Abstract
A matched-asymptotics approach is proposed to show the occurrence of two distinct characteristic length scales in the carbonation process. The separation of these scales arises due to the strong competition between reaction and diffusion effects. We show that for sufficiently large times τ the width of the carbonated region is proportional to \(\sqrt{\tau}\) , while the width of the reaction front is proportional to \(\tau^{\frac{p-1}{2(p+1)}}\) for carbonation-reaction rates with a power law structure like k[CO2]p[Ca(OH)2]q, where k>0 and p,q>1 and identify the proportionality coefficient asymptotically. We emphasize the occurrence of a water barrier in the reaction zone which may hinder the penetration of CO2 by locally filling with water air parts of the pores. This non-linear effect may be one of the causes why a purely linear extrapolation of accelerated carbonation test results to natural carbonation settings is (even theoretically) not reasonable. Finally, we compare our asymptotic penetration law against measured penetration depths from Bune (Zum Karbonatisierungsbedingten Verlust der Dauerhaftigkeit von Außenbauteilen aus Stahlbeton, 1994). The novelty consists in the fact that the factor multiplying \(\sqrt{\tau}\) is now identified asymptotically by solving a non-linear system of ordinary differential equations, and hence, fitting arguments are not necessary to estimate its size. We offer an alternative to the (asymptotic) \(\sqrt{\tau}\) expression of the carbonation-front position obtained in Papadakis et al. (AIChE J. 35:1639, 1989).
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References
Barenbaltt GI (1979) Similarity, self-similarity, and intermediate asymptotics. Consultants Bureau, NY
Bary B, Sellier A (2004) Coupled moisture-carbon dioxide-calcium transfer model for carbonation of concrete. Cem Concr Res 34:1859–1872
Bazant MZ, Stone HA (2000) Asymptotics of reaction-diffusion fronts with one static and one-diffusing reactant. Physica D 147:95–121
Bunte D (1994) Zum Karbonatisierungsbedingten Verlust der Dauerhaftigkeit von Außenbauteilen aus Stahlbeton. Dissertation, TU Braunschweig
Cahyadi JH, Uomoto T (1993) Influence of environmental relative humidity on carbonation of concrete (mathematical modeling). Durability of building materials and components, vol 6 (Omiya, Japan), pp 1142–1151
Chaussadent T (1999) États de lieux et réflexions sur la carbonatation du béton armé. Rapport OA 29, LCPC, Paris
Do DD (1982) On the validity of the shrinking core model in non-catalytic gas-solid reactions. Chem Engng Sci 37:1477–1481
Emmerich H (2003) The diffuse interface approach in material sciences. Springer, Berlin
Fife PC (1988) Dynamics of internal layers and diffusive interfaces. SIAM, Philadelphia
Fila M, Souplet P (2001) Decay of global solutions, stability and blow-up for a reaction-diffusion problem with free boundary. Interfaces Free Bound 3:337–344
Hinch EJ (1991) Perturbation methods. Cambridge University Press, Cambridge
Houst Y, Wittmann FH, Roelfstra P (1983) A model to predict service life of concrete structures. Proc. Int. Conf. at Technische Akademie Esslingen, pp 181–186
Kropp J (1995) Relations between transport characteristics and durability. Performance criteria for concrete durability, RILEM Report 12 (Eds. J. Kropp, H.K. Hilsdorf) E and Fn Spon Editions, pp 97–137
Leger C, Argoul F, Bazant MZ (1999) Front dynamics during diffusion-limited corrosion of ramified electrodeposits. J Phys Chem B 103:5841–5851
Logan JD (2001) Transport modeling in hydrogeochemical systems. Springer, Berlin
Mainguy M (1999) Modèles de diffusion non-linéaires en millieux poreaux. Application a la dissolution et au séchage des matériaux cimentaires. These de doctorat, Ecole Normale des Ponts et Chaussées, Paris
Mainguy M, Coussy O (2000) Propagation fronts during calcium leaching and chloride penetration. ASCE J Engng Mech 3:252–257
Meier SA, Peter MA, Muntean A, Böhm M (2007) Dynamics of the internal reaction layer arising during concrete carbonation. Chem Engng Sci 162:1125–1137
Muntean A, Meier SA, Peter MA, Böhm M (2005) A note on the limitations of the use of accelerated concrete-carbonation tests for service-life predictions. Berichte aus der Technomathematik, Tec. Report 05-04
Muntean A, Böhm M (2006) Dynamics of a moving reaction interface in a concrete wall. In: Free and moving boundary problems. theory and applications. Int series of num math, vol 154. Birkhäuser, Basel, pp 317–326
Muntean A, Böhm M (2006) Length scales in the concrete carbonation process and water barrier effect: a matched asymptotics approach. Berichte aus der Technomathematik, Tec. Report 07-06
Muntean A (2006) A moving-boundary problem: modeling, analysis and simulation of concrete carbonation. Cuvillier, Göttingen
Papadakis VG, Vayenas CG, Fardis MN (1989) A reaction engineering approach to the problem of concrete carbonation. AIChE J 35:1639
Saetta AV, Schrefler BA, Vitaliani RV (1993) The carbonation of concrete and the mechanism of moisture, heat and carbon dioxide flow through porous materials. Cem Concr Res 23(4):761–772
Schenkel A, Witter P, Stubbe J (1993) Asymptotics of solutions in an A+B→C reaction-diffusion system. Physica D 69:135–147
Sedov LI (1972) A course in continuum mechanics, vol. 2, Physical foundations and formulations of problems. Wolters-Nordoff, Groningen
Shampine LE, Gladwell I, Thompson S (2003) Solving ODEs with MATLAB. Cambridge University Press, Cambridge
Souplet P, Ghidousche H, Tarzia D (2001) Decay of global solutions, stability and blow-up for a reaction-diffusion problem with free boundary. Proc Am Math Soc 129:781–792
Steffens A (2000) Modellierung von Karbonatisierung und Chloridbildung zur numerischen Analyse der Korrosionsgefärdung der Betonbewehrung. Dissertation, Institut für Statik, Universität Braunschweig
Thiery M (2005) Modélisation de la carbonatation atmospherique des matériaux cimentaires. Rapport OA 52 (These de doctorat), LCPC, Paris
Thiery M, Baroghel-Bouny V, Dangla P, Villain G (2007) Numerical modeling of concrete carbonation based on durability indicators. CANMET/ACI Int. Conf. on Durability of Concrete, pp 765–780
Thiery M, Villain G, Dangla P, Platret G (2007) Investigation of the carbonation front shape on cementitious materials: effects of the chemical kinetics. Cem Concr Res 37:1047–1058
Yen A, Lin AL, Koo L, Vilensky B, Taitelbaum H, Kopelman R (1997) Spatiotemporal patterns and nonclassical kinetics of competing elementary reactions: chronium complex formation with xylenol orange in a capillary. J Phys Chem A 101:2819–2827
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Muntean, A. On the interplay between fast reaction and slow diffusion in the concrete carbonation process: a matched-asymptotics approach. Meccanica 44, 35–46 (2009). https://doi.org/10.1007/s11012-008-9140-8
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DOI: https://doi.org/10.1007/s11012-008-9140-8