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 T-c. In microgravity, useful data were obtained within 0.1 mK of T-c, corr esponding to a reduced temperature t =(T- T-c)/T-c= 3 X 10(-7). Because the y avoid the detrimental effects of gravity at temperatures two decades clos er to T-c than the best ground measurements, the data directly reveal the e xpected power-law behavior eta proportional to t(-nu z 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 cros sover 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0.067+/- 0.002 obtained from a recent two-loop perturbation expansion [H. Hao, R.A. Ferrell, and J.K. Bha ttacharjee, (unpublished)]. The measurements spanned the frequency range 2 Hz less than or equal to f less than or equal to 12 Hz and revealed viscoel asticity when t less than or equal to 10(-5), further from T-c than predict ed. The viscoelasticity's frequency dependence scales as Af tau, where tau is the fluctuation-decay time. The fitted value of the viscoelastic time-sc ale parameter A is 2.0+/-0.3 times the result of a one-loop perturbation ca lculation. Near T-c, the xenon's calculated time constant for thermal diffu sion 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. Delibe rately bad choices led to large density :inhomogeneities. At t>10(-5), the xenon approached equilibrium much faster than expected, suggesting that con vection driven by microgravity and by electric fields slowly stirred the sa mple. [S1063-651X(99)04210-5].