The Response of a Mechanical Oscillator at the Superfluid 3He AB Interface

From our long experience of using profiled magnetic fields to stabilize and manipulate the AB phase boundary in superfluid ³He in the zero-temperature limit, we have constructed a cell where we can place the AB interface in the vicinity of a pair of crossed vibrating wire resonators (VWRs). The VWRs provide sensitive mechanical probes of the A and B phase energy gaps and textures. Here we present preliminary resugts where we observe the dynamic response of the VWR at the AB interface.     

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.     

Viscosity of the3He-4He dilute phase in the mixing chamber of a dilution refrigerator

The viscosity of the dilute phase of a³He-⁴He solution has been measured using a vibrating wire viscometer situated in the mixing chamber of a dilution refrigerator. The viscosity was extracted from the damping of the resonator for temperatures between 3.7 mK and 100 mK. In the low-temperature Fermi liquid regime T²=48×10^–9 N sec m^–2 K². For temperatures less than 100 mK, the viscometer is a useful secondary thermometer that is not strongly dependent on the applied magnetic field.     

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.     

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.     

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     

Refrigeration and thermometry of liquid3He-4He mixtures in the ballistic regime

The ballistic regime of liquid³He-⁴He mixtures is characterized by a large mean free path of the thermal excitations compared to the characteristic dimension of the experiment. We report on investigations of the transport properties of mixtures as well as superfluid³He in the ballistic regime by means of the vibrating wire technique. In order to avoid possible sources of heat leaks into the liquid, the experimental setup was built as far as possible of pure materials only. The contribution of a Ag sinter to the heat leak as well as its influence on the attainable minimum temperature of the mixtures were investigated by performing measurements in two similar setups which differed in the size of the heat exchanger by about one order of magnitude. Moreover, we have used the vibrating wire partly immersed in the superfluid³He-B phase of a phase-separated mixture as a very sensitive, continuously monitoring thermometer for liquid mixtures in their ballistic regime. The achieved minimum temperature of a 6.8%-mixture atp = 0.35 bar and of a 9.5%-mixture atp = 9.8 bar was 130 K. This value can be considered as an upper limit for the temperature of the mixtures as the damping of the vibrating wire thermometer saturates at this temperature due to its intrinsic properties.     

Phase equilibrium in a polarized saturated3He—4He mixture

We present experimental results on the phase equilibrium of a saturated³He−⁴He mixture, which has been cooled to a temperature of 10–15 mK and polarized in a⁴He circulating dilution refrigerator to a stationary polarization of 15%, 7 times higher than the equilibrium polarization in the external field of 7 T. The pressure dependence of the polarization enhancement in the refrigerator shows that the molar susceptibilities of the concentrated and dilute phase of a saturared³He-⁴He mixture are equal atp=2.60±0.04 bar. This result affects the Fermi liquid parameters of the dilute phase. The osmotic pressure in the dilute phase has been measured as a function of the polarization of the coexisting concentrated phase up to 15%. We find that the osmotic pressure at low polarization (<7%) agrees well with thermodynamics using the new Fermi liquid parameters of the dilute phase.     

NMR,optical, and plastic flow experiments in bcc3He —4 He mixture crystals — in pursuit of a vacancy fluid

We describe experiments on the properties of bcc³He —⁴ He solid mixtures on the melting curve between 0.5K and 1.9K. In this paper we focus on effects related to the presence of thermal vacancies. First, we used NMR to image the³He distribution within the solid in equilibrium with the superfluid, as well as its T₁ and t₂. The most surprising result was that above about 1K, vacancy related motion of³He atoms in the solid becomes faster than in the liquid. To check the macroscopic aspects of this motion, we used the vibrating wire technique to look at plastic flow of the bcc solid phase, by moving the wire through the crystal. The temperature dependence of the plastic flow velocity indicates that the vacancy population in the bcc solid behaves like a viscous fluid. The extent to which the vacancy population causes the solid to have liquid like properties is best demonstrated through optical observations of the distillation of³He atoms out of the crystal, which takes place via formation of fluid bubbles within the solid, which then percolate into the liquid, creating a vivid impression of boiling.     

The mechanical behavior of a vibrating wire in superfluid3He-B in the ballistic limit

An experimental procedure is described for the characterization of the response of very small vibrating wires to liquid³He at temperatures down to 120 µK. The relative scales of the mean free path in the liquid and the radius of the wire play a significant role in the interpretation of the results. It is shown that the same ideas concerning the transition from hydrodynamic to ballistic behavior as the temperature is reduced can be applied both to saturated³He-⁴He solutions and to superfluid³He-B.     

Phonon transmission across the interface between solid helium and a3He-4He dilute solution

We report phonon transmission studies of the interface between solid helium and dilute solutions of³He in liquid⁴He. We have measured the transmission of phonons from the solid into the liquid and the rate of exchange of energy between the phonons in the solid and the³He quasiparticles in the liquid. We compare the results with two theoretical calculations; in the first it is assumed that the interface is atomically rough and mobile; in the second the interface is assumed to be facetted, and therefore immobile. The experimental results indicate strongly that the interface in our experiment is rough. Agreement between theory and experiment is good.     

Vibrating wire measurements in liquid3He II. The superfluid B phase

Measurements with a vibrating wire viscometer in superfluid³He-B at temperatures down to 0.6 mK are described. The need to consider compressibility of the superfluid component in any analysis of vibrating wire measurements is clearly demonstrated and a theoretical calculation of the force acting on a vibrating wire in a finite compressible superfluid is given. The experimental data are consistent with this calculation if theoretical values of the second viscosity ξ₃ are used in the analysis. The failure of the hydrodynamic theory when the quasiparticle mean free path1 is comparable to the wire radius a was observed, and an expression has been deduced for the force acting on the wire when1 is finite. Experimental and theoretical evidence is presented to show that this expression is valid for arbitrary1/a. Values of the viscosity obtained using this expression agree with those obtained in other experimental work and confirm the large discrepancy with theoretical calculations at low reduced temperatures.     

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.     

Thermometry in Normal Liquid 3He Using a Quartz Tuning Fork Viscometer

We have developed the use of quartz tuning forks for thermometry in normal liquid ³He. We have used a standard 32 kHz tuning fork to measure the viscosity of liquid ³He over a wide temperature range, 6 mK<T<1.8 K, at SVP. For thermometry above 40 mK we used a calibrated ruthenium oxide resistor. At lower temperatures we used vibrating wire thermometry. Our data compare well with previous viscosity measurements, and we give a simple empirical formula which fits the viscosity data over the full temperature range. We discuss how tuning forks can be used as convenient thermometers in this range of temperatures with just a single parameter needed for calibration.     

Non-linear Mechanical Response of the A-like Phase of Superfluid 3He in Aerogel

We present measurements of the response of the A-like phase of superfluid ³He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid ³He at low temperatures and relatively high magnetic fields such that the aerogel confined superfluid is in the A-like phase, while the surrounding fluid is in the bulk B-phase. We observe a variety of interesting non-linear and hysteretic effects when the resonator is driven to higher velocities. We present some of our preliminary findings and speculate on their implications.     

A microscopic calculation of the force on a wire moving through superfluid3He-B in the ballistic regime

When a macroscopic object moves through superfluid³He, it experiences a force arising from the effect of quasiparticle scattering. We develop a three-dimensional microscopic model to calculate the force on a smooth cylinder moving at constant velocityv as a model of a vibrating wire. At large (subcritical) wire velocity, the force tends to an asymptotic value as 1/v ², rather than exponentially as in a one-dimensional calculation. At lowv the force is linear inv. We briefly discuss the agreement of our calculations with experimental measurements on a vibrating wire below 0.2T _c, where the quasiparticle trajectories are ballistic.     

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.     

Measurements on a Dynamic A-B Phase Boundary in Superfluid 3He at Very Low Temperatures

We present preliminary measurements of the dynamics of a moving A-B phase interface in superfluid ³ He at temperatures below 0.2T _c We initially stabilise the interface at low temperatures with a shaped magnetic field. We can then move the interface in a controlled manner by applying small additional time-dependent fields. The interface is created inside a quasiparticle radiator consisting of a cylindrical chamber in weak thermal contact with the refrigerant. Vibrating wire resonators inside the radiator allow us to monitor the temperature of the superfluid and to infer the heat generated by the interface motion. When we oscillate the interface at low frequencies, we measure spectacular oscillatory swings of the liquid temperature arising from the enormous change in the low lying density of states as the volume of the A-phase superfluid is alternately compressed and expanded. We have also observed hysteresis in the transition as a function of magnetic field. In particular, we observe a small history-dependent super-magnetisation of the B-phase prior to A-phase nucleation in the experimental chamber. When the system is in the metastable super-magnetised state we are able to observe a higher nucleation probability of the A-phase when the cryostat is exposed to neutrons.     

Vibrating wire measurements in liquid3He. I. The normal state

A vibrating wire viscometer has been constructed using superconducting wire of diameter 58 µm in the form of a semicircular loop of radius 1.4 cm fixed at both ends and oscillating in a direction perpendicular to the plane of the loop. The use of the viscometer to measure the viscosity of normal phase³He is described and the corrections that have been applied to the data to allow for the finiteQ of the resonance, a quasiparticle mean free path comparable to the wire diameter, and a viscous penetration depth comparable to the size of the channel containing the wire are discussed. The measured viscosities show small departures from the ηT ²=const law of Fermi liquid theory similar to those observed in some but not all previous measurements. The values of the viscosity at the superfluid transition temperature agree with those obtained in other measurements.     

Visual Observation of a Sound-Induced Bubble in Liquid 3He–4He Mixtures

We report visual observation of a sound-induced bubble in superfluid ³He–⁴He liquid mixtures using a high-speed camera at a rate of 1 msec/frame. The experiments were performed in the ³He dilute phase of phase-separated mixtures at 300 mK. The resonant frequency of the piezoelectric transducer was 9.36 MHz and the diameter of the active electrode was about 4 mm. When an acoustic wave pulse of sufficient magnitude was applied to the dilute phase from the transducer under saturated vapor pressure, a single bubble was nucleated on the active area. The bubble expanded almost spherically on the transducer, as it reached maximum size, it started shrinking, detached from the transducer, and collapsed. We also investigated the motion of the bubble in mixtures with a ³He concentration of 25% at 750 mK. In this case, the bubble grew elliptically on the transducer and detached from it without much change in shape.