Shear viscosity of liquid4He and3He-4He mixtures, especially near the superfluid transition

Abstract

High-resolution measurements of ρη are reported for liquid4He and3He-4He mixtures at saturated vapor pressures between 1.2 and 4.2 K with particular emphasis on the superfluid transition. Here ρ is the mass density, η the shear viscosity, and in the superfluid phase both ρ and η are the contributions from the normal component of the fluid (ρ n and η n ). The experiments were performed with a torsional oscillator operating at 151 Hz. The mole fraction X of3He in the mixtures ranged from 0.03 to 0.65. New data for the total density and data for ρ n by various authors led to the calculation of η. For4He, the results for η are compared with published ones, both in the normal and superfluid phases, and also with predictions in the normal phase both over a broad range and close to Tλ. The behavior of ρη and of η in mixtures if presented. The slopedη/dT near Tλ and its change at the superfluid transition are found to decrease with increasing3He concentration. Measurements at one temperature of η versus pressure indicate a decreasing dependence of η on molar volume asX(3He) increases. Comparison of η at Tλ, the minimum of η n in the superfluid phase and the temperature of this minimum is made with previous measurements. Thermal conductivity measurements in the mixtures, carried out simultaneously with those of ρη, revealed no difference in the recorded superfluid transition, contrary to earlier work. In the appendices, we present data from new measurements of the total density for the same mixtures used in viscosity experiments. Furthermore, we discuss the data for ρ n determined for4He and for3He-4He mixtures, and which are used in the analysis of the ρη data.