A scaling generalization of the Smoluchowski equation is used to treat fluctuation effects in aggregation problems. In particular, we investigate the diffusion-limited cluster-cluster aggregation subject to the condition that single particles are fed into the system at a constant rate, h, while clusters larger than a fixed size are removed. Considering the zero-feed-rate limit as a critical point, we find that h plays the role of an external field conjugate to the order parameter which turns out to be the cluster density. The cluster density obeys dynamic scaling and, because of the finiteness of a kinetic coefficient, the dynamic critical exponents are expressible in terms of a static exponent. The exponents are determined by arguing that the zero-feed-rate process is in one universality class with the A+A0 diffusive annihilation problem. Our scaling theory is in agreement with available Monte Carlo simulation data.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics