Mathematical modelling of a mushy region formation during  sulphation of calcium carbonate

Christos V. Nikolopoulos; Christos V. Nikolopoulos

doi:10.3934/nhm.2014.9.635

Networks and Heterogeneous Media

2014, Volume 9, Issue 4: 635-654. doi: 10.3934/nhm.2014.9.635

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Mathematical modelling of a mushy region formation during sulphation of calcium carbonate

Christos V. Nikolopoulos ^{1
,}

1.
Department of Mathematics, University of the Aegean, GR-832 00 Karlovassi, Samos

Received: 01 March 2014 Revised: 01 September 2014
Primary: 35Q92, 35R37; Secondary: 35K57, 74G10, 74S05.

The subject of the present paper is the derivation and asymptotic analysis of a mathematical model for the formation of a mushy region during sulphation of calcium carbonate. The model is 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 on the microscopic scale. The derived macroscopic model is solved numerically with the use of a finite element method. The results of some simulations and a relevant discussion are also presented.
- Monument corrosion,
- sulphation,
- moving boundary problems,
- perturbation methods,
- asymptotic analysis
Citation: Christos V. Nikolopoulos. Mathematical modelling of a mushy region formation during sulphation of calcium carbonate[J]. Networks and Heterogeneous Media, 2014, 9(4): 635-654. doi: 10.3934/nhm.2014.9.635

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Abstract

The subject of the present paper is the derivation and asymptotic analysis of a mathematical model for the formation of a mushy region during sulphation of calcium carbonate. The model is 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 on the microscopic scale. The derived macroscopic model is solved numerically with the use of a finite element method. The results of some simulations and a relevant discussion are also presented.

References

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