2018-(I)-Critical Contribution, Dynamic Scaling and Crossover Theory
Article Index
The crossover theory in ternary mixtures:
The crossover theory has been developed for binary mixtures. It is not self-evident that this theory is also valid for ternary mixtures. Moreover, the renormalization group ε-expansion predicts a dependence of the critical exponent of viscosity Zη upon the dimension of the considered system.
with ε (note, in this case ε is not the reduced temperature), the critical dimension dc = 4, and ε = dc −d , where d is the dimension of the system. Consequently, the value ε/19 for a 3d-Ising system, in first order for Zη . Taking into account the second order corrections, Zη = 0.065 results. This value has been predicted by the mode-coupling theory. In the case of tricritical point the critical dimension is reduced to dc = 3, as has been given by Pfeuty. As a consequence, ε = 0 and therefore Zη=0. It seems that there is no critical divergence of the viscosity. However, the ternary system, that has been investigated it this work is of type 2a and belongs to the same universality class for dynamical properties as the binary fluids. Thus, there is no reason to treat the experimental data different from the binary mixtures. Furthermore, it can be expected, that the crossover corrections are likewise valid.