Transition from nucleation to ripening in the classical nucleation model

With the use of the classical nucleation model, the passage from the initial stage of nucleation to the final stage of Ostwald ripening is studied. Direct numerical integration confirms that, under weak initial supersaturation, the drop of supersaturation occurs with a long delay but the relative drop is deep. For various initial supersaturation, the cluster size distribution approaches the single Lifshits-Slyozov-Wagner form. Based on an analysis of current in the cluster size space, a single variable model to describe the time evolution of supersaturation is proposed. A transition point from nucleation stage to ripening is given in terms of the surface free energy and the initial supersaturation. Several characteristic features of the distribution function and supersaturation are discussed, and the von Weimarn rules are derived.