In a general sense, successful solvent pair recrystallization depends on the solubility characteristics of the solute in the selected solvents. A good solvent pair should have one solvent in which the solute is highly soluble when hot and poorly soluble when cold, and another solvent in which the solute is poorly soluble at all temperatures. This principle allows for the selective crystallization of the desired compound while leaving impurities in the solution.
For instance, if one solvent is water and the other is ethanol, water would dissolve a polar compound well when heated but not when cold, whereas ethanol could be a poor solvent for the same compound across temperatures. This setup allows the target compound to crystallize out efficiently.
In contrast, if a solvent pair consists of two solvents in which the solute remains highly soluble at both high and low temperatures or where both solvents allow for consistent solubility of impurities, then that pair would not be suitable for recrystallization. This lack of differential solubility undermines the fundamental strategy of separating the desired product from undesired materials through temperature manipulation.