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 spatiallyseparated 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.
|Title of host publication||Multiscale Mathematics: Hierarchy of collective phenomena and interrelations between hierarchical structures (Fukuoka, Japan, December 8-11, 2011)|
|Place of Publication||Fukuoka|
|Publisher||Institute of Mathematics for Industry, Kyushu University|
|Publication status||Published - 2012|
|Name||COE Lecture Note Series|