\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Mathematical modelling of a mushy region formation during sulphation of calcium carbonate

Abstract Related Papers Cited by
  • The subject of the present paper is the derivation and asymptotic analysis of a mathematical model for the formation of a mushy region during sulphation of calcium carbonate. The model is derived by averaging, with the use of the multiple scales method, applied on microscopic moving - boundary problems. The latter problems describe the transformation of calcium carbonate into gypsum on the microscopic scale. The derived macroscopic model is solved numerically with the use of a finite element method. The results of some simulations and a relevant discussion are also presented.
    Mathematics Subject Classification: Primary: 35Q92, 35R37; Secondary: 35K57, 74G10, 74S05.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    G. Ali, V. Furuholt, R. Natalini and I. Torcicollo, A mathematical model of sulphite chemical aggression of limestones with high permeability. Part I. Modeling and qualitative analysis, Transport in Porous Media, 69 (2007), 109-122.doi: 10.1007/s11242-006-9067-2.

    [2]

    G. Ali, V. Furuholt, R. Natalini and I. Torcicollo, A mathematical model of sulphite chemical aggression of limestones with high permeability. Part II: Numerical approximation, Transport in Porous Media, 69 (2007), 175-188.doi: 10.1007/s11242-006-9068-1.

    [3]

    D. Aregba-Driollet, F. Diele and R. Natalini, A Mathematical Model for the SO2 Aggression to Calcium Carbonate Stones: Numerical Approximation and Asymptotic Analysis, SIAM J. APPL. MATH. , 64 (2004), 1636-1667.doi: 10.1137/S003613990342829X.

    [4]

    F. Clareli, A. Fasano and R. Natalini, Mathematics and monument conservation: Free boundary models of marble sulfation, SIAM Journal on Applied Mathematics, 69 (2008), 149-168.doi: 10.1137/070695125.

    [5]

    A. Fasano and R. Natalini, Lost Beauties of the Acropolis: What Mathematics Can Say, SIAM news, 2006.

    [6]

    T. Fatima, Multiscale Reaction Diffusion Systems Describing Concrete Corrosion: Modelling and Analysis, Ph.D thesis, Technical University of Eindhoven, 2013.

    [7]

    T. Fatima, N. Arab, E. P. Zemskov and A. Muntean, Homogenization of a reaction - diffusion system modeling sulfate corrosion of concrete in locally periodic perforated domains, Journal of Engineering Mathematics, 69 (2011), 261-276.doi: 10.1007/s10665-010-9396-6.

    [8]

    T. Fatima and A. Muntean, Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence, Nonlinear Analysis: Real World Applications, 15 (2014), 326-344.doi: 10.1016/j.nonrwa.2012.01.019.

    [9]

    T. Fatima, A. Muntean and T. Aiki, Distributed space scales in a semilinear reaction-diffusion system including a parabolic variational inequality: A well-posedness study, Adv. Math. Sci. Appl., 22 (2012), 295-318.

    [10]

    T. Fatima, A. Muntean and M. Ptashnyk, Unfolding-based corrector estimates for a reaction - diffusion system predicting concrete corrosion, Applicable Analysis, 91 (2012), 1129-1154.doi: 10.1080/00036811.2011.625016.

    [11]

    F. R. Guarguaglini and R. Natalini, Fast reaction limit and large time behavior of solutions to a nonlinear model of sulphation phenomena, Commun. Partial Differ. Equations, 32 (2007), 163-189.doi: 10.1080/03605300500361438.

    [12]

    F. R. Guarguaglini and R. Natalini, Global existence of solutions to a nonlinear model of sulphation phenomena in calcium carbonate stones, Nonlinear Analysis: Real World Applications, 6 (2005), 477-494.doi: 10.1016/j.nonrwa.2004.09.007.

    [13]

    E. J. Hinch, Perturbation Methods, Cambridge University Press, 1991.doi: 10.1017/CBO9781139172189.

    [14]

    A. A. Lacey and L. A. Herraiz, Macroscopic models for melting derived from averaging microscopic Stefan problems I: Simple geometries with kinetic undercooling or surface tension, Euro. Jnl. of Applied Mathematics, 11 (2002), 153-169.doi: 10.1017/S0956792599004027.

    [15]

    A. A. Lacey and L. A. Herraiz, Macroscopic models for melting derived from averaging microscopic Stefan problems II: Effect of varying geometry and composition, Euro. Jnl. of Applied Mathematics, 13 (2002), 261-282.doi: 10.1017/S0956792501004818.

    [16]

    R. J. Leveque, Finite Volume Methods for Hyperbolic Problems, Caimbridge University Press, 2002.doi: 10.1017/CBO9780511791253.

    [17]

    C. V. Nikolopoulos, A mushy region in concrete corrosion, Applied Mathematical Modelling, 34 (2010), 4012-4030.doi: 10.1016/j.apm.2010.04.005.

    [18]

    C. V. Nikolopoulos, Macroscopic models for a mushy region in concrete corrosion, Journal of Engineering Mathematics, 2014, DOI 10.1007/s10665-014-9743-0.

    [19]

    J. L. Schnoor, Enviromental Modeling, Fate and transport of pollutants in water, air, and soil, John Willey and Sons, Inc., 1996.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(64) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return