Effective dispersion equations for reactive flows involving free boundaries at the micro-scale

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

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Abstract

We consider a pore-scale model for reactive flow in a thin 2-D 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 non-negligible 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
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages35
Publication statusPublished - 2010

Publication series

NameCASA-report
Volume1043
ISSN (Print)0926-4507

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