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 ͑1981͒; Phys. Rev. A 31, 1788 ͑1985͔͒ and near the gas-liquid critical point with experiments in the 3 He-4 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.

On the universality class of a magnetic liquid in an external field

“…As already mentioned above a similar situation arises for the densities describing the sound mode when the minimal subtraction scheme is used [18,19]. There the unrenormalized coupling constant between the density and the longitudinal part of the momentum current has to go to infinity.…”

“…The time scale ratioẘ is irrelevant as can be seen from its cut-off dimension and, therefore, has to be set to zero in expressions within perturbation expansion in order to obtain a theory renormalizable with minimal subtraction. The dynamic equations (67)- (69) have the same form as in the case of binary liquid mixtures at the plait point [19]. Having considered the dynamical critical phenomena in the Heisenberg liquid, one can now proceed along the lines developed in [32,33].…”

“…Apart from the Gaussian terms of the transverse spin components, which do not contribute to the critical behavior, the static functional (49) is the same as those of binary liquid mixtures at the plait point [19]. All thermodynamic relations can be taken over from this system if one replaces the concentration c and the chemical potential ∆ of the liquid mixture by the spin density µ m and the magnetic field H z of the magnetic liquid.…”

“…It turns out [20] that the critical dynamics belongs to the universality class of a pure fluid [21] (model H [16]), whereas the non-asymptotic behavior belongs to the case of a mixture [19,22].…”

“…In order to treat dissipation we have to append the dissipative currents [28] to equations (14), (16), (17) and (19). The total energy current contains two dissipative processes.…”