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4 Critical Contribution, Dynamic Scaling and Crossover Theory

The function FBF(Ω) in Eq.(4.16), is the so-called scaling function, which plays a central role it the Bhattacharjee-Ferrell theory. The properties of this special function will be treated with more details in the next section.

4.3 The scaling function Fx(Ω)

Last decades, various theoretical expressions for the universal scaling function of ultra- sonic attenuation spectra have been presented for critically demixing binary fluids. In Fig.(4.3) three prominent examples are shown.

Figure 4.2: Three prominent examples of scaling functions: the full line represents the Bhattacharjee-Ferrell (BF), the dashed line the Folk-Moser (FM), and the dotted line the Onuki (On) function [67].

In 1981 Bhattacharjee and Ferrell have presented the scaling function for sonic attenua- tion in analytical form [18]:

Because of the difficulties to treat this integral, an empirical function has been developed

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