A model for particle dissolution was formulated for the case of several simultaneously diffusing and strongly interacting alloying elements. The model was analyzed by using diagonalization of the diffusion matrix. A numerical solution procedure, also based upon diagonalization, was proposed. Further, self-similar solutions for the resulting moving boundary problem were derived for the case of both a diagonalizable and non-diagonalizable diffusion matrix. Finally, this technique was used to approximate a 2-dimensional problem with finite elements.

Cross-Diffusion Controlled Particle Dissolution in Metallic Alloys. F.J.Vermolen, C.Vuik, S.van der Zwaag: Computing and Visualization in Science, 2005, 8[1], 27-33