Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence

Details Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence

2010-11-26

arxiv.org/abs/1011.5781v1

Mathematics

Analysis of PDEs

Scientific paper

We explore the homogenization limit and rigorously derive upscaled equations for a microscopic reaction-diffusion system modeling sulfate corrosion in sewer pipes made of concrete. The system, defined in a periodically-perforated domain, is semi-linear, partially dissipative and weakly coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level. Firstly, we show the well-posedness of the microscopic model. We then apply homogenization techniques based on two-scale convergence for an uniformly periodic domain and derive upscaled equations together with explicit formulae for the effective diffusion coefficients and reaction constants. We use a boundary unfolding method to pass to the homogenization limit in the non-linear ordinary differential equation. Finally, besides giving its strong formulation, we also prove that the upscaled two-scale model admits a unique solution.

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