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.