Nonscaling and source-induced scaling behaviour in aggregation model of movable monomers and immovable clusters

Abstract

General discussion of the aggregation kinetics for the wide class of aggregation models in which cluster growth occurs by bonding reactions between movable monomers and immovable clusters is presented. The study is carried out in terms of Smoluchowski's rate equations. The authors treat a general homogeneous case where the monomer-cluster reaction rates vary as kgamma , with the cluster size k. For models with 0< gamma <1 without a source they find that systems evolve to a final 'frozen' state. Evolution behaviour of the system appears to be nonscaling, but the deviation from a frozen state has a self-similar form. For the systems with a source, they have found that the solution has a scaling form in the most important party of the cluster-size distribution except for an asymptotically ignorable tail. They also carried out the analysis of the structure of the tail and of the thin boundary layer separating the scaling and nonscaling tail regions. The qualitative explanation of nonscaling and source-induced scaling behaviour may be made in terms of 'internal' time inherent for the models of these types.