Denucleation rates during Ostwald ripening: Distribution kinetics of unstable clusters

During Ostwald ripening in vapor–liquid or liquid–solid systems, unstable clusters, which are smaller than the critical nucleus size, rapidly disappear. This denucleation process is distinct from the reversible dissolution of stable clusters that are larger than the critical size but are more soluble than larger clusters because of the Gibbs–Thomson effect. Thus, ripening involves larger clusters growing, smaller clusters shrinking, and unstable clusters rapidly disintegrating. We show how the denucleation rate can be estimated based on the appropriate cluster distribution dynamics (population balance) equations. Monomer addition and dissociation from an unstable cluster occur at rates determined by the energy profile, which is formulated with classical nucleation concepts. Effectively, the cluster loses free energy as monomers dissociate, and falls down the energy stair steps. Numerical results for the distribution dynamics equations reveal the influence of the minimum number of dimensionless parameters, and demonstrate that denucleation is very fast compared to the ripening rate