Modelling solid-solid reactions: Contact-point approach

Abstract

In the modelling of solid-solid reacting systems, only a few attempts made till date account for the fact that contact between reactants only occurs at a finite number of points of contact on the surface. The Dalvi-Suresh model is among the few, and shows the correct asymptotic behavior in the limit of large number of contact points. However, the assumptions made in order to keep the model mathematically tractable have not been validated rigorously. In this work, we formulate a general contact-point based model for solid-solid reactions and simulate it using a finite element methodology on the COMSOL Multiphysics® platform. The model takes account the limited contact between two reactants at specific ‘contact-points’, the unsteady-state behavior of the reaction, and spans the entire gamut of regimes from complete kinetic control to complete diffusion control. The diffusion-controlled case is particularly important, being a very likely scenario in solid-solid reactions, and also because a number of asymptotic cases for this case are available in the literature. It is shown by solving and comparing the results of the present rigorous model with the Dalvi and Suresh model that the applicability of the latter extends over significant ranges of the parameters involved, but one assumption that of approximating the unsteady state behavior by a pseudo-steady state treatment, may limit its accuracy for intermediate number of contact points.