Kinetics of Precipitation Processes at Non-Zero Input Fluxes of Segregating Particles

We consider the process of formation and growth of clusters of a new phase in segregation processes in solid or liquid solutions in an open system when segregating particles are added continuously to it with a given rate of input fluxes, Φ. As shown here, the value of the input flux significantly affects the number of supercritical clusters formed, their growth kinetics, and, in particular, the coarsening behavior in the late stages of the process. The detailed specification of the respective dependencies is the aim of the present analysis, which combines numerical computations with an analytical treatment of the obtained results. In particular, a treatment of the coarsening kinetics is developed, allowing a description of the development of the number of clusters and their average sizes in the late stages of the segregation processes in open systems, which goes beyond the scope of the classical Lifshitz, Slezov and Wagner theory. As is also shown, in its basic ingredients, this approach supplies us with a general tool for the theoretical description of Ostwald ripening in open systems, or systems where the boundary conditions, like temperature or pressure, vary with time. Having this method at one's disposal supplies us with the possibility that conditions can be theoretically tested, leading to cluster size distributions that are most appropriate for desired applications.