Mathematics – Numerical Analysis
Scientific paper
2012-01-31
Mathematics
Numerical Analysis
10 pages, 5 figures, to be published in proceedings of "Multiscale Mathematics: Hierarchy of Collective Phenomena and Interrel
Scientific paper
We consider a two-scale reaction diffusion system able to capture the corrosion of concrete with sulfates. Our aim here is to define and compute two macroscopic corrosion indicators: typical pH drop and gypsum profiles. Mathematically, the system is coupled, endowed with micro-macro transmission conditions, and posed on two different spatially-separated scales: one microscopic (pore scale) and one macroscopic (sewer pipe scale). We use a logarithmic expression to compute values of pH from the volume averaged concentration of sulfuric acid which is obtained by resolving numerically the two-scale system (microscopic equations with direct feedback with the macroscopic diffusion of one of the reactants). Furthermore, we also evaluate the content of the main sulfatation reaction (corrosion) product---the gypsum---and point out numerically a persistent kink in gypsum's concentration profile. Finally, we illustrate numerically the position of the free boundary separating corroded from not-yet-corroded regions.
Chalupecký Vladimír
Fatima Tasnim
Kruschwitz Jens
Muntean Adrian
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