Exchange Driven Growth

Original · EN

We study a class of growth processes in which clusters evolve via exchange of particles. We show that depending on the rate of exchange there are three possibilities: I) Growth: Clusters grow indefinitely; II) Gelation: All mass is transformed into an infinite gel in a finite time; and III) Instant Gelation. In regimes I and II, the cluster size distribution attains a self-similar form. The large size tail of the scaling distribution is Phi(x) exp(-x²⁻ν), where nu is a homogeneity degree of the rate of exchange. At the borderline case nu=2, the distribution exhibits a generic algebraic tail, Phi(x) x⁻⁵. In regime III, the gel nucleates immediately and consumes the entire system. For finite systems, the gelation time vanishes logarithmically, T [N]⁻⁽ν⁻²⁾, in the large system size limit N→∞. The theory is applied to coarsening in the infinite range Ising-Kawasaki model and in electrostatically driven granular layers.