Scaling in Aggregation Process with a Kernel Related to the Reaction Activities

We study the kinetics of a reversible aggregation model in which an aggregation reaction occurs between any two clusters and the fragmentation of the larger clusters occurs simultaneously. By investigating the mean-field rate equation of the process with a kernel related to the reaction activities we obtain the asymptotic solution of the cluster-mass distribution. It is found that the kinetic evolution behaviour of the clusters depends crucially on the details of the rate kernel. The cluster-mass distribution in the irreversible aggregation system obeys a conventional scaling law; while for the reversible case, the conventional scaling description of the cluster-mass distribution breaks down and the system falls in a modified scaling region.