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

Abstract

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) ∝ l ν and the catalysis-fragmentation rate kernel F (i, j; l) ∝ l µ , 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 a k (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 a k (t) approaches the scale-free form; and in other cases, a balance is established between the two competing processes at large times and a k (t) obeys a modified scaling law.