We study scalar mixing in heterogeneous conductivity fields, whose structural disorder varies from weak to strong. A range of stretching regimes is observed, depending on the level of structural heterogeneity, measured by the log-conductivity field variance. We propose a unified framework to quantify the overall concentration distribution predicting its shape and rate of deformation as it progresses toward uniformity in the medium. The scalar mixture is represented by a set of stretched lamellae whose rate of diffusive smoothing is locally enhanced by kinematic stretching. Overlap between the lamellae is enforced by confinement of the scalar line support within the dispersion area. Based on these elementary processes, we derive analytical expressions for the concentration distribution, resulting from the interplay between stretching, diffusion, and random overlaps, holding for all field heterogeneities, residence times, and Péclet numbers.

Stretching, Coalescence and Mixing in Porous Media

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

An experiment combining wicking and evaporation of a NaCl solution and leading to the formation of salt efflorescence is presented. The experiment shows that efflorescence develops over the porous medium surface exposed to evaporation except in the bottom region of the sample. This region remains free of efflorescence and is called the exclusion zone. It is shown that the exclusion zone extent depends on the solute concentration in the bottom reservoir. A model is developed, and it helps understand the exclusion phenomenon. The arch shape of the exclusion zone upper boundary is explained and modeled. The study is also seen as a successful test for the model of efflorescence growth driven by evaporation and salt precipitation presented in a previous study. The modeling approach is expected to help develop better models of salt transport with crystallization at the surface of porous media in relation with soil salinization issues or the salt weathering of porous materials.

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Combined wicking and evaporation of NaCl solution with efflorescence formation: The efflorescence exclusion zone

Soil salt crust can change the structure of aeolian soil and improve its resistance to wind erosion. Four ions (Na+, Ca2+, Cl-, and SO42-) with high contents in aeolian soil were selected for a salt crust experiment. The experiment set a variety of gradients of soil salt contents and salt mixing ratios of Na2SO4 and CaCl2. The physical properties of the salt crust were tested, and the wind erosion resistance of the salt crust was discussed. The results showed that the soil salt contents and salt mixing ratio influenced the resistance of the salt crust, especially in terms of its compressive strength and toughness. The former affected the compressive strength of the salt crust by changing the amount of cemented soil salt. The latter affected the kinds of crystals by changing the ion ratio, thus changing the structure of the salt crust and affecting its wind erosion resistance. The wind erosion resistance of the salt crust is complicated by the interaction between the soil salt content and salt mixing ratio. A multilayer crust can be formed in mixed salt, which has a strong wind erosion resistance. This result provides new findings on flowing sand soil and a new method for the treatment of flowing sand soil.

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Characteristics of soil salt crust formed by mixing calcium chloride with sodium sulfate and the possibility of inhibiting wind-sand flow.

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 permeability 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 permeability 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.

https://hal.insa-toulouse.fr/hal-02278716/document

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

The evaporation of a saline solution from a heterogeneous porous medium formed by the assembly of a coarse medium column and a fine medium column is studied numerically. We concentrate on the locus of the formation of first crystals on the evaporative surface from the computation of the ion mass fraction distribution at the surface prior to the efflorescence development. Two basic situations considered in previous works, namely the evaporation–wicking situation and the drying situation are considered. The study makes clear that each situation leads to a markedly different locus of the efflorescence formation, except, however, for very high initial salt concentrations. The study emphasizes the key-role of the velocity field induced in the porous domain in the case of the evaporation–wicking situation. In the case of the drying situation, a key aspect lies in the local increase in the ion mass fraction due to the local desaturation, i.e. the local shrinking of the liquid volume containing the ions.

/pdf/locus-of-first-crystals-on-the-evaporative-surface-of-a-4c40vx6y63.pdf

Babacar Diouf

Papers

Locus of first crystals on the evaporative surface of a vertically textured porous medium

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