Numerical Simulation of Ostwald Ripening using the Phase-Field Model

"The Ostwald ripening and growth and coarsening of the secondary dendrite arm are studied using a phase-field model. The phase-field parameters are obtained at a thin interface limit proposed by Kim et al. In Ostwald ripening analysis, the difference of the concentration due ·to· the curvature effect is shown. The third power of the average particle radius Rav is proportional to time and the ripening constant shows a good agreement with the value by Deppers et al. The particle radii distribution shows the transition behavior to attain a self-similar stationary shape. The growth and coarsening behavior of the secondary dendrite arm is also analyzed using a phase-field model. The estimated arm spacing and its dependence on time are in good agreements with experimental data.IntroductionThe ripening or coarsening process controls the microstructure during the late stage of solidification. The ripening phenomena are recognized firstly by the Ostwald [1]. The first quantitative analysis for the Ostwald ripening in the limit of vanishing solid fraction was provided by Lifshitz, Slyozov and Wagner (LSW) [2,3]. In their study, that the mean radius grows proportional to the cubic root of time and the size distribution of precipitations shows a ""self-similar"" shape are shown. Most of the studies for the Ostwald ripening confirm or predict these two general rules above. In case of finite solid fraction, the general rules are observed but the ripening constant is larger and the self-similar shape is wider than the LSW prediction respectively [4-6]. To analyze· the high solid fraction system, the theories that consider the solute field correlation are proposed [4,7-8]. In the theory, however, since the particle is treated as the point, the effect of the concentration field deviation from the monopole field should be taken into account. Recently the numerical simulation, in which not only diffusive transportation of solute but also convection effect is considered, has been done using a phase-field model [9]."