关键词: kinetic behaviour, migration, aggregate growth, scaling law

Abstract: We study the kinetic behaviour of the growth of aggregates driven by reversible migration between any two aggregates. For a simple model with the migration rate $K(i;j)=K^′(i;j)\varpropto i^uj^v$ at which the monomers migrate from the aggregates of size i to those of size j, we find that the aggregate size distribution in the system with $u+v\leq3$ and $u<2$ approaches a conventional scaling form, which reduces to the Smoluchovski form in the $u=1$ case. On the other hand, for the system with $u<2$, the average aggregate size $S(t)$ grows exponentially in the $u+v=3$ case and as $(t\ln t)^{1/(5-2u)}$ in another special case of $v=u-2$. Moreover, this typical size $S(t)$ grows as $t^{1/(3-u-v)}$ in the general $u-2<v<3-u$ case; while it always grows as $t^{1/(5-2v)}$ in the $v<u-2$ case.

Key words: kinetic behaviour, migration, aggregate growth, scaling law