Abstract
We formulate a 1D partly dissipative moving-boundary reaction-diffusion system that describes the penetration of a reaction front into a concrete wall. We state the well-posedness of the model and the existence of non-trivial upper and lower bounds for the concentrations, speed of the interface, and shut-down time of the process. A numerical example illustrates the typical behavior of concentrations and interface penetration in a real-world application.
This work was completed with the partial support of DFG-SPP1122 Prediction of the Course of Physicochemical Damage Processes Involving Mineral Materials.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
V. Alexiades, A.D. Solomon, Mathematical Modeling of Melting and Freezing Processes. Hemisphere Publishing Group, 1993.
P. Binding, The differential equation x′ = f º x. J. Diff. Eqs. 31(1979), 183–199.
M. Böhm, G. Rosen, Global weak solutions and uniqueness for a moving boundary problem for a coupled system of quasilinear diffusion-reaction equations arising as a model of chemical corrosion of concrete surfaces. Humboldt University, 1997.
M. Böhm, J. Kropp, A. Muntean, On a prediction model for concrete carbonation based on moving interfaces — Interface concentrated reactions. Berichte aus der Technomathematik 03-03, University of Bremen, Germany, 2003.
L.M. Brieger, F.H. Wittmann, Numerical simulation of concrete carbonation. Werkstoffwissenschaften und Bausanierung, Int. Koll. Esslingen, Germany, 1986, 635–640.
D. Bunte, Zum Karbonatisierungsbedingten Verlust der Dauerhaftigkeit von Außenbauteilen aus Stahlbeton. Dissertation, TU Braunschweig, Germany, 1994.
A. Muntean, M. Böhm, On a prediction model for the service life of concrete structures based on moving interfaces. In Proceedings of ICLODC, (edited by Stangenberg, F., et al.), 209–218, Ruhr-Universität Bochum, Germany, 2004.
A. Muntean, A Moving-Boundary Problem: Modeling, Analysis and Simulation of Concrete Carbonation, PhD thesis, University of Bremen, Cuvillier Verlag, Göttingen, Germany.
P.J. Ortoleva, Geochemical Self-Organization. Oxford University Press, 1994.
A. Pawell, K.D. Krannich, Dissolution effects in porous media. SIAM J. Appl. Math. 1 (1996), 89–118.
A. Schmidt, A. Muntean, M. Böhm, Numerical experiments with self-adaptive finite element simulations in 2D for the concrete carbonation. Berichte aus der Technomathematik 05-01, University of Bremen, Germany, 2005.
E. Vannini, A reaction-diffusion problem with a reaction front. Math. Meth. Appl. Sci. 21 (1998), 417–432.
W. Xie, The Stefan problem with a kinetic condition at the free boundary. SIAM J. Math. Anal. 21 (1990), 362–373.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Birkhäuser Verlag Basel/Switzerland
About this paper
Cite this paper
Muntean, A., Böhm, M. (2006). Dynamics of a Moving Reaction Interface in a Concrete Wall. In: Figueiredo, I.N., Rodrigues, J.F., Santos, L. (eds) Free Boundary Problems. International Series of Numerical Mathematics, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7719-9_31
Download citation
DOI: https://doi.org/10.1007/978-3-7643-7719-9_31
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-7718-2
Online ISBN: 978-3-7643-7719-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)