TY - BOOK
T1 - Variable choices of scaling in the homogenization of a Nernst-Planck-Poisson problem
AU - Ray, N.
AU - Eck, C.
AU - Muntean, A.
AU - Knabner, P.
PY - 2011
Y1 - 2011
N2 - We perform the periodic homogenization (i. e. e ¿ 0) of the non-stationary Nernst-Planck-Poisson system using two-scale convergence, where e is a suitable scale parameter. The objective is to investigate the influence of variable choices of scaling in e 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 electric drift term. As a direct result of the homogenization procedure, various classes of upscaled model equations are obtained.
Keywords: Homogenization, two-scale convergence, porous media, Nernst-Planck-Poisson
system, colloidal transport
AB - We perform the periodic homogenization (i. e. e ¿ 0) of the non-stationary Nernst-Planck-Poisson system using two-scale convergence, where e is a suitable scale parameter. The objective is to investigate the influence of variable choices of scaling in e 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 electric drift term. As a direct result of the homogenization procedure, various classes of upscaled model equations are obtained.
Keywords: Homogenization, two-scale convergence, porous media, Nernst-Planck-Poisson
system, colloidal transport
M3 - Report
T3 - Preprints des Instituts für Angewandte Mathematik der Universität Erlangen-Nürnberg
BT - Variable choices of scaling in the homogenization of a Nernst-Planck-Poisson problem
PB - Institut für Angewandte Mathematik, Friedrich-Alexander-Universität
CY - Erlangen-Nürnberg
ER -