A two-scale model for reactive transport in a porous medium with an evolving phase configuration is formulated. The model equations are derived from a pore-scale model by homogenisation and are defined on a time-dependent geometry. Two different settings are considered: In the first one, an evolving pore-water distribution is a-priori given. In the second one, the pore water evolves due to the reaction itself. By transforming the system to a reference configuration, it can be proven that both settings lead to mathematically well-posed problems.
On propose un modèle à deux échelles pour décrire le transport réactif dans des milieux poreux, dont la micro-structure change dans le temps. Les équations du modèle sont définies dans une géométrie spatiale qui dépend du temps et elles sont obtenues a partir d'un modèle microscopique par la méthode d'homogénéisation. Deux situations différentes sont considérés : Dans le premier cas, une évolution de la distribution de l'eau de pores est donnée a priori. Dans le deuxième cas, c'est bien la réaction qui cause l'évolution de l'eau. En outilisant un changement des systèmes de coordonnées, on prouve que les deux situations conduisent à des problèmes qui sont mathématiquement bien posés.
Accepted:
Published online:
Mots-clés : Milieux poreux, Homogénéisation, Réaction et diffusion, Approche multiéchelle
Sebastian Meier 1
@article{CRMECA_2008__336_8_623_0,
author = {Sebastian Meier},
title = {A homogenisation-based two-scale model for reactive transport in media with evolving microstructure},
journal = {Comptes Rendus. M\'ecanique},
pages = {623--628},
publisher = {Elsevier},
volume = {336},
number = {8},
year = {2008},
doi = {10.1016/j.crme.2008.05.006},
language = {en},
}
Sebastian Meier. A homogenisation-based two-scale model for reactive transport in media with evolving microstructure. Comptes Rendus. Mécanique, Volume 336 (2008) no. 8, pp. 623-628. doi : 10.1016/j.crme.2008.05.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.05.006/
[1] Micro-structure models of diffusion in fissured media, J. Math. Anal. Appl., Volume 155 (1991), pp. 1-20
[2] Deriving the double porosity model of single phase flow via homogenization theory, SIAM J. Math. Anal., Volume 21 (1990), pp. 823-863
[3] Homogenization and Porous Media (U. Hornung, ed.), Springer, 1997
[4] Asymptotic Analysis of Periodic Structures, North-Holland, 1978
[5] Non-Homogeneous Media and Vibration Theory, Springer, 1980
[6] Evolving microstructure and homogenization, Contin. Mech. Thermodyn., Volume 12 (2000) no. 4, pp. 235-286
[7] Homogenization of a phase field model for binary mixtures, Multiscale Model. Simul., Volume 3 ( 2004/2005 ) no. 1, pp. 1-27
[8] Homogenisation in domains with evolving microstructure, C. R. Mecanique, Volume 335 (2007) no. 7, pp. 357-362
[9] Homogenisation of a chemical degradation mechanism inducing an evolving microstructure, C. R. Mecanique, Volume 335 (2007) no. 11, pp. 679-684
[10] M.A. Peter, Coupled reaction–diffusion processes inducing an evolution of the microstructure: Analysis and homogenization. Nonlinear Anal., Theory Methods Appl. (2008), in press
[11] Relations between transport characteristics and durability (J. Kropp; H.K. Hilsdorf, eds.), Performance Criteria for Concrete Durability RILEM Report 12, E & FN SPON, 1995, pp. 97-137
[12] T. Chaussadent, États de lieux et réflexions sur la carbonatation du beton armé, Technical Report LCPC OA29, Laboratoire Central de Ponts et Chaussées, Paris, 1999
[13] A two-scale modelling approach to reaction–diffusion processes in porous materials, Comp. Mat. Sci., Volume 39 (2007), pp. 29-34
[14] S.A. Meier, Two-scale models of reactive transport in porous media involving microstructural changes, PhD thesis, University of Bremen. 2008
[15] A two-scale reaction–diffusion system with micro-cell reaction concentrated on a free boundary, C. R. Mecanique, Volume 336 (2008), pp. 481-486
Cited by Sources:
Comments - Policy