Gas–solid reaction model for a shrinking spherical particle with unreacted shrinking core

A heterogeneous reaction model is developed to represent the gas–solid reaction consisting of two-step reactions: formation of a solid intermediate on the core of unreacted solid and consumption of the solid intermediate. The presented model takes into account the shrinkage of both the unreacted core and the solid particle itself. The model successfully represents the fluorination of uranium dioxide where uranium hexafluoride gas is produced through uranyl fluoride as a solid intermediate. The rates of the shrinkage are discussed in detail for general cases by solving an ordinary differential equation for two radii of the particle and the unreacted core. Two parameters, the ratio of the reaction rates between the two steps and the non-dimensional diffusion rate of a reactant gas into the intermediate, control the rates of the shrinkage. Effective range of the model is specified in terms of the two parameters.