Exchange-driven growth

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 Φ(x)∼exp(-x^2-ν), where ν is a homogeneity degree of the rate of exchange. At the borderline case ν=2, the distribution exhibits a generic algebraic tail, Φ(x)∼x^-5. In regime III, the gel nucleates immediately and consumes the entire system. For finite systems, the gelation time vanishes logarithmically, T∼[lnN]^-(ν-2), in the large system size limit N⃗∞. The theory is applied to coarsening in the infinite range Ising-Kawasaki model and in electrostatically driven granular layers.