Solvable n-species aggregation processes with joint annihilation.
We study the kinetic behavior of the aggregation-annihilation processes of an n-species (n> or =3) system, in which an irreversible aggregation reaction occurs between any two clusters of the same species and an irreversible complete annihilation reaction occurs only between one certain A(n) species and each of the other A(m) species (m=1,2,...n-1). Based on the mean-field theory, we investigate the rate equations of the processes to obtain the asymptotic solutions of the cluster-mass distributions in several different cases. The results show that the evolution behavior of the system depends crucially on the ratios of the equivalent aggregation rate of A(m) species and the aggregation rate of A(n) species to the annihilation rate. The cluster-mass distribution of each species always obeys a conventional scaling law or a modified one, and the scaling exponents depend only on the reaction rates for most cases. However, when both the equivalent aggregation rate of A(m) species and the aggregation rate of A(n) species are twice as large as the annihilation rate, the scaling exponents depend on the reaction rates as well as the initial concentrations.
Ke
Jianhong
J
Department of Physics, Wenzhou Normal College, Wenzhou 325027, China. kejianhong@163.com
Lin
Zhenquan
Z