A local dynamical scaling behavior of the Ostwald ripening in nonuniform systems

Abstract

The Ostwald ripening of droplets of precipitates in nonuniform systems is investigated by using dynamical scaling assumptions and by performing numerical simulations. First, we analytically study the Ostwald ripening in nonuniform systems by using dynamical scaling assumptions. To examine validity of the dynamical scaling assumptions, we numerically solve the basic model evolution equations for both the supersaturation of the solute and the size distribution functions of droplets for the nonuniform system where several homogeneous cells are coupled together by the diffusion of the solute. We found an important effect of the initially large droplets, which govern the late stage dynamics of the coarsening process. Next, to investigate the nonuniform system which consists of many cells, we perform a reduction of the degrees of freedom of the size distribution function and construct a simplified model (a reduced model). In deriving this reduced model, we take into account the importance of the large size droplets by dividing the size distribution function of droplets into two parts; one is for smaller droplets and the other for the larger droplets. We perform numerical simulations of the reduced model and study the formation of the spatial structure of precipitations. An appreciable mass transport is induced by an initial spatial inhomogeneity in the size distribution function of large droplets which dominates the system at later times. Depending on the spatial inhomogeneity of the system, the size distribution function of droplets is locally characterized by a new scaling function, which is related to the changing rate of the total volume of droplets in the region and is different from the Lifshitz–Slyozov–Wagner (LSW) universal scaling function for uniform systems.