Aggregation according to classical kinetics: from nucleation to coarsening

A previous paper [Y. Farjoun and J. C. Neu, Phys. Rev. E 78, 051402 (2008)] presents a simple kinetic model of the initial creation transient, starting from pure monomer. During this transient the majority of clusters are created, and the distribution of cluster sizes that emerges from it is predicted to be discontinuous at the largest cluster size. It is well known that the further evolution according to the Lifshitz-Slyozov model of coarsening preserves this discontinuity. The result is at odds with the original proposal of Lifshitz and Slyozov, that the physical late-stage coarsening distribution is the smooth one. The current paper presents an analytic-numerical solution of the Lifshitz-Slyozov equations, starting from the discontinuous creation distribution. Of course, this analysis selects the discontinuous late-stage coarsening distribution, but there is much more. It resolves the intermediate stages between the creation transient and late-state coarsening and provides specific scales of time and cluster size that characterize the onset of coarsening.