Continuum Mechanics and Thermodynamics

, Volume 21, Issue 2, pp 125–140

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

Original Article

DOI: 10.1007/s00161-009-0099-z

Cite this article as:
Choquet, C. & Mikelić, A. Continuum Mech. Thermodyn. (2009) 21: 125. doi:10.1007/s00161-009-0099-z

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 L2 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.

Keywords

Taylor’s dispersion Asymptotic expansion Large Péclet number Large Damköhler’s number Anisotropic singular perturbation Multi-scale modelling 

PACS

02.30.Jr 47.56.+r 47.70.Fw 47.87.lk 82.40 82.65.+r 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Faculté des Sciences et Techniques de Saint-JérômeUniversité P. Cézanne, LATP UMR 6632Marseille Cedex 20France
  2. 2.Université de Savoie, LAMA UMR 5127Le Bourget du Lac CedexFrance
  3. 3.Université de LyonLyonFrance
  4. 4.Institut Camille JordanUniversité Lyon 1, UMR CNRS 5208Villeurbanne CedexFrance

Personalised recommendations