Nonasymptotic Transport Properties in Fluids and Mixtures Near a Critical Point

Abstract

We review the critical dynamics of fluids and mixtures. Special attention in the comparison with experiment is paid to nonasymptotic effects. Our theoretical results are based on the complete model H′ of Siggia, Halperin, and Hohenberg including the sound mode variables. Using the dynamic renormalization group theory, we calculate the temperature dependence of the transport coefficients as well as the frequency-dependent sound velocity and sound attenuation. In mixtures a time ratio between the Onsager coefficients related to the diffusive modes, which is directly related to the critical enhancement of the thermal conductivity near a consolute point, has to be taken into account. The sound mode contains, besides the dynamic parameters, a static coupling related to the logarithmic derivative of the weakly diverging specific heat. The deviation from the asymptotic value of this coupling at finite frequencies and temperature distance from Tc leads to additional nonasymptotic effects. Our theory, which derives the phenomenological ansatz of Ferrell and Bhattacharjee for pure fluids and mixtures near a consolute point, is also applicable near a plait point.