Mesoscopic simulation of Ostwald ripening

The self-organization of particles in a two phase system in the coexistence region through a diffusive mechanism is known as Ostwald ripening. This phenomenon is an example of a multiscale problem in that the microscopic level interaction of the particles can greatly impact the macroscale or observable morphology of the system. Ostwald ripening is studied here through the use of a mesoscopic model which is a stochastic partial integrodifferential equation that is derived from a spin exchange Ising model. This model is studied through the use of recently developed and benchmarked spectral schemes for the simulation of solutions to stochastic partial differential equations. The typical cluster size is observed to grow like t^{frac(1, 3)} over range of times with faster growth at later times. The results included here also demonstrate the effect of adjusting the interparticle interaction on the morphological evolution of the system at the macroscopic level.