Transition to Turbulence for a Quartz Tuning Fork in Superfluid 4He

We have studied the resonance of a commercial quartz tuning fork immersed in superfluid ⁴He, at temperatures between 5 mK and 1 K, and at pressures between zero and 25 bar. The force-velocity curves for the tuning fork show a linear damping force at low velocities. On increasing velocity we see a transition corresponding to the appearance of extra drag due to quantized vortex lines in the superfluid. We loosely call this extra contribution “turbulent drag”. The turbulent drag force, obtained after subtracting a linear damping force, is independent of pressure and temperature below 1 K, and is easily fitted by an empirical formula. The transition from linear damping (laminar flow) occurs at a well-defined critical velocity that has the same value for the pressures and temperatures that we have measured. Later experiments using the same fork in a new cell revealed different behaviour, with the velocity stepping discontinuously at the transition, somewhat similar to previous observations on vibrating wire resonators and oscillating spheres. We compare and contrast the observed behaviour of the superfluid drag and inertial forces with that measured for vibrating wires.     

Transition to Turbulence and Critical Velocity in Superfluid Solution of 3He in 4He

By the method of oscillating tuning fork, we carried out researches of the transition to turbulence in superfluid solution of 5% ³He in ⁴He at temperatures of 100 mK–300 mK. The critical velocity υ _c of the turbulence appearance is determined through measuring the volt-ampere characteristics. It is established that in the mixture the temperature dependence of the critical velocity is non-monotonous and differs strongly from that in pure ⁴He. Unlike ⁴He, the step-like anomalies on resonance curves were observed which, presumably, is connected with instability of the vortex system under the conditions where the core of the vortex is filled by the atoms of ³He. It is shown that such anomalies appear at the temperatures below 0.9 K, at the same time at temperatures below ～0.5 K they appear even at υ<υ _c .     

Theory of Decay of Superfluid Turbulence in the Low-Temperature Limit

We review the theory of relaxational kinetics of superfluid turbulence—a tangle of quantized vortex lines—in the limit of very low temperatures when the motion of vortices is conservative. While certain important aspects of the decay kinetics depend on whether the tangle is non-structured, like the one corresponding to the Kibble-Zurek picture, or essentially polarized, like the one that emulates the Richardson-Kolmogorov regime of classical turbulence, there are common fundamental features. In both cases, there exists an asymptotic range in the wavenumber space where the energy flux is supported by the cascade of Kelvin waves (kelvons)—precessing distortions propagating along the vortex filaments. At large enough wavenumbers, the Kelvin-wave cascade is supported by three-kelvon elastic scattering. At zero temperature, the dissipative cutoff of the Kelvin-wave cascade is due to the emission of phonons, in which an elementary process converts two kelvons with almost opposite momenta into one bulk phonon. Along with the standard set of conservation laws, a crucial role in the theory of low-temperature vortex dynamics is played by the fact of integrability of the local induction approximation (LIA) controlled by the parameter Λ=ln?(λ/a ₀), with λ the characteristic kelvon wavelength and a ₀ the vortex core radius. While excluding a straightforward onset of the pure three-kelvon cascade, the integrability of LIA does not plug the cascade because of the natural availability of the kinetic channels associated with vortex line reconnections. We argue that the crossover from Richardson-Kolmogorov to the Kelvin-wave cascade is due to eventual dominance of local induction of a single line over the collective induction of polarized eddies, which causes the breakdown of classical-fluid regime and gives rise to a reconnection-driven inertial range.     

Computer Simulation of the High-Velocity Motion of Electron Bubbles in Superfluid Helium

We have performed computer simulations of the motion of electron bubbles through superfluid helium. The helium is modeled through the use of a modified version of the Gross-Pitaevskii equation. We find that by the time the bubble reaches the velocity at which vortex nucleation occurs the shape has changed significantly from spherical.     

Interactions of Phonons and Rotons with Interfaces in Superfluid Helium

We solve the problem of beams of phonons and rotons incident on, and interacting with, solid surfaces. Phonons and rotons are the quasiparticles of superfluid helium and have a unique dispersion curve. The dispersion curve controls the transmission, reflection and mode change of these quasiparticles at the interface with another medium. We develop a non-local hydrodynamic theory in a consistent and unified way. The structure of the solutions in the quantum fluid is discussed. The creation probabilities of all quasiparticles are derived when any one of them is incident on the interface. The dependencies on frequency and angle are analyzed and the backward reflection and refraction for R ^? rotons are discussed.     

Homogeneous Turbulence in Superfluid 4He in the Low-Temperature Limit: Experimental Progress

Selected advances in the research on the dynamics of tangles of quantized vortices in superfluid helium with little normal component during the last 50 years are briefly reviewed. The main emphasis is on the experimental techniques of generating and probing homogeneous one-component superfluid turbulence of various energy spectra in superfluid ⁴He in the low-temperature limit. The most recent experimental progress, modern theoretical concepts and future outlook are summarized.     

History Dependence of Turbulence Generated by a Vibrating Wire in Superfluid 4He at 1.5 K

We report on the onset of turbulence in normal and superfluid ⁴He using several 13.5 μm diameter vibrating wire resonators placed in a cell, filtered from the surrounding helium bath. We measured the force-velocity characteristics of the wires in normal and superfluid helium over a velocity range up to several meters per second. The transition from laminar to turbulent behavior can be clearly identified. Surprisingly we find that, depending on the cooling history, turbulence in the superfluid does not always develop fully.     

Developed Capillary Turbulence on the Surface of Normal and Superfluid 4He

The capillary turbulence on the surface of normal and superfluid liquid ⁴He has been studied experimentally. It is observed for the first time that the value of the high-frequency boundary ω _b of the inertial interval increases significantly when liquid helium transits from normal to superfluid state, and that in superfluid He-II the correlation function of the surface deviation from equilibrium state in frequency representation can be described well by a power dependence with the index m close to −4.3.      

Decay of Turbulence Generated by Spin-Down to Rest in Superfluid 4He

We report on the extension of the experiments (P.M. Walmsley et al., Phys. Rev. Lett. 99:265302, 2007) on the decay of quasiclassical turbulence generated by an impulsive spin-down from angular velocity Ω to rest of superfluid ⁴He in a cubic container at temperatures 0.15 K–1.6 K. The density of quantized vortex lines L is measured by scattering negative ions. Following the spin-down, the maximal density of vortices is observed after time t～10Ω^?1. By observing the propagation of ions along the axis of the initial rotation, the transient dynamics of the turbulence spreading from the perimeter of the container into its central region is investigated. Nearly homogeneous turbulence develops after time t～100Ω^?1 and decays as L ∝ t ^?3/2. The effective kinematic viscosity in T=0 limit is ν=0.003κ, where κ=10^?3 cm²?s^?1 is the circulation quantum.     

Instability of Small Deuterium Clusters in Superfluid Helium near the λ Point

We present the results of quasielastic small-angle neutron scattering study of deuterium clusters immersed in superfluid ⁴He. Diffraction intensities exhibit a very strong change in a character at temperatures above 1.95 K but below the λ point. They are compared with calculations based on the assumption that clusters with different sizes and structures as well as single molecules may contribute in a total diffraction pattern with their particular varied relative weights. We have found that small clusters with N<300 molecules intensively decrease in size and a big abundance of free deuterium molecules form inside superfluid ⁴He below the λ point that evidences in favor of instability of smallest deuterium clusters at 1.95<T<2.17 K while larger clusters undergo only minor growth.     

Observation of Single Compton-Electron Tracks in Superfluid Helium-4 and Trace Detection of Metastable Helium Molecules by Laser-Induced-Fluorescence Imaging

We use laser-induced fluorescence enhanced by a cycling transition to image metastable helium molecules in liquid helium-4. We demonstrate that the method achieves sufficient sensitivity to image the trail of helium molecules that forms along the track of a single high-energy electron created by Compton scattering of a 511 keV gamma ray in liquid helium. The experiments show that a liquid helium detector with optical readout can function as an electron-tracking Compton camera when combined with conventional gamma-ray detectors. The demonstrated sensitivity for imaging helium molecules could also find application in the spectroscopy and imaging of neutrons, detection of electronic and nuclear recoil events, and investigation of superfluid or normal-fluid flow in liquid helium using the molecules as passive tracer particles.     

Tuning the dispersion of multiwall carbon nanotubes in co-continuous polymer blends: a generic approach

Melt-mixed blends of polyamide 6 and acrylonitrile-butadiene-styrene (PA6/ABS) with multiwall carbon nanotubes (MWNTs) were prepared with the intention to develop conducting composites. A generic strategy, namely specific interactions combined with reactive coupling, was adopted to facilitate and to retain the 'network-like' structure of MWNTs during melt-mixing. This was facilitated by the sodium salt of 6-amino hexanoic acid (Na-AHA) and certain phosphonium based modifiers, where it was envisaged that these modifiers would establish specific interactions (either 'cation-π' or 'π-π' ) with the 'π-electron' clouds of MWNTs, as well as restricting them in the PA6 phase of the blends via reactive coupling. This route eventually led to a remarkable increase in the electrical conductivity and dielectric constant in the blends with MWNTs. Raman, FTIR and TEM investigations further supported these observations.     

Formation of a Mesa Shaped Phonon Pulse in Superfluid 4He

We present a theory for the formation of a mesa shaped phonon pulse in superfluid ⁴He. Starting from the hydrodynamic equations of superfluid helium, we obtain the system of equations which describe the evolution of strongly anisotropic phonon systems. Such systems can be created experimentally. The solution of the equations are simple waves, which correspond to second sound in the moving phonon pulse. Using these exact solutions, we describe the expansion of phonon pulses in superfluid helium at zero temperature. This theory gives an explanation for the mesa shape observed in the measured phonon angular distributions. Almost all dependencies of the mesa shape on the system parameters can be qualitatively understood.     

Dispersion-Induced Splitting of the Collective Mode Spectrum in Axial and Planar Phases of Superfluid 3He

The whole collective mode spectrum in axial and planar phases of superfluid ³He with dispersion corrections is calculated for the first time. In axial A-phase the degeneracy of clapping modes depends on the direction of the collective mode momentum k with respect to the vector l (mutual orbital moment of Cooper pairs), namely: the mode degeneracy remains the same as in case of zero momentum k for k‖l only. For any other directions there is a threefold splitting of these modes, which reaches maximum for k ⊥ l. In planar 2D-phase, which exists in the magnetic field (at H>H _C ) we find that for clapping modes the degeneracy depends on the direction of the collective mode momentum k with respect to the external magnetic field H, namely: the mode degeneracy remains the same as in case of zero momentum k for k‖H only. For any other directions different from this one (for example, for k ⊥ H) there is twofold splitting of these modes. The obtained results imply that new interesting features can be observed in ultrasound experiments in axial and planar phases: the change of the number of peaks in ultrasound absorption into clapping mode. One peak, observed for these modes by Ling et al. (J. Low Temp. Phys. 78:187, 1990), will split into two peaks in a planar phase and into three peaks in an axial phase under the change of ultrasound direction with respect to the external magnetic field H in a planar phase and with respect to the vector l in an axial phase. In planar phase, some Goldstone modes in the magnetic field become massive (quasi-Goldstone) and have a similar twofold splitting under the change of ultrasound direction with respect to the external magnetic field H. The obtained results as well will be useful under interpretation of the ultrasound experiments in axial and planar phases of superfluid ³He.     

Direct Optical Detection of a Pure Spin Current in Semiconductor

We predict that a pure spin current in a semiconductor may induce Faraday birefringence even without magnetization. The theory is based on a derived effective interaction between the spin current and a polarized light beam, where the helicity of a photon is mapped to spin 1/2. The effective coupling between the polarized light beam and electron spin current can be realized in direct-gap semiconductors such as GaAs with inherent spin–orbit coupling in valence bands, but it involves neither the Rashba nor the Dresselhaus effect of samples. We estimate the amplitude of the Faraday rotation due to a pure spin current, and we present its incident-beam-angle dependence. We show that this Faraday birefringence can be directly measured.     

Statistics of Intermittent Switching between Potential Flow and Turbulence around an Oscillating Sphere in Superfluid 4He below 0.5 K

The flow of superfluid helium at very low temperatures around an oscillating microsphere is known to be unstable slightly above the critical velocity. The flow pattern switches intermittently between potential flow and turbulence. From time series recorded at constant temperature and driving force the statistical properties of the switching phenomenon are discussed. Based on our recent understanding of the critical velocity v _c of oscillatory superflows, i.e., $v_{c}\sim \sqrt{\kappa\,\omega}$ , where κ is the circulation quantum and ω is the oscillation frequency, the analysis is being refined now. From the exponential distribution of the lifetimes of the turbulent phases quantitative information on the vortex density L can be inferred such as the distribution and the width of the fluctuations of L. The phases of potential flow show a Rayleigh distribution of the excess oscillation amplitude above the amplitude at turbulent flow. The rms value is found to scale as ω ^?3/2.     

Gastrointestinal Transit Time:— An in Vitro Analysis of the Various Parameters Controlling the Critical Flow Velocity of Particles in a Horizontal Tube

Abstract

The factors which affect the critical flow velocity (V_c) of particles of barium sulphate, bismuth subcarbonate, kaolin, sulphadiazine and latex particles has been determined in a horizontal tube. These factors were particle size, particle density, fluid viscosity and tube diameter. V_c was found to increase with increasing particle diameter, particle density and tube diameter but decreases as viscosity of the flowing fluid. The results obtained were found to fit the models of Wicks, Durand and Wasp for the flow conditions of settled beds.     

Two-Dimensional Regime in the Angular Dependence of the Upper Critical Field of Superconducting/Normal Metal Hybrids

The temperature and angular dependence of the upper critical magnetic field H _c2 in Nb/Pd superconducting multilayers were investigated with a particular attention given to the region where the system is in the two-dimensional (2D) regime. The influence of the proximity effect on the 2D region as obtained from the H _c2 angular behavior was explicitly analyzed.     

Transport of Electrons on Liquid Helium Across a Tunable Potential Barrier in a Point Contact-like Geometry

We present transport measurements of electrons bound to the surface of superfluid ⁴He in a microchannel of width 10 μm. A set of electrodes 2 μm beneath the helium surface, fabricated in a split-gate configuration using electron beam lithography, are used to control the current along the microchannel as in a point contact device. As the split-gate bias V _SG is swept negative the current decreases to zero. The value of V _SG at which the current is suppressed is dependent on the AC driving voltage applied to the electron system. We explain our results using a simple model in which a potential barrier created by the split-gate electrodes must be overcome in order to allow current to flow in the microchannel. The control of electron transport in such confined geometries may offer new possibilities for mesoscopic experiments with electrons on the surface of liquid helium.     

Mechanical Response of <Superscript>4</Superscript>He Films Adsorbed on Graphite with a Quartz Tuning Fork

We have carried out quartz-crystal microbalance (QCM) experiments of 32 kHz quartz tuning fork for ⁴He films adsorbed on Grafoil, and have measured the temperature dependence of the resonance frequency and Q value for various areal densities. It was found that the frequency does not decrease exactly in proportion to the areal density. This means that the film still undergoes decoupling partly, although it is strongly suppressed from that of 5 MHz QCM measurements. Above the three-atom thick film, the decoupling due to the superfluidity of the overlayer is observed. In addition, we found that the competition between the superfluidity and the slippage takes place for a large oscillation amplitude. From the comparison with 5 MHz QCM measurements, it is concluded that the acceleration of substrate plays an important role in the slippage.