Frequency-dependent viscosity of xenon near the critical point

We used a novel, overdamped oscillator aboard the Space Shuttle to measure the viscosity eta of xenon near its critical density rho(c) and temperature Tc. In microgravity, useful data were obtained within 0.1 mK of Tc, corresponding to a reduced temperature t=(T-Tc)/Tc=3 x 10(-7). Because they avoid the detrimental effects of gravity at temperatures two decades closer to T(c) than the best ground measurements, the data directly reveal the expected power-law behavior eta proportional, variant t(-nuz(eta)). Here nu is the correlation length exponent, and our result for the viscosity exponent is z(eta)=0.0690+/-0.0006. (All uncertainties are one standard uncertainty.) Our value for z(eta) depends only weakly on the form of the viscosity crossover function, and it agrees with the value 0.067+/-0.002 obtained from a recent two-loop perturbation expansion [H. Hao, R.A. Ferrell, and J.K. Bhattacharjee, (unpublished)]. The measurements spanned the frequency range 2 Hz< or = f < or =12 Hz and revealed viscoelasticity when t < or = 10(-5), further from Tc than predicted. The viscoelasticity's frequency dependence scales as Aftau, where tau is the fluctuation-decay time. The fitted value of the viscoelastic time-scale parameter A is 2.0+/-0.3 times the result of a one-loop perturbation calculation. Near Tc, the xenon's calculated time constant for thermal diffusion exceeded days. Nevertheless, the viscosity results were independent of the xenon's temperature history, indicating that the density was kept near rho(c) by judicious choices of the temperature versus time program. Deliberately bad choices led to large density inhomogeneities. At t>10(-5), the xenon approached equilibrium much faster than expected, suggesting that convection driven by microgravity and by electric fields slowly stirred the sample.