A discrete model of Ostwald ripening based on multiple pairwise interactions

A discrete multi-particle model of Ostwald ripening based on direct pairwise interactions is developed for particles with incoherent interfaces as an alternative to the classical LSW mean field theory. 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. The multi-particle diffusion is described through the definition of an interaction volume containing all the particles involved in the exchange of solute. At small volume fractions this is proportional to the size of the central particle, at higher volume fractions it gradually reduces as a consequence of diffusion screening described on a geometrical basis. The topological noise present in real systems is also included. 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. An excellent agreement with experiments is obtained for 3D particle size distributions of solid-solid and solid-liquid systems with volume fraction 0.07, 0.30, 0.52 and 0.74. The kinetic constant of the model depends on the cube root of volume fraction up to about 0.1, then increases rapidly with an upward concavity. It is in good agreement with the available literature data on solid-liquid mixtures in the volume fraction range from 0.20 to about 0.75.