Frequency-dependent viscosity of xenon near the critical point

We used a novel, overdamped oscillator aboard the Space Shuttle to measure the viscosity $\ensuremath{\eta}$ of xenon near its critical density ${\ensuremath{\rho}}_{c}$ and temperature ${T}_{c}.$ In microgravity, useful data were obtained within 0.1 mK of ${T}_{c},$ corresponding to a reduced temperature $t=(T\ensuremath{-}{T}_{c}{)/T}_{c}=3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}.$ 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 $\ensuremath{\eta}\ensuremath{\propto}{t}^{\ensuremath{-}\ensuremath{\nu}{z}_{\ensuremath{\eta}}}.$ Here $\ensuremath{\nu}$ is the correlation length exponent, and our result for the viscosity exponent is ${z}_{\ensuremath{\eta}}=0.0690\ifmmode\pm\else\textpm\fi{}0.0006.$ (All uncertainties are one standard uncertainty.) Our value for ${z}_{\ensuremath{\eta}}$ depends only weakly on the form of the viscosity crossover function, and it agrees with the value $0.067\ifmmode\pm\else\textpm\fi{}0.002$ obtained from a recent two-loop perturbation expansion [H. Hao, R.A. Ferrell, and J.K. Bhattacharjee, (unpublished)]. The measurements spanned the frequency range $2\mathrm{Hz}<~f<~12\mathrm{Hz}$ and revealed viscoelasticity when $t<~{10}^{\ensuremath{-}5},$ further from ${T}_{c}$ than predicted. The viscoelasticity's frequency dependence scales as Af$\ensuremath{\tau},$ where $\ensuremath{\tau}$ is the fluctuation-decay time. The fitted value of the viscoelastic time-scale parameter A is $2.0\ifmmode\pm\else\textpm\fi{}0.3$ times the result of a one-loop perturbation calculation. Near ${T}_{c},$ 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 ${\ensuremath{\rho}}_{c}$ by judicious choices of the temperature versus time program. Deliberately bad choices led to large density inhomogeneities. At $t>{10}^{\ensuremath{-}5},$ the xenon approached equilibrium much faster than expected, suggesting that convection driven by microgravity and by electric fields slowly stirred the sample.

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