Markov Models of Coarsening in Two-Dimensional Foams with Edge Rupture

We construct Markov processes for modeling the rupture of edges in a two-dimensional foam. first describe network model tracking topological information foam networks with state space combinatorial embeddings. Through mean-field rule randomly selecting neighboring cells rupturing edge, we consider simplified version sequence $$\ell _1({\mathbb {N}})$$ which counts total numbers $$n\ge 3$$ sides (n-gons). Under large cell limit, show that number densities n-gons mean field are solutions an infinite system nonlinear kinetic equations. This is comparable to Smoluchowski coagulation equation coalescing particles under multiplicative collision kernel, suggesting gelation behavior. Numerical simulations reveal model, and also statistical behavior between models.