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

Shear viscosity measurements with a precision of 0.05% are reported for³He and⁴He along near-critical isochores 0.85</ _c <1.12, where _c is the critical density. The temperature range was –10^–4<<1, where =(T – T _c)/T _c 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 numberq _D, 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 z=0.054, which permits a fit superior to that using z=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 withq _D as the only free parameter. This fit gaveq _D=6 × 10⁷ cm^–1, which in the ideal situation should have been the same asq _D 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 =1.05±0.10, in agreement with predictions from MC and DRG theories. Also, 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 nearT _c.