We discuss a reaction–diffusion system modeling concrete corrosion
in sewer pipes. The system is coupled, semi-linear, and partially dissipative. It is
defined on a locally-periodic perforated domain with nonlinear Robin-type boundary
conditions at water-air and solid-water interfaces. We apply asymptotic homogenization
techniques to obtain upscaled reaction–diffusion models together with
explicit formulae for the effective transport and reaction coefficients. We show that
the averaged system contains additional terms appearing due to the deviation of
the assumed geometry from a purely periodic distribution of perforations for two
relevant parameter regimes: (1) all diffusion coefficients are of order of O(1) and (2)
all diffusion coefficients are of order of O("2) except the one for H2S(g) which is of
order of O(1). In case (1), we obtain a set of macroscopic equations, while in case (2)
we are led to a two-scale model that captures the interplay between microstructural
reaction effects and the macroscopic transport.

Name | CASA-report |
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Volume | 0926 |
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ISSN (Print) | 0926-4507 |
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