Theory of nucleation and growth during phase separation

We present a new model for the entire process of phase-separation that combines steady-state homogeneous nucleation theory with the classical Lifshitz-Slyozov mechanism of ripening, modified to account for the substantial correlations among the droplets. A set of self-consistent interface equations describes the decay of metastable states, incorporating naturally the crossover from early-stage nucleation to the late-stage scaling regime without ad hoc assumptions. We present simulation results for both two and three dimensions. We also present a mean-field, Thomas-Fermi approximation that provides an approximate solution to the many-body problem