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 $K(i,j;l)\propto l^{\nu}$ and the catalysis-fragmentation rate kernel $F(i,j;l)\propto l^{\mu}$ , where l is the size of the catalyst aggregate, and $\nu$ and $\mu$ are two parameters reflecting the dependence of the catalysis reaction on the size of the catalyst aggregate. The relation between the values of parameters $\nu$ and $\mu$ 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 $\nu$ and $\mu$, but also depend on the values of these two parameters. When $\nu> \mu$ and $\nu\geqslant 0$, 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 $\nu<\mu$ and $\nu \geqslant 0$ or $\nu>0$ but $\mu \geqslant 0$, 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.

Key words: kinetic aggregation behaviour, catalysis-coagulation, catalysis-fragmentation, rate equations