Chemically reactive generalized Taylor dispersion phenomena

Michael Shapiro*, Howard Brenner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

Generalized Taylor dispersion theory for nonreactive solutes (Brenner 1980a; 1982) undergoing convection and diffusion is extended to include irreversible first‐order volumetric and surface chemical reactions possessing position‐dependent reactivity coefficients at the microscale. For sufficiently long times the equivalent chemical kinetic description of the rate of solute depletion at the macroscale is shown to manifest itself as a single constant reactivity coefficient K̄* characterizing an apparent first‐order irreversible volumetric reaction. Subtraction of this gross solute depletion rate from the original microscale transport equation permits the resulting Taylor dispersionlike problem to be resolved by a solution scheme closely paralleling that for the comparable nonreactive case. This allows a straightforward determination of the mean global solute velocity vector Ū* and dispersivity dyadic D̄* appearing in the macroscale convection‐diffusion‐reaction equation describing the local‐space averaged mean transport process. By way of example, these three coefficients are explicitly calculated for reacting and diffusing solute particles sedimenting from a solvent flow occurring between two parallel plates onto the reactive surface of one of these plates.

Original languageEnglish
Pages (from-to)1155-1167
Number of pages13
JournalAICHE Journal
Volume33
Issue number7
DOIs
StatePublished - Jul 1987
Externally publishedYes

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