Diffusion, convection, adsorption, and reaction of chemicals in porous media
type: Item
instance of: scholarly article
title: Diffusion, convection, adsorption, and reaction of chemicals in porous media
zbMATH Open document ID: 0731.76080
DOI: 10.1016/0022-0396(91)90047-D
author: Ulrich Hornung
author: Willi Jäger
published in: Journal of Differential Equations
publication date: 1991-01-01T00:00:00Z
review text: The authors apply homogenization techniques to the complex phenomenon of an incompressible flow through a porous medium accompanied by diffusion- convection and diffusion-reaction. Starting from the usual assumption that the system consists of a periodic array of cells with a scale factor \(\epsilon\), first the equations for the micromodel are written, describing the various phenomena in a single cell (i.e. a grain \(+\) the liquid phase), namely: a) the flow, for which Stokes equation is assumed, imposing no-slip conditions on the boundary of the grains, b) the convection-diffusion of a solute, c) the reaction- diffusion on the surface of the skeleton. Of course there is a coupling between the boundary conditions for b) and the reaction term for c) (which is assumed to be linear). The authors develop a complete theory, deriving several estimates on the solutions of the micromodel equations which allow them to show their convergence as \(\epsilon\to 0\) (in a suitable sense) to the solution of the macromodel equation. A comrehensive list of references is given.
Mathematics Subject Classification ID: 76R50
Mathematics Subject Classification ID: 76V05
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 35B27
zbMATH DE Number: 4209843
zbMATH Keywords: homogenization
zbMATH Keywords: incompressible flow
zbMATH Keywords: porous medium
zbMATH Keywords: diffusion-convection
zbMATH Keywords: diffusion-reaction
zbMATH Keywords: Stokes equation
zbMATH Keywords: no-slip conditions
zbMATH Keywords: convergence
reviewed by: Antonio Fasano
MaRDI profile type: Publication
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full work available at URL: 0022-0396(91)90047-d
OpenAlex ID: W2044560400
description: scientific article; zbMATH DE number 4209843