Binary colloidal mixtures in near-critical binary solvents

The phase behavior of a single type of colloid C suspended in near-critical solvents is known to be very rich. Motivated in part by recent experiments [Kodger et al., "Composite colloidal assembly by critical Casimir forces," arXiv:2602.12431 (2026)], we consider a mixture of two colloidal types C1 and C2 in a binary solvent close to its demixing critical point. We extend a mean-field description of a lattice model, previously used to investigate systems with a single type of colloid in two dimensions, to the binary colloid case in three dimensions. The model treats the system as a full four-component mixture. For simplicity, we choose C1 and C2 to be hard spheres with the same radius but with different affinities for one species, B, of the AB binary solvent. We show that intricate interplay between C1-solvent and C2-solvent interactions as well as solvent-solvent interactions and hard sphere packing drive significant changes in the topology of the colloidal phase diagram when the relative volume fractions of the two different colloid types change. The behavior of the two lines of triple points is particularly interesting. Our results can provide some insight into the control of the self-assembly process for colloidal "alloys" mediated by a near-critical solvent and, therefore, controlled by temperature in a reversible manner.