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Frequency-Dependent Viscosity of Xenon Near the Critical Point

Published

Author(s)

Robert F. Berg, Michael R. Moldover, G A. Zimmerli

Abstract

We used a novel, overdamped oscillator aboard the Space Shuttle to measure the viscosity Η of xenon near its critical density ρc and temperature Tc. In microgravity, useful data were obtained within 0.1 mK of Tc, corresponding to a reduced temperature t = (T - Tc ) / Tc = 3x10-7. Because they avoid the detrimental effects of gravity at temperatures two decades closer to Tc than the best ground measurements, the data directly reveal the expected power-law behavior (Η{variation}t-υζΗ^). Here υ is the correlation length exponent, and our result for the small viscosity exponent is ζΗ = 0.0690 ± 0.0006. (All uncertainties are one standard uncertainty.) Our value for ζΗ 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0.067 ± 0.002 obtained from a recent two-loop perturbation expansion [H. Hao, R.A. Ferrell, and J.K. Bhattacharjee, (unpublished)].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 {u-5^, further from Tc than predicted. The viscoelasticity's frequency dependence scales as Afτ, where τ is the fluctuation-decay time. The fitted value of the viscoelastic time-scale parameter A is 2.0 {+or -} 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 ρc by judicious choices of the temperature vs. 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.
Citation
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Volume
60

Keywords

critical point, microgravity, viscoelasticity, viscoelasticity, viscosity exponent, xenon
Created October 1, 1999, Updated February 17, 2017