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

Dissolution of stoichiometric multi-component particles is an important process occurring during the heat treatment of as-cast aluminum 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. A necessary condition for existence of a solution of the moving boundary problem is proposed and investigated using the maximum principle for the parabolic partial differential equation. Furthermore, for an unbounded domain and planar co-ordinates an asymptotic approximation based on self-similarity is derived. 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 solution is compared with solutions obtained by the analytical methods. Finally, an example is shown.