Transport properties of helium near the liquid-vapor critical point. IV. The shear viscosity of3He and4He

Abstract

Shear viscosity measurements with a precision of 0.05% are reported for3He and4He along near-critical isochores 0.85<ρ/ρc<1.12, where ρc is the critical density. The temperature range was −10−4<e<1, where e=(T − Tc)/Tc is the reduced temperature. The experiments were carried out with a torsional oscillator operating at 158 Hz, driven at resonance in a phase-locked loop. The absolute value of the viscosity was obtained by calibration at the superfluid transition of4He, based on published values and from direct calculations using the free decay time constant of the oscillations. The data are analyzed in terms of a model using the recent mode-coupling (MC) expressions by Olchowy and Sengers, and where account is taken of the earth's gravity effects. The theory could be fitted very well to the experiment with a single free parameter, the cutoff wave numberqD, which was found to be 3.0×106 and 7.0×106 cm−1 for3He and4He, respectively. We have used for the critical exponent the MC predicted value of zη=0.054, which permits a fit superior to that using zη=0.064 predicted by dynamic renormalization group (DRG) theories. Detailed comparisons are made between the model calculations and data for various isochores and isotherms and good agreement is obtained. The effects of gravity are described in some detail. The predicted frequency effect in viscosity measurements is calculated for3He and is shown to be obscured by gravity effects. Using the Olchowy-Sengers formulas, we have also fitted the MC theory to the critical thermal conductivity data of3He, again withqD as the only free parameter. This fit gaveqD=6 × 107 cm−1, which in the ideal situation should have been the same asqD from viscosity. We also discuss a representation of the3He viscosity data along the critical isochore by a power law and first correction-to-scaling erm. Using the viscosity and the critical conductivity data for3He, we have calculated the dynamic amplitude ratio and obtained ℛ=1.05±0.10, in agreement with predictions from MC and DRG theories. Also, ℛ agrees with data of classical fluids. Finally, a comparison is made of recent shear viscosity data for CO2 by Bruschi and Torzo with those on He. The CO2 data are also analyzed in terms of the MC theory, and the discrepancies are discussed. In the Appendices, we present the results of new compressibility measurements on3He along the critical isochore, as used in the MC analysis. We also present a brief analysis of the fluid hydrodynamics in the torsional oscillator leading to relations for the viscosity as a function of the measured quantities. Finally, we give a short outline of the vertical density profile calculations from the earth's gravity field for the calculations of the viscosity nearTc.