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Keywords:

  • solid-phase reactions;
  • shrinking core model;
  • uniform reaction model;
  • Ishida–Wen;
  • Ginstling–Brounshtein

Abstract

Models such as the Ishida–Wen, or even more commonly the shrinking core models (Ginstling–Brounshtein being an important example), have long been used in the analyses of reactions in particles, particularly in solid–solid systems. There have been a few analyses of the validity of the assumptions made in these models, but to date, no comparison has been undertaken of these models against a general model to delineate their regions of applicability in the parameter space. In this article, we present a general unsteady-state model that subsumes the earlier models as special cases. Nondimensionalization leads to the identification of two governing parameters in the model, a diffusion-reaction parameter, and a relative abundance parameter. By solving the general model and comparing the solutions with those of the approximate models in the parameter space, conditions under which the approximate models apply, and the errors that result from their application in other situations, have been identified. © 2012 American Institute of Chemical Engineers AIChE J, 58: 3161–3166, 2012