Scaling in steady-state cluster-cluster aggregation

Tams Vicsek, Paul Meakin, Fereydoon Family

Research output: Contribution to journalArticle

94 Citations (Scopus)


The diffusion-limited cluster-cluster aggregation model is investigated under conditions which for long times lead to steady-state coagulation. Single particles are added to the system at a constant rate and the larger clusters appearing as a result of the aggregation process are removed according to various rules. Our results show that the dependence of the number of clusters, N(t), on the feed rate in a unit volume and the time t can be well represented by a scaling form N(t)f(t) with a scaling function f(x)x for x1 and f(x)=1 for x1. The exponents and are found to depend on the spatial dimension d, of the system, but within the statistical errors they always satisfy the relation +=1 in accordance with the prediction of a generalized rate equation discussed by Rcz (see the companion paper). The values we have obtained for and are consistent in two and three dimensions with the corresponding results of the Smoluchowski equation approach but inconsistent in one dimension. This can be considered as an indication of the fact that the upper critical dimension for the kinetics of the diffusion-limited cluster-cluster aggregation model is 2.

Original languageEnglish
Pages (from-to)1122-1128
Number of pages7
JournalPhysical Review A
Issue number2
Publication statusPublished - Jan 1 1985

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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