Reversible crystal growth–dissolution and aggregation–breakage: numerical and moment solutions for population balance equations

A general population balance equation (PBE) is proposed to describe combined monomer addition and dissociation (growth and dissolution) and aggregation and fragmentation. The reversible distribution kinetics has applications to a range of natural and manufacturing phenomena, including crystal growth or dissolution with agglomeration and/or breakage. A numerical solution to the PBE shows the evolution to a steady-state crystal size. The model allows assessment of various parameters, such as the fragmentation kernel, initial particle size distribution, and the aggregation rate. Interfacial energy, through the Gibbs–Thomson effect, has a strong influence on crystal growth–dissolution and denucleation of subcritical nuclei. The denucleation rate as a function of breakage rate coefficient was found to follow a power-law relationship.