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We solve the standard Lifshitz-Slyozov (LS) model with conservation of totalparticles in the limit of small super-saturation. The new element is aneffective initial condition that follows from the initial exhaustion ofnucleation as described in a previous paper [Farjoun and Neu, Phys. Rev. E 78].The effective initial condition is characterized by a narrow distribution ofcluster-sizes, all much larger than critical. In the subsequent solution, oneof the LS similarity solutions emerges as the long-time limit, as expected. Butour solution tells more. In particular, there is a "growth" era prior to whatis usually called "coarsening". During "growth" the clusters (all of nearly thesame size much larger than critical) eventually exhaust the super-saturation(the exhaustion of nucleation in the previous era results from only a smalldecrease in super-saturation). This allows the critical size to catch up to theclusters, and the traditional "coarsening" begins: Subcritical clustersdissolve and fuel the growth of the remaining super-critical clusters. Ouranalysis tracks the evolution of cluster sizes during growth and coarsening bycomplimentary use of asymptotic and numerical methods. We establishcharacteristic times and cluster sizes associated with growth and coarseningfrom physical parameters and the initial super-saturation. The emergingdistribution is discontinuous at the largest cluster size, and our modelselects the discontinuous LS similarity solution as the long time limit. Thereare strong indications that the smooth similarity solution proposed in theoriginal LS paper emerges on a, yet longer, late-coarsening time-scale.

Aggregation According to Classical Kinetics--From Nucleation to Coarsening