Dynamic scaling theory of the critical attenuation and dispersion of sound in a classical fluid: The binary liquid

Abstract

Following the ideas of Herzfeld, Rice, Fixman, and Mistura, we are able to establish the adiabatic temperature oscillations as the sole origin of the critical attenuation and dispersion near the consolute point of a binary liquid. Special attention is given to the scaling function F(Q) for the attenuation normalized to its consolute-point value, where Q is the frequency, scaled by the relaxation rate of the fluid. By imposing some general conditions, we are led to the empirical function F(Q)=(1+Q ' ),whi ch is in excellent agreement with the data of Garland and Sanchez. By including a new hydrodynamic effect, we find that the frequency scale is also in accord with experiment.

Absorption and Dispersion of Ultrasonic Waves in n-Amylic Alcohol-Nitromethane Critical Mixture

“…Essentially, three theories are available for the description of dispersion and absorption of acoustic waves in critical mixtures, namely: renormalisation group theory [1], dynamic scaling theory [2], and mode-coupling theory [3][4][5][6][7]. The last, though initially successful, failed to provide a correct account of the experimental data in a wide range of reduced frequencies ω*.…”

Critical Fluctuations of Membranes: Spectroscopy Meets Thermodynamics

“…Ultrasonic attenuation related to critical demixing and also to fluctuations near the van der Waals critical point has stimulated a variety of theoretical models [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52], based on the conception that the anomalous attenuation results from a time lag in the establishment of longrange correlations of density fluctuations when the system is slightly disturbed by the pressure and temperature variations of the sonic fields. Experimental results are favorably represented by the Bhattacharjee-Ferrell theory ("BF", [46,48]). In conformity with experimental findings, it predicts a very slow decrease of the absorption-perwavelength spectrum, proportional to ν −δ , toward high frequencies ( Fig.…”

“…to the attenuation-per-wavelength spectra has been calculated to gain the scaling function according to [33,46,48] …”

Theory of Critical Sound Attenuation in Ising-Type Magnets

“…The analytic relation (4.5) resembles the corresponding asymptotic formulas for sound attenuation in binary mixtures [13][14][15], where the sound attenuation exponent is also equal to v -a. For high frequencies Eq.…”