Revisiting the Ostwald Ripening: A Discrete Model Based on Multiple Pairwise Interactions

Abstract

A discrete multi-particle model of Ostwald ripening based on direct pairwise interactions between precipitates with incoherent interfaces is presented. Although based on the mean field concept, it is a valid alternative to the classical LSW theory. The main differences with respect to the classical approach can be summarized as follows: i) Particles interact the one another; ii) The first Fick’s law is considered to evaluate the fluxes of matter instead of the quasi stationary solution of the concentration field around particles; iii) The rate of matter exchange depends on the average surface-to-surface interparticle distance, a characteristic feature of the system which naturally incorporates the effect of volume fraction of second phase; iv) The multi-particle diffusion is described through the definition of an interaction volume containing all the particles involved in the exchange of solute. The model is in excellent agreement with the experimental data available in the literature. The shape of the quasi-stationary 3D particle size distribution of solid-solid and solid-liquid systems is well predicted from volume fractions of 0.07, 0.30, 0.52 and 0.74. Similarly, a very good prediction of the dependence of the kinetic constant of the coarsening process on the volume fraction of precipitates is obtained with reference to literature data on solid-liquid mixtures in the volume fraction range from 0.20 to about 0.75. For volume fractions below about 0.1 the model predicts broad and right-skewed stationary size distributions resembling a lognormal function. Above this value, a transition to sharper, more symmetrical but still right-skewed shapes occurs.