PERTURBATION ANALYSIS OF GAS SOLID REACTIONS .2. REDUCTION TO THE DIFFUSION-CONTROLLED SHRINKING CORE

Perturbation solutions to the gas-solid reaction model of Part I are obtained for pi --> infinity and beta --> 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. beta --> 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 psi) it is found that the conversion correction to the shrinking core model predicition can be significant even for reasonably large values of psi, and the error is as serious as that found in Part I for moderate diffusional resistance. For the alternative case of small beta 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