Theoretical consideration on the acoustic anomaly of critical binary mixtures

Existing theories for acoustic anomaly of critical binary mixtures, including both the specific-heat and dynamic-viscosity approach and both mode-coupling and renormalization-group theory, are found to give the same expressions for critical amplitudes of reduced dispersion and absorption after appropriate modifications of the theories from two standpoints: (1) Concentration fluctuations experience the temperature difference from the critical temperature ${T}_{c}$ and the sound wave modulates both the temperatures T and ${T}_{c}$ and (2) thermodynamic quantities with critical anomaly should be correctly generalized to dynamic ones. The unified expressions of critical amplitudes have not only a temperature dependence but also a frequency dependence, indicating that the dynamic scaling does not hold in an exact sense for the acoustic anomaly. The modified Kroll-Ruhland theory gives new reduced expressions for dispersion and absorption. The difference in scaling functions among various theories is discussed.

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