Nucleation, growth, and coarsening for two- and three-dimensional phase transitions

Phase transitions from a metastable state often occur by nucleation accompanied by particle growth and eventually by Ostwald coarsening. In closed systems, the supersaturation declines as particles nucleate and grow, causing an increase in the stable critical nucleus size. Particles below the critical size dissolve spontaneously during coarsening and their mass is released to contribute to further growth of remaining particles. By developing a population balance model that represents nucleation, growth, and coarsening, we here determine the dynamics of particle size distributions (PSDs). The governing equations are solved numerically to show that the transition from nucleation and growth to coarsening occurs over a relatively long time period. The asymptotic coarsening stage reveals a power-law increase in average particle mass as the PSD evolves to a (minimum) polydispersity index of unity for both two-dimensional (2-D) and 3-D phase transitions. The model agrees with published conclusions that nucleation and coarsening overlap when interfacial energy is small or supersaturation is large.