Critical dynamics near plait points in mixtures

Abstract

We set up a dynamical model describing the critical dynamics near a plait point considering the entropy density as the order parameter. This leads to model H' of Siggia, Halperin and Hohenberg, which we treat within a field theoretic renormalization group theory. The temperature dependence of the hydrodynamic transport coefficients is calculated in the crossover region from background to the asymptotic critical region. The asymptotic behavior is described by the same universal values of the amplitude ratios and exponents as in the pure fluid and at the consolute point. Thus agreement with mode-coupling theory in the asymptotic region is shown. We define an experimental expression for the Kawasaki amplitude at the plait point and calculate its theoretical counterpart. The theoretical expression agrees with corresponding result at the consolute point, the nonasymptotic expression for the Kawasaki amplitude is different from the pure fluid. The main reason for the nonuniversal behavior of mixtures at the plait point lies not in a slow flow to the asymptotics of the dynamical parameters of the model, but in the nonuniversal prefactor appearing before the singular part in the transport coefficients.