Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T06:21:41.206Z Has data issue: false hasContentIssue false
  • English
  • Français

Macroscopic models for calcium carbonate corrosion due to sulfation. Variation of diffusion and volume expansion

Published online by Cambridge University Press:  06 June 2018

CHRISTOS V. NIKOLOPOULOS
CHRISTOS V. NIKOLOPOULOS*
Affiliation:
Department of Mathematics, University of the Aegean, Karlovasi, 83200 Samos, Greece email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The subject of the present paper is the derivation and analysis of mathematical models for the formation of a mushy region during calcium carbonate corrosion. More specifically there is emphasis on the variation of the overall diffusion resulting from the changing shape of a single pore due to corrosion process and on the resulting volume expansion of the material as the outcome of the transformation of calcium carbonate to gypsum. These models are 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 in the microscopic scale. The derived macroscopic models are solved numerically with the use of an implicit in time, finite element method. The results of the simulations for various microstructure geometries in the micro-scale and a discussion are also presented.

Keywords

Sulfationconcrete corrosionmonument corrosionmoving boundary problemsperturbation methods
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Issue 3 , June 2019 , pp. 529 - 556
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Ali, G., Furuholt, V., Natalini, R. & Torcicollo, I. (2007) A mathematical model of sulphite chemical aggression of limestones with high permeability. Part I. Modeling and qualitative analysis. Transp. Porous Media 69, 109–122.Google Scholar
[2] Ali, G., Furuholt, V., Natalini, R. & Torcicollo, I. (2007) A mathematical model of sulphite chemical aggression of limestones with high permeability. Part II: numerical approximation. Transp. Porous Media 69, 175–188.Google Scholar
[3] Aregba-Driollet, D., Diele, F. & Natalini, R. (2004) A mathematical model for the sulphur dioxide aggression to calcium carbonate stones: numerical approximation and asymptotic analysis. SIAM J. Appl. Math. 64, 1636–1667.Google Scholar
[4] Beven, K. & Feyen, J. (2002) The future of distributed modelling. Hydrol. Process. 16, 169–172. doi:10.1002/hyp.325.Google Scholar
[5] Böhm, M., Devinny, J., Jahani, F. & Rosen, G. (1998) On a moving-boundary system modelling corrosion in sewer pipes. Appl. Math. Comput. 92, 247–269.Google Scholar
[6] Bohm, M., Devinny, J. S., Jahani, F., Mansfeld, F. B., Rosen, I. G. & Wang, C. (1999) A moving boundary diffusion model for the corrosion of concrete wastewater systems: simulation and experimental validation. In: Proceedings of the American Control Conference, June 1999, San Diego, California, pp. 1739–1743.Google Scholar
[7] Clareli, F., Fasano, A. & Natalini, R. (2008) Mathematics and monument conservation: free boundary models of marble sulfation. SIAM J. Appl. Math. 69 (1), 149–168.Google Scholar
[8] Fasano, A. & Natalini, R. (2006) Lost beauties of the acropolis: what mathematics can say. SIAM News 39 (6), July/August 2006.Google Scholar
[9] Fatima, T., Arab, N., Zemskov, E. P. & Muntean, A. (2011) Homogenization of a reaction–diffusion system modeling sulfate corrosion of concrete in locally periodic perforated domains. J. Eng. Math. 39 (2–3), 261–276.Google Scholar
[10] Fatima, T. & Muntean, A. (2014) Sulfate attack in sewer pipes: derivation of a concrete corrosion model via two-scale convergence. Nonlinear Anal.: Real World Appl., 15, 326–344, doi: 10.1016/j.nonrwa.2012.01.019.Google Scholar
[11] Gregg, S. J. & Sing, K. S. W. (1982) Adsorption, Surface Area and Porosity, Academic Press, London.Google Scholar
[12] Guarguaglini, F. R. & Natalini, R. (2007) Fast reaction limit and large time behavior of solutions to a nonlinear model of sulphation phenomena. Commun. Partial Differ. Equ. 32, 163–189.Google Scholar
[13] Guarguaglini, F. R. & Natalini, R. (2005) Global existence of solutions to a nonlinear model of sulphation phenomena in calcium carbonate stones. Nonlinear Anal.: Real World Appl. 6, 477–494.Google Scholar
[14] Hinch, E. J. (1991) Perturbation Methods, Cambridge University Press, Cambridge.Google Scholar
[15] Howison, S., Lacey, A., Movack, A. & Ockendon, J. (2003) Applied Partial Differential Equations, Oxford University Press, Oxford.Google Scholar
[16] Jaklic, A., Leonardis, A. & Solina, F. (2000) Segmentation and recovery of superquadrics. In: Computational Imaging and Vision, Vol. 20, Kluwer, Dordrecth.Google Scholar
[17] Lacey, A. A. & Herraiz, L. A. (2002) Macroscopic models for melting derived from averaging microscopic Stefan problems I: simple geometries with kinetic undercooling or surface tension. Euro. J. Appl. Math. 11, 153–169.Google Scholar
[18] Lacey, A. A. & Herraiz, L. A. (2002) Macroscopic models for melting derived from averaging microscopic Stefan problems II: effect of varying geometry and composition. Euro. J. Appl. Math. 13, 261–282.Google Scholar
[19] Maragos, P. & Butt, M. A. (2000) Curve evolution, differential morphology, and distance transforms applied to multiscale and eikonal problems. Funtamenta Informatica 41, 91–129.Google Scholar
[20] Muntean, A. & Böhm, M. (2009) A moving-boundary problem for concrete carbonation: global existence and uniqueness of weak solutions. J. Math. Anal. Appl. 350 (1), 234–251.Google Scholar
[21] Muntean, A. & Chalupecky, V. (2011) Homogenization method and multiscale modeling. In: Lecture Notes of the Institte for Mathematics for Industry, Vol. 34, Kyushu University, Fukuoka, Japan.Google Scholar
[22] Nikolopoulos, C. V. (2010) A mushy region in concrete corrosion. Appl. Math. Model. 34, 4012–4030.Google Scholar
[23] Nikolopoulos, C. V. (2015) Macroscopic models for a mushy region in concrete corrosion. J. Eng. Math. 91, 143–163.Google Scholar
[24] Nikolopoulos, C. V. (2014) Mathematical modelling of a mushy region formation during sulfation of calcium carbonate. Netw. Heterog. Media 9 (4), 635–654.Google Scholar
[25] Osher, S. & Sethian, J. A. (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79 (1), 12–49.Google Scholar
[26] Persson, P. O. & Strang, G. (1988) A simple mesh generator in MATLAB. SIAM Rev. 46 (2), 329–345.Google Scholar
[27] Schröder, J. (2014) A numerical two-scale homogenization scheme: the FE2-method. In: Schröder, J. & Hackl, K. (editors), Plasticity and Beyond. CISM International Centre for Mechanical Sciences, Vol. 550, Springer, Vienna.Google Scholar