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Title: Curvature, slip, and viscosity in {sup 3}He-{sup 4}He mixtures

Abstract

We report vibrating wire viscometer experiments in the concentrated and dilute phase of saturated {sup 3}He-{sup 4}He mixtures showing that the slip length may become orders of magnitude larger than the mean free path due to specular scattering of the {sup 3}He quasiparticles with a {sup 4}He coating adsorbed at the surface of the wire. Since the liquid does not almost stick to the surface, the boundary conditions for fluid flow are unusual and not accounted for by the current theory for slip [H. Hoejgaard Jensen et al., J. Low Temp. Phys. 41, 473 (1980)]. The experimental results are in excellent agreement with a recent theory for slip [R. Bowley and J. Owers-Bradley, J. Low Temp. Phys. 136, 15 (2004)] which accounts for the effect of the cylindrical geometry and for velocity slip in directions normal as well as tangential to the surface of the wire. We find that our viscosity measurements in the dilute phase resulting from the data analysis based on the recent slip theory are in better agreement with the Fermi liquid theory than previous experimental results.

Authors:
;  [1]
  1. Centre de Recherche sur les Tres Basses Temperatures, CNRS, Boite Postale 166, 38402 Grenoble Cedex 9 (France)
Publication Date:
OSTI Identifier:
20788047
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 73; Journal Issue: 13; Other Information: DOI: 10.1103/PhysRevB.73.134517; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ADSORPTION; BOUNDARY CONDITIONS; DATA ANALYSIS; FERMI GAS; GEOMETRY; HELIUM 3; HELIUM 4; LIQUIDS; MEAN FREE PATH; MIXTURES; QUASI PARTICLES; SCATTERING; SLIP; SLIP FLOW; SURFACES; VISCOSITY

Citation Formats

Perisanu, Sorin, and Vermeulen, Gerard. Curvature, slip, and viscosity in {sup 3}He-{sup 4}He mixtures. United States: N. p., 2006. Web. doi:10.1103/PHYSREVB.73.1.
Perisanu, Sorin, & Vermeulen, Gerard. Curvature, slip, and viscosity in {sup 3}He-{sup 4}He mixtures. United States. doi:10.1103/PHYSREVB.73.1.
Perisanu, Sorin, and Vermeulen, Gerard. Sat . "Curvature, slip, and viscosity in {sup 3}He-{sup 4}He mixtures". United States. doi:10.1103/PHYSREVB.73.1.
@article{osti_20788047,
title = {Curvature, slip, and viscosity in {sup 3}He-{sup 4}He mixtures},
author = {Perisanu, Sorin and Vermeulen, Gerard},
abstractNote = {We report vibrating wire viscometer experiments in the concentrated and dilute phase of saturated {sup 3}He-{sup 4}He mixtures showing that the slip length may become orders of magnitude larger than the mean free path due to specular scattering of the {sup 3}He quasiparticles with a {sup 4}He coating adsorbed at the surface of the wire. Since the liquid does not almost stick to the surface, the boundary conditions for fluid flow are unusual and not accounted for by the current theory for slip [H. Hoejgaard Jensen et al., J. Low Temp. Phys. 41, 473 (1980)]. The experimental results are in excellent agreement with a recent theory for slip [R. Bowley and J. Owers-Bradley, J. Low Temp. Phys. 136, 15 (2004)] which accounts for the effect of the cylindrical geometry and for velocity slip in directions normal as well as tangential to the surface of the wire. We find that our viscosity measurements in the dilute phase resulting from the data analysis based on the recent slip theory are in better agreement with the Fermi liquid theory than previous experimental results.},
doi = {10.1103/PHYSREVB.73.1},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 13,
volume = 73,
place = {United States},
year = {Sat Apr 01 00:00:00 EST 2006},
month = {Sat Apr 01 00:00:00 EST 2006}
}
  • A torsional oscillator cell is described, by means of which simultaneous precision measurements of ({rho}{eta}) and of the molar volume can be made in liquid {sup 4}He-{sup 4}He mixtures over the temperature range between 0.5 and 3 K. Here {rho} is the mass density, {eta} the shear viscosity, and in the superfluid phase they become the contributions {rho}{sub n} and {eta}{sub n} of the normal component. The results of {eta} for {sup 4}He near the superfluid transition are compared with the predictions by Schloms, Pankert and Dohm, and by Ferrell. Measurements of ({rho}{eta}) are reported for mixtures with 0.64 {le}more » X {le} 0.74, where X is the {sup 3}He mole fraction. Those for X = 0.67 and 0.70 are compared with data by Lai and Kitchens. The viscosity experiments show no evidence of a weak singularity at the tricritical point.« less
  • High-resolution measurements of {rho}{eta} are reported for liquid {sup 4}He and {sup 3}He-{sup 4}He mixtures at saturated vapor pressures between 1.2 and 4.2 K with particular emphasis on the superfluid transition. Here {rho} is the mass density, {eta} the shear viscosity, and in the superfluid phase both {rho} and {eta} are the contributions from the normal component of the fluid ({rho}{sub n} and {eta}{sub n}). New data for the total density and data for {rho}{sub n} by various authors led to the calculation of {eta}. For {sup 4}He, the results for {eta} are compared with published ones, both in themore » normal and superfluid phases, and also with predictions in the normal phase both over a broad range and close to T{sub {lambda}}. The behavior of {rho}{eta} and of {eta} in mixtures is presented.« less
  • Starting with the Boltzmann transport equation, the first viscosity of dilute [sup 3]He-[sup 4]He mixtures for various [sup 3]He concentrations x is evaluated up to around T[approx equal]0.6 K by including the contribution from three-phonon processes (3PP) in the anomalous elementary excitation spectrum of liquid [sup 4]He. Due to 3PP, the characteristic time [tau][sub [eta]] for [sup 3]He viscosity at high temperatures, i.e., T[>=]2T[sub F] where T[sub F] is the [sup 3]He Fermi temperature, is evaluated as 5 x 10[sup [minus]12]/xT, which is smaller than the value estimated by Rosenbaum et al. This is interpolated with [tau][sub [eta]] in themore » degenerative (quantum) region, T << T[sub F]. The obtained viscosities are in better agreement with experimental results than those of Baym and Saam, whose theory does not include 3PP. However, at very low concentrations there exists a discrepancy between the present theory and experiments, so that an alternate treatment should be considered.« less
  • Simultaneous measurements of ({rho}{eta}) and of the molar volume are reported for liquid mixtures of {sup 3}He in {sup 4}He over the temperature range between 0.5 and 2.5 K. Here {eta} is the shear viscosity and {rho} is the mass density. In the superfluid phase, the product of the normal components, {rho}{sub n} and {eta}{sub n}, is measured. The mixtures with {sup 3}He mole fractions 0.30 < X < 0.80 are studied with emphasis on the region near the superfluid transition T{sub {lambda}} and near the phase-separation curve. Along the latter, they are compared with data by Lai and Kitchens.more » For X > 0.5, the viscosity singularity near T{sub {lambda}} becomes a faint peak, which however fades into the temperature-dependent background viscosity as X tends to the tricritical concentration X{sub t}. Likewise, no singularity in {eta} is apparent when T{sub t} is approached along the phase separation branches {sigma}{sub {minus}} and {sigma}{sub +}. Furthermore, viscosity data are reported for {sup 3}He and compared with previous work. Finally, for dilute mixtures with 0.01 {le} X {le} 0.05, the results for {eta} are compared with previous data and with predictions.« less
  • We have investigated {sup 3}He-{sup 4}He mixtures at {sup 3}He-concentrations 0.98% {le} x {le} 9.5% by the vibrating wire technique in the temperature range 1 mK {le} T {le} 100 mK and at pressures 0 bar {le} p {le} 20 bar. In the degenerate regime of the mixtures the Landau theory of Fermi liquids predicts a temperature dependence of the viscosity {eta} proportional T{sup {minus}1}. We report on the first observation of this behaviour at 3 mK {le} T {le} 10 mK for all investigated concentrations and pressures. At temperatures below about 20 mK slip corrections had to be takenmore » into account due to the increase of the quasiparticle mean free path at very low temperatures. The low-temperature cut-off in {eta} T{sup 2} = constant indicates the transition into the ballistic regime of the mixtures, where the mean free path of the quasiparticles exceeds the radius of the vibrating wire. Our results for the pressure dependence of the viscosity as well as for its magnitude show substantial differences from predictions based on pseudopotential theory. However, a calculation of {eta} with the quasiparticle interaction potential of recent solubility measurements in mixtures agrees well with our experimental data, in particular the pressure independence of {eta}.« less