Fluid-phase behavior of binary mixtures in which one component can have two critical points

We investigate theoretically the binary fluid-phase behavior of mixtures in which one water-like component can have two critical points. We consider three equal-sized nonpolar solutes that differ in the strength of their dispersive interactions (a1 < a2 < a3, where a denotes the van Der Waals attractive parameter). In each case, we compare the phase behavior predicted using two sets of parameters for water: one giving rise to a pure component low-temperature liquid-liquid transition terminating at a critical point (two-critical-point parameter set), and one in which no such second critical point exists (singularity-free parameter set). Regardless of the parameter values used, we find five mixture critical lines. Using the two-critical-point parameter set, we find that a critical line originates at water's second critical point for aqueous mixtures involving solutes 1, 2, or 3. For mixtures involving solutes 1 or 2, this line extends towards low pressures and high temperatures as the solute mole fraction increases, and is closely related to the critical line originating at water's ordinary vapor-liquid critical point: these two critical lines are loci of upper and lower consolute points corresponding to the same liquid-liquid transition. In mixtures involving solute 2, the critical locus emanating from water's second critical point is shifted to higher temperatures compared to mixtures involving solute 1, and extends up to T≈310 K at moderate pressures (ca. 200 bars). This suggests the possibility of an experimentally accessible manifestation of the existence of a second critical point in water. For binary mixtures involving solutes 1 or 2, changing the water parameters from the two critical points to the singularity-free case causes the disappearance of a lower consolute point at moderate pressures. For binary mixtures involving solute 3, the differences between two-critical-point and singularity-free behaviors occur only in the experimentally difficult-to-probe low-temperature and high-pressure region.