Discrete Salt Crystallization at the Surface of a Porous Medium

Efflorescence refers to crystallized salt structures that form at the surface of a porous medium. The challenge is to understand why these structures do not form everywhere at the surface of the porous medium but at some specific locations and why there exists an exclusion distance around an efflorescence where no new efflorescence forms. These are explained from a visualization experiment, pore-network simulations and a simple efflorescence growth model.

Figure 1

Sketch of wicking-evaporation experiment. A pack of 1 mm glass beads ($d_b\approx 1\mathrm{mm}$) in a 50 mm long hollow cylinder of radius $r_w=19\mathrm{mm}$ forms a porous medium. The packing of height $L$ is in contact at its bottom with a NaCl near saturated aqueous solution ($C=C_0=25\mathrm{g}$ $\mathrm{NaCl}/100\mathrm{g}$ solution; the saturation concentration is $C_{\mathrm{sat}}=26.4\mathrm{g}$ $\mathrm{NaCl}/100\mathrm{g}$ solution). The liquid level $h$ in the reservoir is at any time such that the wick remains fully saturated owing to capillary effects. The system is set in a cylindrical enclosure of controlled temperature ($T\approx 22°\mathrm{C}$) and relative humidity (thanks to a LiBr saline solution, $\mathrm{RH}\approx 7\%$). The evaporation rate at the wick surface is varied by changing the distance $\delta$ between the wick surface and the hollow cylinder entrance.

Figure 2

Efflorescence discrete structures (top view of wick surface). The white spots are efflorescence. The projected vertical surface area of the white spots onto the wick surface is about the same in the three images.

Figure 3

Distribution of evaporation flux $j$ at the porous medium surface. The reference flux $j_{\mathrm{ref}}$ is equal to $J/A$ where $J$ is the evaporation rate and $A$ is the porous medium surface area: $J=2.7\times {10}^{-8}\mathrm{kg}/\mathrm{s}$, $2.37\times {10}^{-8}\mathrm{kg}/\mathrm{s}$ and $2.02\times {10}^{-8}\mathrm{kg}/\mathrm{s}$ for $\delta =2.5$, 7.5 and 15 mm, respectively. The evaporation rate is measured from weighing the set–up and also computed solving numerically the vapor transport equations in the enclosure with a finite element code [4, 11]. A good agreement is found with the measurements provided that free convection effects are included in the computations. The flux distributions are deduced from the numerical computations. The crucial point is that the evaporation flux distribution at the surface varies with $\delta$. When $\delta$ is small enough ($\delta =2.5\mathrm{mm}$), the evaporation flux is significantly higher at the periphery (somewhat similarly as in the classical coffee ring problem [5]) whereas for a sufficiently large $\delta$ ($\delta =15\mathrm{mm}$) the evaporation flux is much more uniform ($j(r,\delta )\approx J(\delta )/A$) over the surface. One can refer to 11 for more details.

Figure 4

Pore-network simulation of salt concentration maxima distribution at porous medium surface. The red dots correspond to the menisci where the reduced salt concentration $C^{*}$ is greater than 0.8.

Figure 5

Efflorescence is porous and pumps by capillarity the liquid solution traveling in the underlying porous medium [10]. Efflorescence grows owing to the salt deposition occurring preferentially in efflorescence upper regions where evaporation is higher. As a result of efflorescence growth, evaporation from surface pores located between two efflorescence structures is screened (the evaporation flux becomes negligible) and the crystallization concentration is not reached in these screened pores. By contrast, the liquid flow rate in a surface pore in contact with efflorescence increases. Compared to flow before the onset of crystallization, this induces a reorganization of the flow structure within the upper layer of porous medium, which explains why the efflorescence continues to grow forming discrete and isolated structures.

Figure 6

Efflorescence pumping effect: evolution of evaporation rate $J_{\mathrm{eff}}$ from one efflorescence structure as a function of structure size $V_{\mathrm{eff}}$ (in number of cells). The screening effect is illustrated in the inset top, which shows the evolution of dimensionless mean evaporation flux between two efflorescence structures (along the thick dashed line in Fig. 5) as a function of structure size (the reference flux is the flux in the absence of efflorescence); an example of efflorescence computed shape is shown in the inset bottom.