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4 Critical Contribution, Dynamic Scaling and Crossover Theory

The following Chapter deals with the dynamic scaling aspects within the framework of Bhattacharjee-Ferrell theory. Furthermore, relationships between the critical sound at- tenuation and the dynamic scaling function are presented. Moreover, crossover effects for binary and ternary fluids are presented.

4.1 Bhattacharjee-Ferrell scaling hypothesis - binary systems

Critical phenomena, as all continuous phase transitions, Show universal characteristics of their thermodynamic properties, if they belong to the same universality class and if their dimension is identical. In Section (2.3.3) the concepts and consequences of critical slow- ing down have been presented. In particular, the light scattering is well represented and described by dynamic scaling theories, resulting from the mode-coupling considerations. However, the treatment of critical ultrasonic attenuation necessitates the development of new theories in order to get an access to critical fluctuations in a sound field. Bhattachar- jee and Ferrell have presented [18], [19] a general theory of the critical ultrasonic attenua- tion, based on an extension of the concept of the frequency-dependent specific heat. This conception was firstly introduced by Herzfeld and Rice [65] in 1928.

4.2 Critical sound attenuation

For understanding the nature of critical sound attenuation, it is important to study the propagation velocity cs of low-frequency sound in the vicinity of the critical point [20]. This kind of considerations allows to understand the coupling between the sound propa- gation and sound attenuation as well as the sound dispersion of sound velocity near the consolute point. The first thermodynamic studies of Bhattacharjee and Ferrell concen- trated on the variation of volume V with pressure p, due to sound propagation at constant entropy S. As consequence of this examinations they got the isentropic compressibility βS at constant S:

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