A population balance approach to the modeling of solid phase reactions

Abstract

A population balance approach is used to model solid phase reactions in terms of nuclei of the product phase dispersed in the reactant matrix. A conversion-time relationship is obtained by the solution of a set of moment equations derived from the population balance. Some previously known solutions for both homogeneous and heterogeneous nucleation are developed by this approach to demonstrate the relative ease of solution when compared with previously used integral techniques. A model for nucleus impingement at low conversions is formulated and applied to published data on the oxidation of cuprous iodide to illustrate the practical use of this technique. The classical Avrami model (Avrami, 1939, 1940, 1941) is modified to include the initial volume of a nucleus, and it is shown that insensitivities in the original model are removed by this improvement. The need for direct measurements of nucleation and growth rates is emphasized.