Upscaling nonlinear adsorption in periodic porous media – homogenization approach. Issue 10 (2nd October 2016)

• Record Type: Journal Article
• Authors: Allaire, Grégoire; Hutridurga, Harsha
• Is Part Of: Applicable analysis. Volume 95:Issue 10(2016)
• Page Start: 2126
• Page End: 2161
• Publication Date: 2016-10-02
• Subjects: homogenization -- reactive transport -- porous media; 35B27 -- 35K55 -- 35B50 -- 74Q15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1038254
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : We consider the homogenization of a model of reactive flows through periodic porous media involving a single solute which can be absorbed and desorbed on the pore boundaries. This is a system of two convection–diffusion equations, one in the bulk and one on the pore boundaries, coupled by an exchange reaction term. The novelty of our work is to consider a nonlinear reaction term, a so-called Langmuir isotherm, in an asymptotic regime of strong convection. We therefore generalize previous works on a similar linear model. Under a technical assumption of equal drift velocities in the bulk and on the pore boundaries, we obtain a nonlinear monotone diffusion equation as the homogenized model. Our main technical tool is the method of two-scale convergence with drift.