Ostwald Ripening of precipitates and self similarity of size distributions in reaction controlled growth

We present a mathematical model to describe competitive growth of spherical precipitates in reaction-controlled systems. In this model the flux of solute atoms through the interface depends on the interface migration velocity and on the differences of chemical potential at the interface. The growth-rate obtained is dependent on the precipitate radius, much like in the diffusion-controlled case. Numerical simulations were performed using a modified finite-difference approach where the time-step increase changes during evolution to avoid dissolution of more than one precipitate each step. By using the continuity equation we obtained an analytical function that represents the self-similar shape of the precipitate-size distribution dependent of the growth-parameter ν. The effect of ν on the coarsening evolution was investigated. Our results show that the precipitate size distribution obtained from the numerical simulations agrees well with the analytical solution. As predicted by the theory, we obtained the growth parameter (ν = 4) and the temporal dependence of the mean-radius (t ^1/2) different of the diffusion case, ν = 6.75 and t ^1/3. We also show that the self-similarity of the PSD is independent of the initial PSD.