Abstract
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. First, we show the well-posedness of the microscopic model. We then apply homogenization techniques based on two-scale convergence for a uniformly periodic domain and derive upscaled equations together with explicit formulas 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, we give the strong formulation of the upscaled system.
Highlights
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 semilinear, partially dissipative and weakly coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level
We 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
Summary
This paper treats the periodic homogenization of a semi-linear reaction-diffusion system coupled with a nonlinear differential equation arising in the modeling of the sulfuric acid attack in sewer pipes made of concrete. 19 November 2010 to be replaced, for instance, at the level of a city like Los Angeles To get good such practical estimates, one needs on one side easy-to-use macroscopic corrosion models to be used for a numerical forecast of corrosion, while on the other side one needs to ensure the reliability of the averaged models by allowing them to incorporate a certain amount of microstructure information. We imagine our concrete piece to be made of a periodically-distributed microstructure Based on this assumption, we provide here a rigorous justification of the formal asymptotic expansion performed by us (in [1]) for this reaction-diffusion scenario. The ode is describing sulfatation reaction at the inner water-solid interface – place where corrosion localizes This aspect makes a rigorous averaging challenging.
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