Ostwald Ripening in Two Dimensions: Treatment with Pairwise Interactions

Ostwald ripening is the last stage of the evolution of a system with two coexisting phases. It is a relatively simple nonequilibrium phenomenon with several interesting features. For example, as the system coarsens it goes through a scaling state, one which looks the same (up to an overall length scale, which grows) at all times. The dynamics of the problem can be mapped, in two dimensions, onto an evolving Coulomb system. In this work we present a brief summary of a novel theoretical approach to this problem, based on an analytic derivation (using a mean-field approach) of an effective two-body interaction between droplets of the minority phase. The resulting interacting many-body dynamics is solved by a very efficient numerical algorithm, allowing us to follow the evolution of more than 10⁶ droplets on a simple workstation. The results are in excellent agreement with recent experiments.