Abstract
We study the possible intantaneous gelation in n-tuple coagulation processes with a pairwise coalescence mechanism. This reaction mechanism, which is characteristic of the many-body aggregation model, and is not shared by the usual binary coagulation, may increase the reaction rate and so make instantaneous gelation a physically possible process for the n-tuple coagulation model. We show that the generalized Smoluchovski coagulation equation (GSE) predicts instantaneous gelation if the reaction kernels behave as as , with an exponent satisfying . This type of reaction kernel is related to the multiple-site n-tuple coagulation process, and corresponds to possible physical systems, in contrast to the case of binary coagulation where such kernels do not occur in the corresponding physical systems. We also study the structure of gel solutions of the GSE. We found that, if , the cluster size distribution approaches a universal form at large times .
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