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Abstract

The Liapunov–Schmidt technique of bifurcation theory is used to spatially average the convection–diffusion–reaction equation over smaller time/length scales to obtain two-mode models (TMMs) for describing mixing effects in homogeneous tubular, loop/recycle and tank reactors. For the isothermal case, these TMMs are described by a pair of coupled balance equations involving the mixing-cup (Cm) and the spatially averaged (〈C〉) concentrations. One equation traces the evolution of Cm with (residence) time, while the other is a local equation that describes mixing resulting from coupling between diffusion, velocity gradients, and reaction at the local scales, in terms of an exchange between the two modes, Cm and 〈C〉. The TMMs have many similarities with the two-phase models of catalytic reactors, with concept of transfer between phases being replaced by that of exchange between the two modes. Examples are presented to illustrate the usefulness of these TMMs in predicting micromixing effects on homogeneous reactions.