Abstract
We introduce a degenerate nonlinear parabolic–elliptic system, which describes the chemical aggression of limestones under the attack of SO2, in high permeability regime. By means of a dimensional scaling, the qualitative behavior of the solutions in the fast reaction limit is investigated. Explicit asymptotic conditions for the front formation are derived.
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Abramowitz M., Stegun I.A. (1972) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. Dover, New York
Alì, G., Furuholt, V., Natalini, R., Torcicollo, I.: A mathematical model of sulphite chemical aggression of limestones with high permeability. Part II: numerical approximation. Trans Porous Med (2006, this issue)
Amoroso G.G., Fassina V. (1983) Stone Decay and Conservation—Atmospheric Pollution, Cleaning, and Protection. Elsevier Science Publishers, Amsterdam
Aregba-Driollet D., Diele F., Natalini R. (2004) A mathematical model for the SO2 aggression to calcium carbonate stones: numerical approximation and asymptotic analysis. SIAM J. Appl. Math. 64(5): 1636–1667
Barenblatt, G.I., Entov, V.M., Ryzhik, V.M.: Theory of Fluid Flows Through Natural Rocks. Kluwer Academic Publisher (1990)
Bebernes, J., Eberly, D.: Mathematical Problems from Combustion Theory. Springer-Verlag (1989)
Borisova E.A., Adler P.M. (2005) Deposition in porous media and clogging on the field scale. Phys. Rev. E 71, 1–19
Chadam J., Hoff D., Merino E., Ortoleva P., Sen A. (1986) Reactive Infiltration Instabilities. IMA J. Appl. Math. 36, 207–221
Chadam J., Ortoleva P., Sen A. (1988) A weakly nonlinear stability analysis of the reactive infiltration interface. SIAM J. Appl. Math. 48(6): 1362–1378
Chadam J., Sen A., Ortoleva P. (1991) Stability of reactive flows in porous media: coupled porosity and viscosity changes. SIAM J. Appl. Math. 51(3): 684–692
Crank J. (1957) The Mathematics of Diffusion. Clarendon Press, Oxford
Gauri, K.L., Bandyopadhyay, J.K.: Carbonate Stone: Chemical Behavior, Durability, and Conservation. Wiley (1999)
Giavarini, C., Incitti, M., Santarelli, M.L., Natalini, R., Furuholt, V.: A nonlinear model of sulphation of calcium carbonate stones: numerical simulations and preliminary laboratory assessments. IAC Report no. 19 (2003)
Guarguaglini F., Natalini R. (2005a) Global existence of solutions to a nonlinear model of sulphation phenomena in calcium carbonate stones. Nonlinear Anal. Real World Appl. 6(3): 477–494
Guarguaglini, F., Natalini, R.: Large time behavior of solutions to a nonlinear model of sulphation of calcium carbonate stones. IAC Report, Communications in PDE 52 (9/2004); PDF file available at http://www.iac.rm.cnr.it/~natalini/postscript/guna2004.pdf (2005b)
Haynie F.H. (1982/1983). Deterioration of marble. Durability Build. Mater. 1, 241–254
Hassanizadeha S.M., Leijnsea A. (1995) A non-linear theory of high-concentration- dispersion in porous media. Adv. Water Resour. 18, 203–215
Hilhorst D., van der Hout R., Peletier L.A. (1996) The fast reaction limit for a reaction-diffusion system. J. Math. Anal. Appl. 199, 349–373
Hoke B.G.D., Turcotte D.L. (2002) Weathering and damage. J. Geophys. Res. 107(B10): 2210
Lichtner, P. C., Steefel, C.I., Oelkers, E.H. (eds.): Reactive Transport In Porous Media (Reviews in Mineralogy, vol. 34). Mineralogy Society of America, Washington, DC (1996)
Lipfert W.T. (1989) Atmospheric damage to calcareous stone: comparison and reconciliation of recent experimental findings. Atmos. Environ. 23, 415–429
Liu X., Ormond A., Bartko K., Li Y., Ortoleva P. (1997) A geochemical reaction-transport simulator for matrix acidizing analysis and design. J. Pet. Sci. Eng. 17, 181
Meirmananov A.M. (1992) The Stefan problem. de Gruyter, Berlin
Nield, D.A., Bejan, A.: Convection in Porous Media. Springer-Verlag (1992)
Skoulikidis Th., Papakonstantinou-Ziotis E. (1981) Mechanism of sulphation by atmospheric SO2 of the limestones and marbles of the ancient monuments and statues. I. Observations in situ (Acropolis) and laboratory measurements. Br. Corrosion J. 16, 63–69
Skoulikidis Th., Charalambous D. (1981) Mechanism of sulphation by atmospheric SO2 of the limestones and marbles of the ancient monuments and statues. II. Hypothesis concerning the rate determining step in the process of sulphation, and its experimental confirmation. Br. Corrosion J. 16, 70–76
Stakgold, I.: Gas–solid reaction with porosity change. Proceedings of the Conference on Nonlinear Differential Equations, Coral Gables, FL (1999). Electron. J. Differ. Equ. Conf., Southwest Texas State Univ., San Marcos, TX 5, 247–252 (2000)
Szekely J., Evans J.W., Sohn H.Y. (1976) Gas–Solid Reaction. Academic Press, New York
Tambe S., Gauri K.L., Li S., Cobourn W.G. (1997) Kinetic study of SO2 reaction with Dolomite. Environ. Sci. Technol. 25, 2071–2075
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Alì, G., Furuholt, V., Natalini, R. et al. A mathematical model of sulphite chemical aggression of limestones with high permeability. Part I. Modeling and qualitative analysis. Transp Porous Med 69, 109–122 (2007). https://doi.org/10.1007/s11242-006-9067-2
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DOI: https://doi.org/10.1007/s11242-006-9067-2