Dynamics of first-order phase transitions: Theory of coarsening (Ostwald ripening) for open systems

Abstract

Late-stage diffusion-controlled coarsening during the process of phase separation is considered. We derive a reduced theory in terms of ordinary differential equations for the cluster density, mean cluster size, width of the cluster size distribution, and supersaturation. Parameters introduced by the approximations are fixed such as to yield agreement with the asymptotic Lifshitz-Slyozov-Wagner theory. The theory improves upon the work of Langer and Schwartz because it includes subcritical clusters as part of the minority phase and explicitly considers the width of the size distribution which controls the rate of coarsening. The theory is constructed in a way which allows treating open systems. For a two-cell model with diffusional coupling we numerically solve the full equation for the size distribution and prove the quality of our theory through the comparison. In addition, we propose an approximate procedure to include the effect of a finite volume fraction of the minority phase and the process of coagulation.