Understanding temperature-induced primary nucleation in dual impinging jet mixers

The discovery that crystal nuclei can be generated by combining hot and cold saturated solutions in a dual-impinging-jet (DIJ) mixer motivates the theoretical analysis in this article. Nucleation is shown to be facilitated in solute-solvent systems that have much higher energy transfer than mass transfer rates near the impingement plane between the two jets. One- and two-dimensional spatial distributions of velocity, temperature, concentration, and supersaturation provide an improved understanding of primary nucleation in cooling DIJ mixers. In the most important spatial region for characterization of nucleation, the two-dimensional fields are shown to be very close to analytical solutions derived from a one-dimensional approximation of the energy and molar balances. This simplification enables the derivation of design criteria that facilitates assessment of whether any particular solute-solvent combination will nucleate crystals in a cooling DIJ mixer, based on the physicochemical properties of the system. These criteria could save time and material by avoiding or reducing trial-and-error experiments, which is helpful at the early stage of pharmaceutical process development.