Analytical approach to particle dissolution in a finite medium

Abstract

An important part in the total production process of extrudable aluminium alloys is the homogenisation treatment of the as cast billets before hot extrusion. During this homogenisation treatment several microstructural changes take place. The most important changes are the dissolution of the precipitates formed during solidification and the homogeneous redistribution of alloying elements. Modelling of the particle dissolution in simple binary systems has recently been achieved by Tundal and Ryum using a numerical model. In their model a moving interface between the particle and the aluminium rich matrix was taken into account as well as the finite size of the cell in which the particles dissolve. Furthermore, conditions of local equilibrium at the particle/matrix interface were assumed at all stages of the dissolution process. This was a significant improvement to earlier analytical models in which the interface was assumed to be stationary. The present work describes the development of a semianalytical model for the dissolution of spherical particles infinite media also assuming a moving boundary. The results of the present semianalytical model are compared to those of the numerical model. A fairly good agreement was obtained for most conditions. At long dissolution times the predictions of the two models deviate due to a simplifying assumption used in the analytical model.