A mathematical model for the dissolution of particles in multi-component alloys

Dissolution of stoichiometric multi-component particles is an important process ocurring during the heat treatment of as-cast aluminium alloys prior to hot extrusion. A mathematical model is proposed to describe such a process. In this model equations are given to determine the position of the particle interface in time, using a number of diffusion equations which are coupled by nonlinear boundary conditions at the interface. This problem is known as a vector valued Stefan problem. Moreover the well-posedness of the moving boundary problem is investigated using the maximum principle for the parabolic partial differential equation. Furthermore, for an unbounded domain and planar co-ordinates an analytical asymptotic approximation based on self-similarity is derived. Moreover, this self-similar solution and the asymptotic approximation are extended to the vector valued Stefan problem. The approaches are compared to each other and the asymptotic approximation is used to gain insight into the influence of all components on the dissolution. Subsequently a numerical treatment of the vector valued Stefan problem is described. The numerical method is compared with solutions by analytical methods. Finally, an example is shown.