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.
Received: 11 July 2003
Revised: 30 October 2003
Accepted manuscript online:
PACS:
05.60.-k
(Transport processes)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 10305009, 10275048 and 10175008) and by the Zhejiang Provincial Natural Science Foundation of China (Grant Nos 102067 and 101002).
Cite this article:
Ke Jian-Hong (柯见洪), Wang Xiang-Hong (王向红), Lin Zhen-Quan (林振权), Zhuang You-Yi (庄友谊) Dynamic scaling of migration-driven aggregate growth 2004 Chinese Physics 13 772
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