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  • 1. Fatima, Tasnim
    et al.
    Muntean, Adrian
    Technical University Eindhoven.
    Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence2014In: Nonlinear Analysis, ISSN 1468-1218, Vol. 15, no 1, p. 326-344Article in journal (Refereed)
    Abstract [en]

    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.

  • 2.
    Kumar, Kundan
    et al.
    Technische Universiteit Eindhoven.
    Pisarenco, Maxim
    Technische Universiteit Eindhoven.
    Rudnaya, Maria
    Technische Universiteit Eindhoven.
    Savcenco, Valeriu
    Technische Universiteit Eindhoven.
    A note on analysis and numerics of algae growth2014In: Nonlinear Analysis, ISSN 1468-1218, Vol. 15, p. 392-403Article in journal (Refereed)
  • 3.
    Muntean, Adrian
    Tech Univ Eindhoven, Dept Math & Comp Sci, CASA Ctr Anal Sci Comp & Applicat, Eindhoven, Netherlands..
    Well-posedness of a moving-boundary problem with two moving reaction strips2009In: Nonlinear Analysis, ISSN 1468-1218, Vol. 10, no 4, p. 2541-2557Article in journal (Refereed)
    Abstract [en]

    We deal with a one-dimensional coupled system of semi-linear reaction-diffusion equations in two a priori unknown moving phases driven by a non-local kinetic condition. The PDEs system models the penetration of gaseous carbon dioxide in unsaturated porous materials (like concrete). The main issue is that the strong competition between carbon dioxide diffusion and the fast reaction of carbon dioxide with calcium hydroxide–which are the main active reactants–leads to a sudden drop in the alkalinity of concrete near the steel reinforcement. This process–called concrete carbonation–facilitates chemical corrosion and drastically influences the lifetime of the material. We present details of a class of moving-boundary models with kinetic condition at the moving boundary and address the local existence, uniqueness and stability of positive weak solutions. We also point out our concept of global solvability. The application of such moving-boundary systems to the prediction of carbonation penetration into ordinary concrete samples is illustrated numerically.

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