Effective dispersion equations for reactive flows involving free boundaries at the microscale

K. Kumar, T.L. Noorden, van, I.S. Pop

Research output: Contribution to journalArticleAcademicpeer-review

27 Citations (Scopus)
105 Downloads (Pure)

Abstract

We consider a pore-scale model for reactive flow in a thin two-dimensional strip, where the convective transport dominates the diffusion. Reactions take place at the lateral boundaries of the strip (the walls), where the reaction product can deposit in a layer with a nonnegligible thickness compared to the width of the strip. This leads to a free boundary problem, in which the moving interface between the fluid and the deposited (solid) layer is explicitly taken into account. Using asymptotic expansion methods, we derive an upscaled, one-dimensional model by averaging in the transversal direction. The result is consistent with (Taylor dispersion) models obtained previously for a constant geometry. Finally, numerical computations are presented to compare the outcome of the effective (upscaled) model with the transversally averaged, two-dimensional solution.
Original languageEnglish
Pages (from-to)29-58
JournalMultiscale Modeling & Simulation
Volume9
Issue number1
DOIs
Publication statusPublished - 2011

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