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4.2 Critical sound attenuation

and

It is assumed that the critical part of the specific heat determines the complex sound veloc- ity in Eq.(4.7). Within the scope of dynamic scaling it is possible to write the dependence of Cp on the reduced temperature ε:

where ˜α0 denotes the critical exponent. With the aid of the relationship of critical diffu- sion coefficient in [66], [22], that controls the relaxation of the concentration fluctuations and relates the diffusion coefficient D, to the viscosity ηs and the correlation length ξ of critical fluctuations:

(with the Boltzmanns’s constant kB, and absolute temperature T), it is possible to give an expression for the characteristic relaxation rate of a fluid:

where ˜ν denotes the critical exponent of the correlation length and Z0 denotes the dy- namic critical exponent. The amplitude Γ0 is a characteristic system-dependent constant. The system dependent values Γ0 of several binary systems are presented in Table (5.10, s.121). However, with regard to ultrasonic spectroscopy, it might be interesting to inves- tigate the frequency dependence of the specific heat Cp. Using Eq.(4.11) one can express the temperature dependence in Cp in terms of the characteristic relaxation rate Γ:

where the value of the exponent is:

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