The dissolution of an $Al_2Cu$ particle is considered. A characteristic property is that initially the particle has a non-smooth boundary. Furthermore the dissolution may be controlled by an interface reaction. The mathematical model of this dissolution process contains a description of the particle interface, of which the position varies in time. Such a model is called a Stefan problem. We use the finite element method to solve this problem numerically. The displacement of the free boundary is computed by a method based on the balance of atoms. This method leads to good results, also for non-smooth boundaries. Some numerical experiments are given for the dissolution of an $Al_2Cu$ particle in an $Al$-$Cu$ alloy, with a varying rate of the interface reaction.

Theoretical approximation to solutions (msc 35A35), Free boundary problems (msc 35R35), Finite difference methods (msc 65M06), Stefan problems, phase changes, etc. (msc 80A22)
Modelling, Analysis and Simulation [MAS]

Vuik, C, Segal, G, & Vermolen, F.J. (1999). A conserving discretization for a Stefan problem with an interface reaction at the free boundary. Modelling, Analysis and Simulation [MAS]. CWI.