This work presents a mathematical model that describes growth, homogeneous nucleation, and secondary nucleation that is caused by interparticle interactions between seed crystals and molecular clusters in suspension. The model is developed by incorporating the role of interparticle energies into a kinetic rate equation model, which yields the time evolution of nucleus and seed crystal populations, as in a population balance equation model, and additionally that of subcritical molecular clusters, thus revealing an important role of each population in crystallization. Seeded batch crystallization at a constant temperature has been simulated to demonstrate that the interparticle interactions increase the concentration of the critical clusters by several orders of magnitude, thus causing secondary nucleation. This explains how secondary nucleation can occur at a low supersaturation that is insufficient to trigger primary nucleation. Moreover, a sensitivity analysis has shown that the intensity of the interparticle energies has a major effect on secondary nucleation, while its effective distance has a minor effect. Finally, the simulation results are qualitatively compared with experimental observations in the literature, thus showing that the model can identify operating conditions at which primary or secondary nucleation is more prone to occur, which can be used as a useful tool for process design.
© 2021 The Authors. Published by American Chemical Society.