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

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(\ensuremath{\Omega}) for the attenuation normalized to its consolute-point value, where \ensuremath{\Omega} is the frequency, scaled by the relaxation rate of the fluid. By imposing some general conditions, we are led to the empirical function F(\ensuremath{\Omega})=(1+${\ensuremath{\Omega}}^{\mathrm{\ensuremath{-}}1/2}$${)}^{\mathrm{\ensuremath{-}}2}$, which 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.

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