, Volume 21, Issue 2, pp 125-140
Date: 24 Apr 2009

Rigorous upscaling of the reactive flow with finite kinetics and under dominant Péclet number

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Abstract

We consider the evolution of a reactive soluble substance introduced into the Poiseuille flow in a slit channel. The reactive transport happens in presence of dominant Péclet and Damköhler numbers. We suppose Péclet numbers corresponding to Taylor’s dispersion regime. The two main results of the paper are the following. First, using the anisotropic perturbation technique, we derive rigorously an effective model for the enhanced diffusion. It contains memory effects and contributions to the effective diffusion and effective advection velocity, due to the flow and chemistry reaction regime. Error estimates for the approximation of the physical solution by the upscaled one are presented in the energy norms. Presence of an initial time boundary layer allows only a global error estimate in L 2 with respect to space and time. We use the Laplace’s transform in time to get optimal estimates. Second, we explicit the retardation and memory effects of the adsorption/desorption reactions on the dispersive characteristics and show their importance. The chemistry influences directly the characteristic diffusion width.

Communicated by A. Visintin
Research of the authors was partially supported by the GNR 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 “Modèles de dispersion efficace pour des problèmes de Chimie-Transport: Changement d’échelle dans la modélisation du transport réactif en milieux poreux, en présence des nombres caractéristiques dominants”.