%0 Journal Article
%T Macroscopic corrosion front computations of sulfate attack in sewer pipes based on a micro-macro reaction-diffusion model
%A Vladim¨ªr Chalupecky
%A Tasnim Fatima
%A Jens Kruschwitz
%A Adrian Muntean
%J Physics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1201.6460v1