Stagnation Points as Loci of Solute Concentration Extrema at the Evaporative Surface of a Random Porous Medium

Abstract

Evaporation of a saline solution from a porous medium often leads to the precipitation of salt at the surface of the porous medium. It is commonly observed that the crystallized salt does not form everywhere at the porous medium surface but at some specific locations. This is interpreted at the signature of spatial variations in the salt concentration at the surface of the porous medium prior to the onset of crystallization. We explore numerically the link between the ion concentration spatial variations at the surface and porous medium heterogeneities considering strongly anisotropic short-range correlated permeabil-ity Gaussian fields corresponding to a vertical layering perpendicular to the top evaporative surface for the case of the evaporation-wicking situation. It is shown that the ion concentration extrema at the surfaces correspond to stagnation points with minima corresponding to divergent stagnation points and maxima to convergent stagnation points. Counter-intuitively, the ion concentration maxima are shown to correspond to permeability minima. However, the ion concentration absolute maximum does not necessarily always correspond to the per-meability absolute minimum. More generally, the study emphasizes the key role played by the impact of heterogeneities on the velocity field induced in the medium by the evaporation process. It is also shown that the number of ion mass fraction maxima at the porous medium surface is generally much lower than the naive prediction based on the number of correlation lengths spanning the medium.

From micro-scale to macro-scale modeling of solute transport in drying capillary porous media

“…For instance, if the concentration threshold was selected such that the solute concentration is greater than the considered concentration threshold value in all liquid throats at the surface, the probabilities plotted in Fig. 9 would be simply given by μ abs −mc = number of sur f ace throats in main cluster number of liquid sur f ace throats (15) μ abs −ic = number of sur f ace throats in isol ated cl usters number of liquid sur f ace throats (16) with μ rel−mc = μ abs −mc , μ rel−ic = μ abs −ic for this particular case.…”

“…As discussed in several previous works, e.g. (12)(13)(14)(15)(16)(17), the later corresponds to a situation where the porous sample is fully saturated by the solution as the result of capillary rise. Afthough experimental results in qualitative agreement with the predictions of the ADE have been reported (18], it has been ar gued from other comparisons with experimental data, e.g.…”