Distribution kinetics theory of Ostwald ripening

Ostwald ripening occurs near equilibrium conditions when larger clusters grow at the expense of dissolving smaller clusters. We propose that ripening kinetics for growth and dissolution can be represented by a general population balance equation (PBE) for the cluster size distribution (CSD). This PBE can also describe cluster growth or dissolution in the absence of ripening. The Kelvin equation provides the effect of interfacial energy on solubility in terms of the cluster radius. The continuity equation conventionally applied to ripening or cluster growth is obtained as a Taylor series expansion of the governing PBE. Numerical and moment solutions of the PBE show the evolution of the CSD. The cluster number density declines, and the average cluster mass increases. The variance can initially increase as the CSD broadens by growth of large clusters, and then decrease until eventually vanishing. The final state after a long time is a single large cluster in equilibrium with the fluid solution.