The asymptotic status of the Sherwood-Pigford model in the theory of absorption with chemical reaction

Abstract

The Sherwood-Pigford model for absorption accompanied by instantaneous irreversible chemical reaction is an essentially discontinuous one, where a moving front across which concentration gradients suffer a discontinuity is assumed to exist. The case where the reaction is both instantaneous and irreversible is a doubly singular one. In this paper, a boundary-layer analysis is developed which shows that, for irreversible reactions, the Sherwood-Pigford model equations are approached asymptotically for arbitrary kinetics when an appropriate time scale of the reaction becomes sufficiently small. It is also shown that the same limit is approached for arbitrary stoichiometry in the case of instantaneous reactions when the ratio of the interface to the bulk concentration of volatile component becomes sufficiently large. Finally, a general estimate is obtained of the thickness of the reaction zone (which is assumed to be zero in the Sherwood-Pigford model) for the general case where the reaction is neither instantaneous nor irreversible.