Gelation in kinetic growth models

Abstract

A direct numerical simulation of kinetic aggregation is presented in which the probability of sticking depends on the size of the clusters. It is found that the fractal dimension of the largest cluster is different depending on whether the gelation phenomenon occurs or not. In the case of Brownian diffusion, the model of Witten and Sander is recovered when gelation occurs, while the alternative model of "clustering of clusters" is recovered when gelation does not occur. Another model (with long-range forces) is also considered.