Rigorous homogenization of a Stokes-Nernst-Planck-Poisson system

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:390

Article

Ray, N.¹  Muntean, A.²  Knabner, P.¹ 

[1] Univ Erlangen Nurnberg, Dept Math, Chair Appl Math 1, D-91058 Erlangen, Germany

[2] Tech Univ Eindhoven, Ctr Anal Sci Comp & Applicat CASA, ICMS, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

关键词: Homogenization;    Stokes-Nernst-Planck-Poisson system;    Colloidal transport;    Porous media;    Two-scale convergence;   

DOI  :  10.1016/j.jmaa.2012.01.052

来源: Elsevier

【 摘 要 】

We perform the periodic homogenization (i.e. epsilon -> 0) of a non-stationary Stokes-Nernst-Planck-Poisson system using two-scale convergence, where epsilon is a suitable scale parameter. The objective is to investigate the influence of different boundary conditions and variable choices of scalings in epsilon of the microscopic system of partial differential equations on the structure of the (upscaled) limit model equations. Due to the specific nonlinear coupling of the underlying equations, special attention has to be paid when passing to the limit in the electrostatic drift term. As a direct result of the homogenization procedure, various classes of upscaled model equations are obtained. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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