(560iq) Solid-Solid Reactions: A Variation on a Classical Theme

All the classical models of solid-solid reacting systems, assume that the contact among reacting particles happen in continuous mode like solid-fluid reacting systems. Whereas, to precisely model these systems, only a few attempts made till date based on a rigorous account of the fact that the contact between reacting particles only occurs at a finite number of points on the surface of particles. 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 locations called as ‘contact-points’, also 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. The main assumptions for the study are isothermal conditions, only one (mobile) reactant species is diffusing into the matrix of other (stationary) reactant particles and stationary reactant particle size remains same during course of the reaction. The parameters involved in this models are Thiele Modulus (Th), density parameter (K) and contact points (N_AB). The rigorous formulated model extends over significant ranges of the above mentioned parameters.

Further the present model is compared with the most recent similar approximate Dalvi-Suresh (DS) model in this genre of contact point modelling. Dalvi-Suresh model is among the few which shows the correct asymptotic behavior in the limit of large number of contact points. However, the assumptions made in DS model, in order to keep the model mathematically tractable were not been validated previously in a rigorous way. So, in this work by comparing the results of our rigorously formulated model with the DS model, the applicability of the latter is studied, which proved that the simplified DS model can be applicable in the range of strong diffusion control (High Th) to moderate diffusion control only fails in case of reaction kinetic control (low Th) which is unlikely to happen in solid-solid reacting systems. However for the case of small density difference of the two reactants (low K), the assumption which treats the unsteady state behavior as a pseudo-steady state is limiting its accuracy for intermediate number of contact points.

Currently the work to plot the parametric space diagram for DS model is going on. Also the new model which accounts for the size change of reactant particle during the reaction due to formation of product is under study.