscillator experiment we observed superfluid ⁴ He above n _o . The fraction of the superfluid decoupled from the motion of the substrate is 0.13, which is the same order as 0.18 for packed Pt fine powder and 0.24 for 80 Å-porous glasses. The result indicates that the superfluid state exists in the one-dimensional ⁴ He adatoms formed in the 18 Å diameter pores.     

Transition to Quantum Turbulence Generated by Thin Vibrating Wires in Superfluid 4He

We report the turbulent transition in superfluid ⁴He generated by a vibrating wire as a function of its thickness. The response of a vibrating wire with a 3 μm diameter in superfluid ⁴He at 1.2 K reveals a hysteresis at the turbulent transition between an up sweep and a down sweep of driving force, while no hysteresis appears for wires with a thickness larger than 4.7 μm diameter. These results indicate that the 3 μm wire is efficient for reducing the number of vortex lines attached to it. A cover box and slow cooling also prevent vortex lines from attaching to a wire, resulting in a vortex-free vibrating wire. The effective mass of the vortex-free vibrating wire is almost constant in a wide range of velocities up to 400 mm/s; however, the wire density estimated from the resonance frequency is a half of the expected value of wire material, suggesting that a wire mass becomes lighter or a wire diameter becomes larger in the superfluid effectively.     

Slip in Vibrating Wire Experiments on 3He-4He Mixtures

No Heading We present vibrating wire viscometer experiments in concentrated and dilute ³He-⁴He mixtures showing that the slip length may become orders of magnitude larger than the mean free path due to increased specular scattering of the ³He quasiparticles with the superfluid ⁴He film on the wire. The experimental results are in good agreement with a recent theory for slip which accounts for the cylindrical geometry of the wire and for velocity slip in directions normal as well as tangential to the surface of the wire.PACS numbers: 67.60.Fp, 51.20.+d     

Damping of a Vibrating Wire in Spin Polarized Liquid 3He-4He Mixtures

In this paper we report measurements of the damping of a vibrating wire in spin polarized liquid helium mixtures. The dilute helium solutions have been cooled by nuclear demagnetisation in high magnetic fields such that the spin polarization for a 0.04% mixture is as high 75%. A PtW alloy vibrating wire has been used to probe the viscosity of the liquid. The increase in viscosity on changing the magnetic field from 3 tesla to 11.5 tesla is a factor 3.5 at the lowest temperatures. The results are compared to theory allowing for both s-wave and p-wave scattering.     

The Onset of Vortex Production by a Vibrating Wire in Superfluid 3He-B

We present measurements of the force-velocity response of a vibrating wire resonator in superfluid ³He-B at very low temperatures. At low velocities the response is dominated by intrinsic (vacuum) damping whilst at high velocities it is dominated by pair-breaking. At intermediate velocities there is a series of small plateaus where the velocity often shows small oscillations. We believe that the behaviour results from the stretching of vortices pinned to the wire. The vortices grow and self-reconnect, emitting a vortex ring. The behaviour is very sensitive to the presence of surrounding vortices generated by a neighbouring vibrating wire.     

Slip Effects in Vibrating Wire Experiments on 3He-4He Mixtures

We report enormous slip effects in viscosity measurements on the concentrated and the dilute phase of saturated ³He-⁴He mixtures, using vibrating wires in the temperature range 10-250 mK. The concentrated phase data show that the liquid almost does not stick to the wires. There is striking agreement between the data and the solution of the Navier–Stokes equation with the non-sticking boundary condition of zero transverse momentum between the liquid and the surface of the wire. If the slip is taken into account, we obtain good agreement between the viscosity of concentrated and pure ³He. The dilute phase shows slip of a different nature. The analysis based on Eq. (112) of Højgaard Jensen et al. ¹ resugts in the kinematic viscosity and a parameter β relating the slip length, ζ, to the radius of the wire, a. Instead of the expression for β given in the literature, we propose β=ζ/(2ζ+a), because (1) in the limit of ζ→∞ our expression agrees with the non-sticking boundary condition and (2) only our expression fits under the constraint that ζ∝l _η, where l _η is the viscous mean free path. As long as ζ>2a, our expression fits the data very well with ζ/l _η in the range 50–150, depending on the wire.     

Anomalous Trajectories of H2 Solid Particles Observed Near a Sphere Oscillating in Superfluid Turbulent 4He

Using a relatively low cost apparatus, consisting of a glass dewar and a digital camera capable of taking images at 240 frames per second we have observed trajectories of frozen H₂ particles which follow the flow of liquid helium below 2 K, around a sphere oscillating at 38 Hz. In some of the images the motion is compatible with laminar flow, while at high amplitudes, where we can reach Reynolds numbers of a few thousand in the normal component, the flow is clearly turbulent. In some of the videos taken we find particles being suddenly accelerated to several times the velocity of the oscillating sphere.     

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.     

Observation of Remanent Vortices Attached to Rough Boundaries in Superfluid 4He

We report the study on remanent vortices attached to rough boundaries in superfluid ⁴He after the turbulent transition. We used 2.6 µm vibrating wires with smooth surfaces and rough surfaces, a cover box and slow cooling method, in order to investigate the effect of surface roughness on the condition and the number of vortices attached to a wire. The responses of the wire with smooth surfaces show large hysteresis at the turbulent transition. This result indicates that remanent vortices attached between the wire and surrounding boundaries cause turbulence. At first sweep of driving force of the wire with rough surfaces, we also observed hysteresis as large as the case of the smooth wire: at the other sweeps, however, small hysteresis was observed. These results indicate that once turbulence is generated at a wire velocity during first sweep, vortex lines newly attach between rough surfaces of the wire, which easily cause turbulence at a low wire velocity. Therefore, we conclude that a smooth wire can reduce the number of vortices attached to a wire.     

Polarization Effects in Superfluid 4He

A theory of thermoelectric phenomena in superfluid ⁴He is developed. It is found an estimation of the dipole moment of helium atom arising due to electron shell deformation caused by pushing forces from the side of its surrounding atoms. The corresponding electric signal generated in a liquid consisting of electrically neutral atoms by the ordinary sound waves is found extremely small. The second sound waves in superfluid ⁴He generate the polarization of liquid induced by the relative accelerated motion of the superfluid and the normal component. The derived ratio of the amplitudes of temperature and electric polarization potential was proved to be practically temperature independent. Its magnitude is in reasonable correspondence with the experimental observations. The polarity of electric signal is determined by the sign of temperature gradient in accordance with the measurements. The problem of the roton excitations dipole moment is also discussed.     

Acoustic Turbulence in Superfluid 4He

Recent work on nonlinear second sound wave propagation and acoustic turbulence in superfluid ⁴He is reviewed. Observations of direct and inverse turbulent energy cascades are described. The direct cascade arises due to the huge nonlinear dependence of the second sound wave velocity on its amplitude. The flux of energy injected at the driving frequency is transformed via successively higher harmonics until it is eventually attenuated by viscous dissipation at the short wavelength edge of the spectrum. The onset of the inverse cascade occurs above a critical driving energy density, and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomena is outlined and shown to be in good agreement with the experiments.     

The Effect of Perimeter-Limited Superfluid 4He Fluid Flow on Avalanches in Nuclepore

Superfluid ⁴ He exhibits hysteretic behavior in the percolated nano-porous material Nuclepore during filling and draining of the pores due to capillary condensation, and one observes avalanches in the pore draining within a narrow range of chemical potential. We have previously demonstrated that the avalanches involve pores distributed across the entire sample, and that the avalanches are enabled by the superfluid film. We compare avalanches for Nuclepore that has a highly limited perimeter for ⁴ He film flow draining to avalanches for Nuclepore that has relatively unimpeded flow off the substrate. Time resolved measurements of the avalanche events show that the time duration of the individual avalanches is influenced by the time it takes for the fluid to leave the substrate.     

Vibrating Wire Measurements in 3He-4He Mixtures in the Ballistic Quasiparticle Regime

We present our first high resolution vibrating wire resonator data on dilute ³ He- ⁴ He mixtures at ultra low temperatures. Measurements were performed at saturated vapor pressure with ³ He concentrations below the phase separation limit. The behavior of the damping at very low temperatures does not follow the modified slip correction analysis previously applied to extend the validity of the hydrodynamic treatment.     

Vortex-Loops and Solid Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴He and ³He. Unique to the superfluid phases the solid nucleation involves an extremely fast solidification front. We depart from the usual quasi-static treatment of solid nucleation by proposing that the nucleation of a solid seed is helped by the simultaneous nucleation of vortex-loops in the superfluid around it. It is the composite entity which is nucleated out of the over-pressurized liquid. This occurs when the local release of pressure creates a velocity field in the superfluid which in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with many experiments on heterogeneous nucleation, where the energy barrier is found to differ with the classical theory of homogeneous nucleation by 8 orders of magnitude. We propose several experiments that could show the involvement of vortices with solid nucleation.