Perturbation analysis of gas-solid reactions. II. Reduction to the diffusion-controlled shrinking core

Abstract

Perturbation solutions to the gas-solid reaction model of Part I are obtained for ψ → ∞ and β → 0, both of which are found to yield the product layer diffusion-controlled shrinking core result in the leading order. In the latter case (i.e. β → 0) it is shown that a conceptual difficulty arises for internal structures which require infinite time for complete conversion since a fully reacted product layer cannot form. One-term perturbation corrections for both cases are also obtained using a singular perturbation method. For the first case (i.e. large ψ ) it is found that the conversion correction to the shrinking core model prediction can be significant even for reasonably large values of ψ , and the error is as serious as that found in Part I for moderate diffusional resistance. For the alternative case of small β the error in the shrinking core model prediction for the conversion is found to be inordinately large and even approaching 0.6-0.8 in several cases. It appears from the results that the more viable interpretation of the diffusion-controlled form of the shrinking core model is that of a relatively rapid interfacial reaction on the core surface rather than rapid internal conversion as considered in the literature.