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Rigorous upscaling of the infinite adsorption rate reactive flow under dominant Peclet number through a pore

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Abstract

In this paper we present a rigorous derivation of the effective model for enhanced diffusion through a narrow and long 2D pore. The analysis uses the anisotropic singular perturbation technique. Starting point is a local pore scale model describing the transport by convection and diffusion of a reactive solute. The solute particles undergo an adsorption process at the lateral tube boundary, with high adsorption rate. The transport and reaction parameters are such that we have large, dominant Peclet number with respect to the ratio of characteristic transversal and longitudinal lengths (the small parameter \(\varepsilon\)). We give a formal derivation of the model using the anisotropic multiscale expansion with respect to \(\varepsilon\) . Error estimates for the approximation of the physical solution, by the upscaled one, are presented in the energy norm as well as in L ∞ and L 1 norms with respect to the space variable. They give the approximation error as a power of \(\varepsilon\) and guarantee the validity of the upscaled model through the rigorous mathematical justification of the effective behavior for small \(\varepsilon\).

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Authors and Affiliations

  1. Université de Lyon, 69003, Lyon, France

    Andro Mikelić

  2. Institut Camille Jordan, UFR Mathématiques, Université Lyon 1, Site de Gerland, Bât. A, 50, avenue Tony Garnier, 69367, Lyon Cedex 07, France

    Andro Mikelić

  3. Laboratoire de mathématiques pures et appliquées “Joseph Liouville”, Université du Littoral, 50, rue F. Buisson, B.P. 699, 62228, Calais Cedex, France

    Carole Rosier

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  1. Andro Mikelić
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  2. Carole Rosier
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Correspondence to Andro Mikelić.

Additional information

This article is dedicated to 70th birthday of Professor I. Aganović.

The research of A. Mikelić and C. Rosier was partially supported by the GDR MOMAS (Modélisation Mathématique et Simulations numériques liées aux problèmes de gestion des déchets nucléaires) (PACEN/CNRS, ANDRA, BRGM, CEA, EDF, IRSN) as a part of the project “Changements d’échelle dans la modélisation du transport multiphasique et réactif en milieux poreux : application aux milieux fracturés et aux argiles”.

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Mikelić, A., Rosier, C. Rigorous upscaling of the infinite adsorption rate reactive flow under dominant Peclet number through a pore. Ann. Univ. Ferrara 53, 333–359 (2007). https://doi.org/10.1007/s11565-007-0026-9

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  • DOI: https://doi.org/10.1007/s11565-007-0026-9

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