Abstract
Reaction–diffusion processes, where slow diffusion balances fast reaction, usually exhibit internal loci where the reactions are concentrated. Some modeling and simulation aspects of using kinetic free-boundary conditions to drive fast carbonation reaction fronts into unsaturated porous cement-based materials are discussed. Providing full control on the velocity of the reaction front, such conditions offer a rich description of the coupling between transport, reaction, and change in the shape of the a priori unknown time-dependent regions. New models are formulated and validated by means of numerical simulations and experimental data.
Article PDF
Avoid common mistakes on your manuscript.
References
Ortoleva P (1994) Geochemical self-organization. OUP, Oxford
Ball JM, Knderlehrer D, Podio-Guidugli P, Slemrod M (eds) (1999) Evolving phase interfaces in solids. Springer, Berlin
Tilley BS, Kriegsmann GA (2001) Microwave-enhanced chemical vapor infiltration: a sharp interface model. J Eng Math 534: 971–989
Dewynne JN, Fowler AC, Hagan PS (1993) Multiple reaction fronts in the oxidation-reduction of iron-rich uranium ores. SIAM J Appl Math 534: 971–989
Visintin A (1986) A new model for supercooling and superheating effects IMA. J Appl Math 36: 141–157
Evans JD, King JR (1996) On the derivation of heterogeneous reaction kinetics from a homogeneous reaction model. SIAM J Appl Math 60(6): 1977–1996
Clarelli F, Fasano A, Natalini R (2008) Mathematics and monuments conservation: free boundary models of marble sulphation. SIAM J Appl Math 69(1): 149–168
Muntean A, Böhm M (2006) Dynamics of a moving reaction interface in a concrete wall. In: Rodrigues JF et al (eds) Free and moving boundary problems. Theory and applications. Proceedings of the conference FBP 2005, Int Ser Numer Math, vol 154. Birkhäuser, Basel, pp 317–326
Muntean A (2006) A moving-boundary problem: modeling, analysis and simulation of concrete carbonation. Cuvillier Verlag, Göttingen
Muntean A (2007) Concentration blow up in a two-phase non-equilibrium model with source term. Meccanica 42: 409–411
Muntean A (2009) Well-posedness of a moving-boundary problem with two moving reaction strips. Nonlinear Anal Real World Appl 10(4): 2541–2557
Taylor HFW (1997) Cement chemistry. Thomas Telford, London
Salhan A, Billingham J, King AC (2003) The effect of a retarder on the early stages of the hydration of calcium silicate. J Eng Math 45: 367–377
Papadakis VG, Vayenas CG, Fardis MN (1989) A reaction engineering approach to the problem of concrete carbonation. AIChE J 35: 1639–1650
Lagerblad B (2005) Carbon dioxide uptake during concrete life cycle-State of the art. NI-project 03018, Swedish Cement and Concrete Research Institute, Stockholm
Peter M, Muntean A, Meier S, Böhm M (2008) Competition of several carbonaton reactions: a parametric study. Cement Concr Res 38: 1385–1393
Meier SA, Peter MA, Muntean A, Böhm M (2007) Dynamics of the internal reaction layer arising during carbonation of concrete. Chem Eng Sci 62: 1125–1137
Saetta AV, Schrefler BA, Vitaliani RV (1995) 2D model for carbonation, moisture/heat flow in porous materials. Cement Concr Res 32: 939–941
Matkowsky BJ, Sivashinsky GI (1979) An asymptotic deriavtion of two models in flame theory associated with the contant density approximation. SIAM J Appl Math 37(3): 686–699
Matkowsky BJ, Sivashinsky GI (1978) Propagation of a pulsating reaction front in solid fuel combustion. SIAM J Appl Math 35(3): 465–478
Chaussadent T (1999) États des lieux et réflexions sur la carbonatation du beton armé. LCPC, Paris
Böhm M, Kropp J, Muntean A (2003) A two-reaction-zones moving-interface model for predicting Ca(OH)2 carbonation in concrete. Berichte aus der Technomathematik, University of Bremen, 03–04
Schmidt A, Muntean A, Böhm M (2007) Moving carbonation fronts around corners: a self-adaptive finite element approach. In: 5th International Essen Workshop, Transcon, pp 467–476
Schmidt A, Siebert KG (2005) Design of adaptive finite element software: the finite element toolbox ALBERTA. LNCSE Series 42 Springer, Verlag, Berlin
Froment G, Bischoff KB (1996) Chemical reactor analysis and design. Wiley, New York
Tuutti K (1982) Corrosion of steel in concrete. Swedish Cement and Concrete Research Institute (CBI), Stockholm
Meirmanov A (1992) The Stefan problem. Walter de Gruyter, Berlin
Stefan J (1890) Über die Theorie der Eisbildung. Monatshefte der Mathematik und Physik 1(1): 1–6
Alexiades V, Solomon A (1993) Mathematical modeling of melting and freezing processes. Hemisphere, Washington
Chalmers B (1977) Principles of solidification. Krieger, New York
Borsi I, Farina A, Primicerio M (2006) A rain infiltration model with unilateral boundary condition: qualitative analysis and numerical simulations. Math Methods Appl Sci 29: 2047–2077
Gurtin M (1992) Thermomechanics of evolving phase boundaries in the plane. Clarendon, Oxford
Bunte D (1994) Zum Karbonatisierungsbedingten Verlust der Dauerhaftigkeit von Aussenbauteuilen aus Stahlbeton. Dissertation, TU Braunschweig
Steffens A, Dinkler D, Ahrens H (2002) Modeling carbonation for corrosion risk prediction of concrete structures. Cement Concr Res 32: 935–941
Muntean A, Meier S, Peter M, Böhm M, Kropp J (2006) A note on the limitations of the use of accelerated concrete-carbonation tests for service life predictions. Berichte aus der Technomathematik, University of Bremen, 04–06
Crooks ECM, Dancer EN, Hilhorst D, Mimura M, Ninomiya H (2004) Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions. Nonlinear Anal Real World Appl 5: 645–665
Seidman TI (2009) Interface conditions for a singular reaction-diffusion system. Discret Contin Dyn Syst (to appear)
Bazant MZ, Stone HA (2000) Asymptotics of reaction-diffusion fronts with one static and one diffusing reactant. Physica D 147: 95–121
Muntean A (2008) On the interplay between fast reaction and slow diffusion in the concrete carbonation process: a matched-asymptotics approach. Meccanica 44(1): 35–46
Fila M, Souplet P (2001) Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Interfaces Free Bound 3: 1089–1112
Fife PC (1988) Dynamics of internal layers and diffusive interfaces. SIAM, Philadelphia
Acknowledgments
We acknowledge the financial support of the German Science Foundation (DFG) under the grant SPP 1122 Prediction of the course of physicochemical damage processes involving mineral materials. The authors thank the two reviewers for their comments and suggestions that essentially contributed to the final version of the paper.
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Muntean, A., Böhm, M. Interface conditions for fast-reaction fronts in wet porous mineral materials: the case of concrete carbonation. J Eng Math 65, 89–100 (2009). https://doi.org/10.1007/s10665-009-9295-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10665-009-9295-x