Mathematics and Monument Conservation: Free Boundary Models of Marble Sulfation

Clarelli, Fabrizio; Fasano, Antonio; Natalini, Roberto

doi:10.1137/070695125

Cited by 21 publications

(17 citation statements)

References 6 publications

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“…In the second case, monument corrosion, we may have penetration of sulfur dioxide inside the pores resulting in a similar reaction, see [7,8]. The basic reaction in this case describing the fact that SO 2 reacts with calcium carbonate CaCO 3 forming gypsum CaSO 4 • 2H 2 O and causing the corrosion of the monument, is the following:…”

Section: Presentation Of the Modelmentioning

confidence: 99%

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

Nikolopoulos

2018

Eur. J. Appl. Math

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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.

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Section: Presentation Of the Modelmentioning

confidence: 99%

“…This model was further analysed in later papers as in [6,9,10,20]. In the case of monument corrosion, again a model of Stefan type was presented in [7,8]. Additionally, a hydrodynamic model for sulfation of calcium carbonate stones in the form of a reaction diffusion system was presented and analysed extensively in [1-3, 12, 13].…”

Section: Introductionmentioning

confidence: 99%

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

Nikolopoulos

2018

Eur. J. Appl. Math

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“…Equation 7 is a sort of dilation of (4). More modeling work is needed to obtain a better variant of (7). Note that the expression of the velocity s (defined by the non-local law (7)) possesses a certain regularizing effect (compared to the sharp-interface case).…”

Section: Derivation Of the Kinetic Conditionmentioning

confidence: 99%

Interface conditions for fast-reaction fronts in wet porous mineral materials: the case of concrete carbonation

Muntean

Böhm

2009

J Eng Math

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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.

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“…The mathematical community has addressed this corrosion issue mainly from a single-scale or multiple-scale reaction-diffusion perspective. Usually, the single scale approach involves one or two moving sharp reaction interfaces [1,12,17,18,29,30], while the multiple scale setting prefers exploiting a better understanding of the porosity and tortuosity of the material without involving free boundaries [2,10,16]. There are still a number of open issues concerning on how poro-mechanics of the material couples with chemical reactions, flow, diffusion and heat transfer hindering a successful forecast of the durability of the concrete exposed to sulfate attack.…”

Section: Introductionmentioning

confidence: 99%

A mixture theory-based concrete corrosion model coupling chemical reactions, diffusion and mechanics

2018

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A 3-D continuum mixture model describing the corrosion of concrete with sulfuric acid is built. Essentially, the chemical reaction transforms slaked lime (calcium hydroxide) and sulfuric acid into gypsum releasing water. The model incorporates the evolution of chemical reaction, diffusion of species within the porous material and mechanical deformations. This model is applied to a 1-D problem of a plate-layer between concrete and sewer air. The influx of slaked lime from the concrete and sulfuric acid from the sewer air sustains a gypsum creating chemical reaction (sulfatation or sulfate attack). The combination of the influx of matter and the chemical reaction causes a net growth in the thickness of the gypsum layer on top of the concrete base. The model allows for the determination of the plate layer thickness h = h(t) as function of time, which indicates both the amount of gypsum being created due to concrete corrosion and the amount of slaked lime and sulfuric acid in the material. The existence of a parameter regime for which the model yields a non-decreasing plate layer thickness h(t) is identified numerically. The robustness of the model with respect to changes in the model parameters is also investigated.

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Mathematics and Monument Conservation: Free Boundary Models of Marble Sulfation

Cited by 21 publications

References 6 publications

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

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

Interface conditions for fast-reaction fronts in wet porous mineral materials: the case of concrete carbonation

A mixture theory-based concrete corrosion model coupling chemical reactions, diffusion and mechanics

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