Premium
Two‐mode models for describing mixing effects in homogeneous reactors
Author(s) -
Chakraborty Saikat,
Balakotaiah Vemuri
Publication year - 2002
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690481116
Subject(s) - micromixing , mixing (physics) , thermodynamics , isothermal process , chemistry , diffusion , homogeneous , mechanics , bifurcation , damköhler numbers , physics , nonlinear system , turbulence , microfluidics , quantum mechanics
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 (C m ) and the spatially averaged (〈C〉) concentrations. One equation traces the evolution of C m 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, C m 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.