Smoluchowski Coagulation — Kernel Scaling

Cluster aggregation: dN_k/dt = ½Σ K(i,j)N_i N_j − N_k Σ K(k,j)N_j. Different kernels give power-law size distributions or finite-time gelation.

Kernel type

Rate scale 0.10

Initial clusters N₀ 400

Clusters: 0 Max size: 0 Time: 0.00 Gel: No

Flory-Stockmayer gelation: Product kernel K(i,j)=ij gelates at t_gel=1/2. The gel fraction rises abruptly — a second-order phase transition. Constant kernel: N(k,t) ~ k^(-3/2) e^(-2k/N̄) (log-normal). Sum kernel: borderline gelation (t_gel→∞). Brownian: Smoluchowski's original derivation from diffusion-limited aggregation.