Abstract
Based on a representation of the sound velocity of critical liquids in terms of a frequency-dependent complex specific heat at constant pressure, a simple relation between the low-frequency normalized sonic attenuation coefficient and the correlation length of fluctuations is derived. This relation provides a promising alternative for the determination of the dynamics exponent and thus the critical exponent of the shear viscosity. Sonic attenuation data from the literature, measured at frequencies down to 50 kHz, are re-evaluated with a view of the viscosity exponent determination. It is found that only in a small temperature range, the major requirement of the approach is fulfilled with the available data. Close to the critical temperature, the frequencies of measurement are still insufficiently small as compared to the inverse relaxation time of order parameter fluctuations. Criteria for future experiments are discussed briefly.
Highlights
In fluids near a critical point, the behavior of the systems is largely dominated by longrange fluctuations
Vertex corrections resulted in xη = 0.070 ± 0.008 [8] and renormalization-group theory [9] as well as mode-coupling theory [10] of the critical dynamics yielded xη = 0.065
The latter value is in fair agreement with xη = 0.0635 ± 0.0004, as directly obtained from shear viscosity data [11,12], and with xη = 0.063 ± 0.024 from extrapolation of the decay rate of order parameter fluctuations as derived from photon-correlation spectroscopy [13]
Summary
In fluids near a critical point, the behavior of the systems is largely dominated by longrange fluctuations. Vertex corrections resulted in xη = 0.070 ± 0.008 [8] and renormalization-group theory [9] as well as mode-coupling theory [10] of the critical dynamics yielded xη = 0.065 The latter value is in fair agreement with xη = 0.0635 ± 0.0004, as directly obtained from shear viscosity data [11,12], and with xη = 0.063 ± 0.024 from extrapolation of the decay rate of order parameter fluctuations as derived from photon-correlation spectroscopy [13]. The issue that we would like to address is whether there is a terrestrial indirect experiment which can be precise as the direct determination in a space shuttle It is the quasi-elastic light scattering experiments by Burstyn and Sengers [13] which provide the prime source for an alternative determination of the viscosity exponent. Binary liquids are ideally suited for this purpose, because the specific heat in such mixtures is dominated by the large non-critical background contribution that exists at the consolute point
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