A model for particle dissolution in multi-component alloys
by
Fred Vermolen
Mathematics and Computing Centre, Amsterdam, Netherlands
Coauthors: Kees Vuik (Faculty of Technical Mathematics and Informatics, Delft), Sybrand van der Zwaag (Laboratory for Materials Science, Delft)

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.

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 approach based on self-similarity is given. Moreover, this self-similar solution is extended to the vector valued Stefan problem. From this extension follows that we can approximate the dissolution rate for the vector valued Stefan problem using a quasi-scalar Stefan problem (a Stefan problem with only one diffusing phase) for some cases. The effective diffusion coefficient is then obtained by a geometric mean of all diffusion coefficients. The weight factors come from the concentrations in the particle.

Subsequently a numerical solution of the vector valued Stefan problem is described. This solution is based on a finite volume discretisation of the diffusion equations for all components. The nonlinear boundary conditions are solved using a discrete Newton Raphson iteration procedure. The numerical method is compared with solutions by analytical methods.

In the above described model the particle and the cell in which the particle dissolves have the same geometry. For a Stefan problem with only one component (a scalar Stefan problem), we compare this model to a model with two spatial co-ordinates using finite element calculations, where the particle and cell have different geometry.

Date received: February 15, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caco-08.