Critical dynamics in mixtures

Abstract

We derive the nonasymptotic expressions for the frequency- and temperature-dependent sound velocity and sound absorption near a critical point in a mixture within renormalization group theory in one-loop order. The dynamic model considered is an extension of the corresponding model for pure fluids including concentration fluctuations. The theoretical result for the complex sound velocity is the same as at consolute points and gas-liquid critical points reflecting universality. Differences observed in the experiments at the two critical points mentioned are due to the different behavior of the sound velocity at ${T}_{c},$ which is finite in mixtures and zero in pure fluids, as well as due to nonasymptotic effects. Near the consolute point we compare our result with the phenomenological theory of Ferrell and Bhattacharjee [Phys. Rev. B 24, 4095 (1981); Phys. Rev. A 31, 1788 (1985)] and near the gas-liquid critical point with experiments in the ${}^{3}{\mathrm{H}\mathrm{e}\ensuremath{-}}^{4}\mathrm{He}$ mixture. A genuine dynamic parameter not considered so far and related to the critical enhancement of the thermal conductivity appears in the nonasymptotic expressions of the transport coefficients and the complex sound velocity. All nonuniversal background parameters of the complex sound velocity are fixed by a comparison of the corresponding theoretical expressions for the transport coefficients with experiments.