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Drying of salt contaminated porous media: Effect of primary and secondary nucleationDesarnaud, J.E.; Derluyn, H.; Molari, L.; de Miranda, S.; Cnudde, V.; Shahidzadeh, N.F. Published in:Journal of Applied Physics DOI:10.1063/1.4930292 Link to publication Citation for published version (APA):Desarnaud, J., Derluyn, H., Molari, L., de Miranda, S., Cnudde, V., & Shahidzadeh, N. (2015). Drying of salt contaminated porous media: Effect of primary and secondary nucleation. Journal of Applied Physics, 118(11), [114901]. DOI: 10.1063/1.4930292 General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. The drying of porous media is of major importance for civil engineering, geophysics, petrophysics, and the conservation of stone artworks and buildings. More often than not, stones contain salts that can be mobilized by water (e.g., rain) and crystallize during drying. The drying speed is strongly influenced by the crystallization of the salts, but its dynamics remains incompletely understood. Here, we report that the mechanisms of salt precipitation, specifically the primary or secondary nucleation, and the crystal growth are the key factors that determine the drying behaviour of salt contaminated porous materials and the physical weathering generated by salt crystallization. When the same amount of water is used to dissolve the salt present in a stone, depending on whether this is done by a rapid saturation with liquid water or by a slow saturation using water vapor, different evaporation kinetics and salt weathering due to different crystallization pathways are observed.

The numerical approximation of 2D elasticity problems is considered, in the framework of the small strain theory and in connection with the mixed Hellinger-Reissner variational formulation. A low-order Virtual Element Method (VEM) with a-priori symmetric stresses is proposed. Several numerical tests are provided, along with a rigorous stability and convergence analysis.we consider the (mixed) Hellinger-Reissner functional (see, for instance, [12,14]) as the starting point of the discretization procedure. Thus, the numerical scheme approximates both the stress and the displacement fields.It is well-known that in the Finite Element practice, designing a stable and accurate element for the Hellinger-Reissner functional, is not at all a trivial task. Essentially, one is led either to consider quite cumbersome schemes, or to relax the symmetry of the Cauchy stress field, or to employ composite elements (a discussion about this issue can be found in [12], for instance). We here exploit the flexibility of the VEM approach to propose and study a low-order scheme, with a-priori symmetric Cauchy stresses, that can be used for general polygons, from triangular shapes on. Furthermore, the method is robust with respect to the compressibility parameter, and therefore can be used for nearly incompressible situations. Our scheme approximates the stress field by using traction degrees of freedom (three per each edge), while the displacement field inside each polygon is essentially a rigid body motion. The VEM concept is then applied essentially for the stress field. We also remark that the construction of the discrete stress field is somehow similar to the construction of the discrete velocity field used for the Stokes problem in [10]. Instead, the displacement field is modelled with polynomial functions, in accordance with the classical Finite Element procedure.An outline of the paper is as follows. In Section 2 we briefly introduce the Hellinger-Reissner variational formulation of the elasticity problem. Section 3 concerns with the discrete problem: all the bilinear and linear forms are introduced and detailed. Numerical experiments are reported in Section 4, where suitable error measures are considered. These numerical tests are supported by the stability and convergence analysis developed in Section 5. Finally, Section 6 draws some conclusions, including possible future extensions of the present study.Throughout the paper, given two quantities a and b, we use the notation a b to mean: there exists a constant C, independent of the mesh-size, such that a ≤ C b. Moreover, we use standard notations for Sobolev spaces, norms and semi-norms (cf.[27], for example). The elasticity problem in mixed formIn this section we briefly present the elasticity problem as it stems from the Hellinger-Reissner principle. More details can be found in [12,14].

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