A level set method for three dimensional vector Stefan problems: Dissolution of stoichiometric particles in multi-component alloys

A sharp interface method is proposed for the dissolution of stoichiometric particles in multi-component alloys occurring during the heat treatments of as-cast aluminium alloys prior to hot extrusion. In the mathematical model, a number of non-linearly coupled diffusion equations are given to determine the position of the particle interface and the interfacial concentrations. A level set method is used to determine the interface position at each time step. Once the front position is known, a fixed-point iteration is used to find the interfacial concentrations. The model is applicable to both complete and incomplete dissolution in two and three spatial dimensions, and handles topological changes in a natural fashion. The numerical solution is compared with steady-state and self-similar exact solutions available for simple particle geometries. Subsequently, the model is applied to an AlMgSi-alloy to investigate the influence of the particle morphology in the dissolution kinetics.