Crossover between vapor-liquid and consolute critical phenomena

The application of the principle of critical-point universality to fluid mixtures near plait points is generalized to encompass crossover between the one-component vapor-liquid critical limit and the liquid-liquid critical limit of incompressible liquid mixtures. This goal is accomplished by generalizing the scaling fields to linear combinations of three physical field variables related to the temperature and the chemical potentials of the two components. We show how one recovers from the general expressions for the scaling fields the limiting critical behavior of dilute mixtures near the vapor-liquid critical point and of weakly compressible liquid mixtures near the consolute point. In addition we elucidate the consequences for the critical behavior in some special cases, namely, near an azeotropic critical point, near a reentrant critical point, and when the critical temperature goes through a maximum or a minimum as a function of concentration.