Competing role of catalysis-coagulation and catalysis-fragmentation in kinetic aggregation behaviours

We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation, while the catalyst aggregates of the same species B or C perform self-coagulation processes. By means of the generalized Smoluchowski rate equation based on the mean-field assumption, we study the kinetic behaviours of the system with the catalysis-coagulation rate kernel K(i,j;l) ∝ lν and the catalysis-fragmentation rate kernel F(i,j;l) ∝ lμ, where l is the size of the catalyst aggregate, and ν and μ are two parameters reflecting the dependence of the catalysis reaction on the size of the catalyst aggregate. The relation between the values of parameters ν and μ reflects the competing roles between the two catalysis processes in the kinetic evolution of species A. It is found that the competing roles of the catalysis-coagulation and catalysis-fragmentation in the kinetic aggregation behaviours are not determined simply by the relation between the two parameters ν and μ, but also depend on the values of these two parameters. When ν > μ and ν ≥ 0, the kinetic evolution of species A is dominated by the catalysis-coagulation and its aggregate size distribution ak(t) obeys the conventional or generalized scaling law; when ν < μ and ν ≥ 0 or ν < 0 but μ ≥ 0, the catalysis-fragmentation process may play a dominating role and ak(t) approaches the scale-free form; and in other cases, a balance is established between the two competing processes at large times and ak(t) obeys a modified scaling law. (cross-disciplinary physics and related areas of science and technology)