Numerical analysis of Ostwald ripening in two-dimensional systems

This work addresses theory of Ostwald ripening based on the continuum second order kinetic equation for the size distribution of embryos over sizes. Numerical studies are performed with two-dimensional condensing systems having different growth laws of islands, using different forms of kinetic equation. The material influx into the system is terminated to enable the Ostwald ripening process. We obtain numerical solutions for the size distributions with and without fluctuation effects described by the second derivative in the kinetic equation. We show that fluctuations lead to a considerable broadening of size distribution at the early Ostwald ripening step in the diffusion limited growth of islands. Comparison of our numerical distributions with the deterministic Lifshitz-Slezov shape shows that the latter in principle withstands fluctuations. However, the correspondence between the numerical large time asymptotes and the Lifshitz-Slezov spectra is not perfect, particularly in the diffusion-induced growth regime, and becomes worse when the fluctuations are included.