Particle nucleation and growth models

This review concentrates on the progress of modeling the nucleation process of particles by the balanced nucleation-growth (BNG) process. The BNG model will be compared with other models that try to predict material nucleation. Compared to other models, the BNG model allows quantifying the nucleation rate, maximum growth rate, and supersaturation during the nucleation period as a function of nucleation efficiency and maximum growth rate of the crystals. From this model, equations are derived that correlate the number of stable crystals formed with molar addition rate of reactants, solubility of the crystals, and temperature. The BNG model predicts the experimental result that many crystallization processes result in a limited number of crystals followed by growth. The model also predicts that factors like diffusion and kinetically controlled growth process, Ostwald ripening agents and growth restrainers control the crystal number. Equations are given for each of the variables that agree with experiments. The BNG model predicts the conditions for renucleation (formation of new crystals during precipitation). It leads to new equations for the prediction of crystal number and crystal size during controlled continuous precipitation in the continuous stirred tank reactor (CSTR) as a function of precipitation conditions.