SIMULATION OF PARTICLE GROWTH AND OSTWALD RIPENING VIA THE CAHN-HILLIARD EQUATION

The Cahn-Hilliard-equation (CHE) is a diffusion equation extended by terms taking interfacial energies into account. It has been established as a useful tool to understand phase separation of a binary system in a qualitatively correct frame. We study the processes of phase separation by numerical simulations based on the CHE. Specifically we consider the growth of particles in a supersaturated matrix as well as the process of Ostwald ripening. In both cases the results are compared with established theories such as Zener's law and the LSW-theory for Ostwald ripening. The numerical simulation, especially in the case of Ostwald ripening, can be helpful to answer open questions concerning the dependence of the growth rate and the asymptotic distribution of the particle sizes as a function of the volume fraction of the precipitate. As an example for the parameters of the CHE we have chosen the monotectic alloy aluminium-indium.