Combined evaporation and salt precipitation in homogeneous and heterogeneous porous media
Department of Environmental Hydrology and Microbiology,, Zuckerberg Institute for Water Research and Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev,, Midreshet Ben-Gurion,, Israel
 While soil evaporation studies have typically focused on pure or low salinity water evaporation, higher salinity soil conditions are becoming more prevalent. This work explores the combined effect of matrix heterogeneity and salt precipitation on evaporation from soils. Long-term evaporation processes were studied using sand columns, in which heterogeneity consisted of two layers with different grain sizes, and X-ray computed tomography (CT) scanning to quantify salt deposition within pores. For saline solutions, three new stages of evaporation were defined: SS1, SS2, and SS3. SS1 exhibits a low and gradual decrease in evaporation rate because of increasing osmotic potential. During SS2, evaporation rate falls progressively because of salt-crust formation. SS3 is characterized by a constant low evaporation rate. Even though phenomenologically similar to the well-defined classical evaporation stages for pure water, these saline stages correspond to different mechanisms. It is shown that SS2 and SS3 take place while matrix water content can still support first-stage evaporation. Salinity suppressed evaporation more strongly in homogeneous rather than in heterogeneous media. CT scans indicated preferential salt precipitation in the fine-textured regions. Heterogeneous spatial distribution of salt precipitates within the media enabled vapor transport via large pores, while small pores were clogged with precipitated salts. A mathematical model was formulated that simulates evaporation for saline solutions from homogeneous and heterogeneous soils. The model was used to differentiate and quantify the mechanisms controlling each stage of the evaporation process.
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 Evaporation of water from porous media (e.g., soil and rock) impacts many aspects of water management, global water cycle, soil and groundwater salinization, agriculture, and other environmental processes and concerns. While a significant amount of work has been done to understand evaporation from bare homogeneous soils under natural conditions [e.g., Ben-Asher et al., 1983; Blight, 2002; Evett et al., 1994; Penman, 1948] and from cultivated fields [e.g., Daamen and Simmonds, 1996; Van Wesemael et al., 1996], evaporation from heterogeneous porous media has been less studied.
 Recently, Lehmann and Or  investigated the physics of evaporation from heterogeneous porous media with a sharp vertical textural interface. This setup, consisting of two texturally different homogeneous matrices separated by a sharp interface perpendicular to the evaporation front, is relevant to some natural settings, such as sedimentary environments [Press and Siever, 1986]. Sedimentary layers may be exposed to evaporation perpendicular to the orientation of the layers when conjugated with vertical fractures, vole holes, and steep walls such as river banks, or because of geological deformations that expose layer interfaces to the surface. Man-made conditions, including cultivated fields, building materials, and building construction may also present this type of heterogeneity to the evaporation process.
Lehmann and Or  reported higher evaporation of pure water from heterogeneous porous media than from their homogeneous counterparts. In this study, we expand on their work and explore the important process of saline evaporation for homogeneous and heterogeneous media. Since under natural conditions pore water commonly contains dissolved substances, understanding the dynamics and impact of salt accumulation and precipitation on the evaporation process is crucial.
 Several researchers have investigated the characteristics of salt accumulation near the land surface within the vadose zone, especially in arid areas [e.g., Amit and Gerson, 1986; Glendon and Daniel, 1988; Scanlon et al., 1997]. Mineral deposition and crystallization within porous media play a significant role in the evolution of media properties. Haloclastic erosion [e.g., Goudie, 1986; Goudie et al., 1970; Rodriguez-Navarro and Doehne, 1999; Smith and McGreevy, 1983] has been the focus of many studies because of the challenge it presents to the preservation of archeological structures, sculptures, and monuments [Scherer et al., 2001]. These studies have led to wide acceptance of the model that salt precipitation causes more damage to rocks containing a large proportion of micropores connected to macropores. This is explained by the thermodynamic assumption that salts growing in the macropores have lower free energies of formation and tend to be supplied with solution from the micropores [Wellman and Wilson, 1965; Zehnder and Arnold, 1989]. It is usually assumed that the crystals will not grow into the smaller pores because that would require a significant increase in surface area relative to the small addition of volume, resulting in a large increase in the crystal–liquid interfacial free energy. Thus, the crystals in the large pores will continue growing, generating pressure against the pore walls that might eventually result in damage to the host material [Wellman and Wilson, 1965, 1968]. There are, however, other studies showing the opposite behavior under evaporative conditions where precipitates tend to accumulate within smaller pores because of higher capillary forces that draw solution from the larger pores [Pipujol and Buurman, 1997; Scherer, 2004].
 While the complexities of salt crystallization as a function of solution chemistry, environmental conditions, and porous medium properties have been studied in the context of weathering phenomena [Rodriguez-Navarro and Doehne, 1999], salt has been largely ignored in relation to its impact on primary hydrological properties of porous media and on the evaporation process that coexists with salt precipitation.
 Two major mechanisms affect evaporation rates from porous media under saline conditions: (1) lowering solution vapor pressure by increasing solution osmotic potential [Salhotra et al., 1985] and (2) development of efflorescence (surface salt crust) or subflorescence (salt precipitation within the matrix), both of which lead to a reduction in vapor and liquid matrix permeability. Chen  reported that a salt crust of only a few millimeters can reduce evaporation to a small percentage of the potential evaporation rate. Shimojima et al.  investigated the effect of solute crystals that formed in the dry surface layer of sand and glass beads, with initial conditions of residual water content, under very low evaporative potential. They reported significant accumulation of salt in the upper ∼10 mm of the samples and a reduction of 70 and 30% in evaporation rates from dune-sand and glass-bead columns, respectively. Nassar and Horton  compared evaporation rates from compacted and loose soils with KCl solution and solute-free pore water, and reported a 5 to 22% reduction in evaporation rate for the salinized columns, respectively. Recently, Fujimaki et al.  measured the influence of salt-crust accumulation on evaporation rates from homogeneous soils under constant matric pressure. They found a more than 50% reduction in evaporation rates as a result of the salt crust, which blocked the matrix. Measurements from natural playas with high groundwater salinity and in the presence of salt crust are consistent with laboratory experiments, indicating a reduction in evaporation rates of similar magnitude [e.g., Malek et al., 1990; Tyler et al., 1997; Malek, 2003; Kampf et al., 2005].
 These cited works only considered evaporation and salt precipitation for homogeneous porous media; no publications were found investigating the synergistic processes of evaporation and salt precipitation in the context of heterogeneous media. Moreover, the studies mentioned typically focused only on the early stages of evaporation, whereas the study presented here follows the evolution of saline evaporation through all three stages of evaporation. This study sheds new light on the mechanisms controlling salt precipitation and evaporation at the macro and pore scales in both homogeneous and heterogeneous porous media.
2.1. Evaporation From Homogeneous and Heterogeneous Porous Media
 Evaporation from porous media in the absence of a constant water supply or in the case of a deep water table was found to occur in three stages for natural soils [Fisher, 1923]. Lehmann et al.  further elaborated on the first and second stages by studying evaporation from well-sorted sand. The working definitions for the three stages of evaporation used in this study are as follows. Stage 1 (S1), an initial constant high evaporation rate, exists as long as there is hydraulic connection between drying front and matrix surface by capillary flow [Lehmann et al., 2008]. When hydraulic connections break, evaporation becomes vapor diffusion–limited and the second stage of evaporation (S2) begins [Lehmann et al. 2008]. A residual slow-rate stage (Stage 3, S3) is established when the evaporation front is deep below the matrix surface and evaporation is governed by diffusive vapor transport [Fisher, 1923].
 [Lehmann et al. 2008] and Lehmann and Or  showed that the duration of S1 depends on the difference in air-entry values between the smallest and largest pores. Those researchers introduced a characteristic length (Lcap) which determines conditions for the transition between S1 and S2. The value of Lcap also depends on liquid viscosity, but for high permeability media, as were used for this study, the role of viscosity can be ignored, and Lcap is expressed as a function of the largest and smallest capillary radii (Rmax and Rmin):
where (N/m) is the liquid surface tension, g (m/s2) is the acceleration because of gravity and (kg/m3) is the water density. Once the meniscus recedes into the smaller capillary, water is transported to the surface by vapor diffusion.
 Generally, in a homogeneous matrix, the difference between Rmin and Rmax is relatively small (corresponding to a lower Lcap value), whereas for a heterogeneous configuration this difference can be much larger, resulting in earlier transition to S2 for homogeneous relative to heterogeneous conditions (Figure 1).
 The duration of S1, t (d), can be estimated from a simple model in which all evaporation takes place from the fine matrix and the S1–S2 transition occurs when the drying front reaches Lcap:
where Afine and Acoarse (m2) are the surface areas of the fine and coarse sections, respectively, e0 (m3/m2 d) is the potential evaporation rate from the matrix surface, and is the porosity. The numerator in equation (2) represents the amount of water evaporated to reach Lcap, while the denominator expresses evaporation rate from the fine sand.
 While vapor transport in porous media can be driven by advection and diffusion, in this study we assume only diffusive transport for vapor flux within the matrix and from the matrix surface to the atmosphere [Fick, 1855]. Under isothermal conditions, which were maintained in the experiments presented herein, vapor flux is controlled by vapor pressure gradients and the vapor-diffusion coefficient.
 Capillary pressure suppresses evaporation by lowering water energy and reducing equilibrium vapor pressure, as expressed by the Kelvin equation (derived for capillary tubes by Ho ). For the pore dimensions presented in this work, with typical sizes of sand grains, the effect of capillary pressure is negligible, i.e., smaller than 0.001%.
 Evaporation during S2 and S3 depends strongly on capillary forces within the media. For fine media, while high capillarity increases the duration of S1 by increasing Lcap, during S2 and S3, strong capillarity supports a large volume of residual water content within the media, lowering air-filled porosity and decreasing the effective vapor-diffusion coefficient (Deff) [Ho, 2006]. On the other hand, a matrix with large pores produces a short S1 duration and insignificant S1 cumulative evaporation because of fast gravity drainage and low air-entry pressure [Kozak and Ahuja, 2005]. However, during S2 and S3, low capillary forces result in lower residual water content and higher Deff, supporting higher evaporation rates. Moreover, low Lcap values in coarse media support even higher evaporation rates during S2 and S3 because of proximity of the evaporation front to the surface.
 In the work presented herein, two effects of salinity on evaporation are emphasized: (1) vapor-pressure lowering by osmotic potential, and (2) reduction of the vapor-diffusion coefficient because of mechanical clogging of the matrix by precipitated salt. Both mechanisms depend on the rate of ion accumulation at the evaporation surface. This rate can be investigated via the Péclet (Pe) number of the system, which compares solute transport by advection toward the evaporation front to solute transport by diffusion, which has a propensity to homogenize solution concentration. Pel et al.  define Pe for an evaporating solution as:
where e0 is evaporation rate (m3/m2 s), Lp is a characteristic length of interest (m), Dion is the ion diffusion coefficient (typically 10-9 m2/s) and is the degree of saturation (m3/m3). Pe >> 1 signifies that advective mass flow of the ions is dominant, hence ions will accumulate at the top of the matrix near the evaporation front. Zimmermann et al.  and Barnes and Allison [1983, 1988] explored isotope (18O and 2H) and chloride ion distribution profiles in saturated and unsaturated soil columns undergoing evaporation. The authors showed that these isotopes and ions accumulate near the evaporation front and their relative concentration in the solution decreases exponentially with depth (z), proportional to exp(–z/Dion/e0). This correlation, as well as Pe, enables calculation of the solution depth, which is affected by the salt accumulation at the evaporation front.
 As solution concentration increases near the evaporating surface, the solution osmotic potential increases respectively and decreases vapor pressure [Ho, 2006]. Vapor pressure (Psal (Pa)) of a nonvolatile solute (e.g., NaCl or other salts) in a volatile solvent (e.g., water) is shown by Raoult's Law to be proportional to the solvent mole fraction:
where xsolvent is the mole fraction of the solvent and (Pa) is the solvent vapor pressure at saturation [Kotz et al., 2008]. During evaporation, ionic concentration increases until solution saturation is reached and crystals may begin to precipitate. In nature, solution supersaturation is not uncommon prior to crystallization [Espinosa et al., 2008]. During crystal precipitation, the ion concentration of the solution remains constant and the osmotic potential is not expected to change. This is true for simple binary solutions, whereas for more complex ionic solutions concentration can change because of chemical reactions, such as in the case of carbonate and gypsum solution [Rosenberg et al., 2001]. These complex solutions are beyond the scope of this research, which aims to shed new light on the fundamental mechanisms involved in evaporation-salt precipitation processes.
 The second effect of salt on evaporation occurs during the precipitation process. Salts may precipitate as efflorescence above the surface or as subflorescence below the surface within the matrix pores, depending on the salt species, humidity, and thermal conditions [Rodriguez-Navarro and Doehne, 1999]. When precipitating as an efflorescent crust, salt acts as an additional layer above the originally porous media through which vapor needs to diffuse, resulting in vapor flux reduction. Fujimaki et al.  modified the bulk transfer equation [Daamen and Simmonds, 1996; Yakirevich et al., 1997] to take into account the resistance of the additional salt crust to water-vapor transport. The authors showed that matrix resistivity to vapor diffusion increases in proportion to salt-crust thickness.
 Theoretically, the efflorescent crust is deposited during S1, when the solution evaporates at the surface. The salt crust will decrease evaporation by reducing permeability and vapor diffusion, bearing in mind that the vapor pressure was already reduced prior to initiation of crystal formation [e.g., Acero et al., 2007; Chen, 1992; Fujimaki et al., 2006; Kelly and Selker, 2001; Nassar and Horton, 1999; Shimojima et al., 1996; Weisbrod et al., 2003]. As a result, the phenomenological characteristics of S1 will change and duration will appear to be shortened relative to nonsaline evaporation. In addition, the salt crust will reduce evaporation during S2 and S3 by increasing resistance to vapor diffusion. When salt is precipitated as subflorescence, its major effect will be evident during S2 and S3, as it will decrease matrix-unsaturated hydraulic conductivity [Wissmeier and Barry, 2008] and vapor-diffusion coefficients through the matrix because of the reduction in matrix porosity.
 On the basis of this discussion we suggest the following conceptual model for evaporation from heterogeneous porous media under saline conditions: Three new evaporation stages are defined here: SS1, SS2, and SS3. SS1 exhibits a gradual decrease in evaporation rate because of increasing osmotic potential near the evaporation surface (for Pe >> 1). SS2 is defined as a period of sharply decreasing evaporation rate because of decreasing vapor diffusivity through the growing salt crust. Finally, SS3 is a period of very slow constant evaporation rate. Notwithstanding the apparent phenomenological similarity between the three DI and three saline evaporation stages, the mechanisms controlling SS1, SS2, and SS3 are different from those controlling the traditional (DI) periods—S1, S2, and S3. It is important to note that the transition between SS1, SS2, and even SS3 may be observed while the matrix water content and capillary flow still support a moist and even saturated matrix surface, mechanistically considered to be S1.
 Matrix heterogeneity adds an additional degree of complexity. Orientation of heterogeneous layers strongly affects the evaporation process. Herein we discuss layered heterogeneity in which the layer planes intersect (i.e., are perpendicular to) the evaporation front; in this case, the layer with the highest vapor-diffusion coefficient will control the flux during SS2 and SS3 [Warrick, 2001]. In addition, during drying of the coarse media, evaporation also proceeds from the exposed coarse-fine vertical interface. During the first stage of saline evaporation (SS1), the coarse and fine sand segments are expected to have similar evaporation rates, as both media are saturated with equal salt concentrations. However, the coarse sand is expected to move quickly to SS2, not because of salt precipitation on the surface, but because of its hydraulic transition to S2 because of a low air-entry pressure.
 Consequently, the fine-sand segment, with its higher air-entry pressure, will sustain most of the evaporation, resulting in a massive salt crust over the fine media. In contrast, the coarse-sand segment during the SS2 stage supports a lower evaporation rate with much less salt accumulation. This relatively salt-free area may be a key participant in later stages of evaporation (SS2 and SS3), serving as a bypass for vapor blocked by salt that is located within and above the fine-sand segment. If the evaporation rate from the interface is sufficiently high (Pe >> 1), salt precipitation may also occur there. This conceptual model for evaporation of a saline solution from a heterogeneous matrix is examined and quantified numerically and experimentally.
2.3. Numerical Model of Evaporation With Efflorescent Precipitation
 The mathematical model developed in this section is valid for evaporation of distilled water (DI) and saline solutions from homogeneous and heterogeneous porous media. The model includes the effects on the evaporation rate of increases in osmotic potential near the evaporation front, the growing efflorescent salt crust over the fine media, and the increasingly exposed interface between moist fine media and drying coarse media. The model is formulated for the case of an efflorescent salt crust to compare to evaporation experiments using solutions of NaCl, which has a propensity to precipitate as efflorescence [Rodriguez-Navarro and Doehne, 1999]. But, it is also applicable to a number of other salts and minerals that form efflorescent salt crusts in nature [e.g., Malek et al., 1990; Ullman, 1985; Cooke, 1981; Torgersen et al., 1986]. Evaporation rate from a liquid source is dictated by the diffusive vapor flux as per Fick's law [Fick, 1855]:
where Jv (kg/m2 s) is the vapor mass flux, D (m2/s) is the vapor-diffusion coefficient in free air, and and are the differences in vapor concentration (kg/m3) over distance (m). The vapor concentration (C) for a given vapor pressure can be calculated using the ideal gas law:
where Pv is the vapor pressure (∼4.2 kPa for water at 30°C), Ri (J/kg K) is the gas constant for species i, and T (K) is the absolute temperature. Pv can be lowered by increasing the solution osmotic potential [Ho, 2006].
 Hence, a highly porous medium will have a high vapor flux compared to a low-porosity medium. The tortuosity also plays a role in the diffusion process, and this is embedded in equation (7) as a function of porosity.
Equation (9) expresses the vapor flux (J) (kg/m2 s) from the evaporation front to the atmosphere for a homogeneous matrix under conditions of a receding water level, including the effects of osmotic potential and efflorescent salt precipitation:
 The term in brackets in equation (9) is the effective diffusion coefficient for a porous medium with a salt crust above it, modeled as diffusion across a layered system [Warrick, 2001]. La (m) is a characteristic length for the air layer (atmosphere) above the matrix surface participating in the vapor-diffusion process, Ls (m) is the efflorescent salt-crust thickness, and Ld (m) is the depth of the evaporation front below the matrix surface (Figure 2a). To calibrate the system to laboratory conditions, a fitting parameter is added to the vapor-concentration differences between the evaporating surface and ambient air. The factor can be quantified by fitting the model to a reference DI column.
 Two physically significant parameters of proportionality are also introduced: and adjust the theoretically expected value for the matrix diffusion coefficient from equation (7) to the specific porous media used. For example, the maximum air-filled porosity for sand is ∼35%, giving, by equation (7), Deff = 0.25D; but the effect of a residual moisture content of ∼5% [Warrick, 2001] will give Deff = 0.2 D, corresponding to a 20% correction.
 The diffusion coefficient of vapor through a salt crust is unknown; hence, is one of the key parameters of interest to be obtained from this model and is found by fitting the model to the data. Previous works [e.g., Chen, 1992; Fujimaki et al., 2006; Nassar and Horton, 1999; Shimojima et al., 1996] have indicated that the salt crust has a pronounced effect on evaporation from porous media, and therefore is expected to be substantially smaller than .
 Because C, Ls, and Ld are functions of time (i.e., cumulative evaporation), an iterative approach is used to model the evaporation rate (J) over time. Vapor pressure at the solution surface is affected by the osmotic potential (equation (4)), which changes with time as solution concentration (c) increases. As salt starts to crystallize from the solution, the solution concentration remains constant (cs). The solution concentration cs cannot be lower than the salt solubility concentration (26% for NaCl), but can be higher, because supersaturation is common in evaporating solutions: for NaCl, a supersaturation of 2 is common [Flatt, 2002; Scherer, 1999]. Increases in precipitated salt mass increase Ls and reduce vapor diffusivity. Ld increases in response to water mass loss, resulting in additional reduction in vapor diffusivity since Deff < D. Equations (10) and (11) define the evolution of c(t) and Ls(t) during evaporation. Figure 2 presents model parameters and the model flow diagram.
where A (m2) is the surface area of the matrix, t (d) is time and (kg/m3) is the solid salt density. Ms (kg) is the mass of the parcel of water at the top of the matrix where ions are accumulating. The size of the water parcel (Ms) is determined by Pe which defines the appropriate Lp to maintain Pe >> 1 (equation (3)) during SS1. Evaporation-front depth (Ld) is proportional to the water mass loss, matrix porosity, water density , and capillary rise, which elevates the evaporation front above the water table:
 An additional contribution to evaporation in a heterogeneous matrix comes from the fine–coarse interface when the fine section is saturated but the coarse section is drying, enabling vapor flow through the coarse section. Interface evaporation rate Ji is calculated by integrating the contribution from all depths (z) along the fine–coarse interface, as follows:
where Lsi is the salt-crust thickness forming at the interface. The final mathematical model is composed of the family of equations (equations (9) to (13)). Total evaporation from a heterogeneous media is solved by this model by computing the individual contributions of each segment separately (fine, coarse, and interface) and then summing them at each time step.
3. Materials and Methods
 Two methods were used in this study: (1) evaporation experiments from homogeneous and heterogeneous sand columns saturated with DI or NaCl solution (Exp 1), and (2) X-ray computed tomography (CT) scans of sand columns (Exp 2) and a Berea sandstone core (Exp 3) performed prior to, during, and after evaporation of NaI solution.
3.1. Column Experiments
 Experiments were carried out to measure the impact of salt precipitation on evaporation rate from homogeneous and heterogeneous soil columns. All experiments were conducted in a climate-controlled room (CCR), where the air temperature was fully controlled (30 ± 0.5°C) and monitored. Heating/cooling of the CCR is affected by radiation alone, thus eliminating uncontrolled wind sources that may affect evaporation rates. Ten identical miniventilators (GlacialTech, Silent Blade 120 mm, Taiwan) with wind speed of 2.1 m/s were placed 1 cm above each column, blowing a constant and steady wind to accelerate the evaporation process and reduce experiment duration. An initial experiment under no-wind conditions was performed to ascertain that the ventilators did not change the internal dynamics of the evaporation process.
 Eight Plexiglas columns (50 cm high and 11 cm in diameter) were used for each experiment set. Columns were placed on scales (±1 g, Merav 2000, SHEKEL, Beit Keshet, Israel) and connected to a data logger (CR10X Campbell Scientific Inc., North Logan, UT, USA) to continuously measure the water loss because of evaporation. Two additional columns (25 cm high and 11 cm in diameter) filled with DI and 5% (by weight) NaCl solutions were used to measure the potential evaporation rate (eo) and the effect of osmotic potential on eo.
 Two sand grades were used to construct the heterogeneous configurations: fine sand (grain size of 150–300 m with average pore radius of 78 m) and coarse sand (grain size of 1–2 mm with average pore radius of 495 m). Pore sizes were calculated from measurements of soil water retention curves [Hillel, 1998] and from grain dimensions [Glover and Walker, 2009]. Column porosity was calculated by measuring the amount of water needed to fully saturate it (see Table 1). Matrix configurations consisted of: (1) homogeneous fine sand (Homo-fine) (Figure 3a); (2) homogeneous coarse sand (Homo-coarse) (Figure 3b); (3) a heterogeneous column with half a column of fine sand next to half a column of coarse sand (Hetero) (Figure 3c).
Table 1. Homogeneous (Homo) and Heterogeneous (Hetero) Column Experiment Setup
 The perimeter of each column was thermally insulated from ambient air with plastic bubble-laminated aluminum foil. Therefore, energy and mass transfer only occurred through the top of the columns.
 To assure maximal uniformity and chemical purity of sands, sands were washed with DI, oven-dried, and sieved before each experiment. Columns were packed dry by pouring the sands from the top. A customized funnel was used for sand pouring, to avoid sand grain sorting. To pack the heterogeneous columns, thin (2 mm) cardboard spacers were used to create the separation between the fine and coarse sand segments. After packing, the spacers were pulled out and the columns were gently shaken to ensure tight packing at the interface.
 After packing, CO2 was injected from the bottom of the column for more than 1 h, to remove trapped air. The CO2 was then slowly replaced with solution (∼20 mL/min), injected from the bottom using a peristaltic pump, until saturation was reached. Initial conditions for all columns were complete saturation with 1 cm of free fluid above the upper boundary of the sand. After saturation, the solution supply was disconnected and the system was allowed to evaporate. Data were collected automatically for 50 days at 1 h resolution. Table 1 summarizes the setup details for the experiment.
3.2. CT Scans of Sand Columns and Berea Sandstone
 CT scans were performed on experiments at two scales: (1) macroscale CT scans of large evaporating sand columns (Exp 2), and (2) microscale CT scans of a small Berea sandstone core (Exp 3). CT scans were performed at the Center for Quantitative Imaging (CQI) at The Pennsylvania State University. The scans were used to observe, measure, and characterize the distribution of solution and salt precipitation within the porous media throughout the evaporation process. NaI solution was used as the evaporating liquid because of its high X-ray attenuation.
 Macroscale soil column scans (Exp 2): Three Plexiglas columns (25 cm long, 5 cm diameter) were packed as for Exp 1 (Figures 3a and 3c) with an additional Heterogeneous column divided into four alternating quarters (Figure 3d). The same experimental procedure as Exp 1 was followed. The average porosity of the columns was 37.5 ± 2%. Columns were saturated with 5% (by weight) NaI solution and left to evaporate in the CCR at 40 ± 0.5°C for 4 weeks. Evaporated samples were scanned in a medical scanner (HD-350 scanner, Universal Systems Inc., Solon, OH, USA) to observe the macroscale distribution of salt precipitation. For these scans an excitation voltage of 120 kV was used, with voxel dimensions of 0.25 × 0.25 mm and a slice thickness of 1 mm. Image resolutions are 512 × 512 pixels.
 Micro-Scale Berea Sandstone Scans (Exp 3): A Berea core was drilled and machined to dimensions of 51 mm high and 8.8 mm in diameter. Berea is a sedimentary rock (sandstone) composed of quartz sand cemented with silica (see www.bereasandstonecores.com). The relatively high porosity and permeability of the Berea sandstone make it a good reservoir rock, hence it has been thoroughly studied and its properties documented in petroleum research [e.g., Bae and Petrick, 1977; Gunn, 1986; Siddiqui et al., 2002].
 The sample porosity was 17%, as measured by water content at saturation. The Berea core had a natural structure composed of parallel layers, typical for sedimentary rocks. Grain and pore size characteristics were relatively homogeneous within each layer, but different for different layers. The natural stacking of several layers created a heterogeneous medium with sharp interfaces between the layers. The Berea core was drilled so the central axis was parallel to the layer plane and normal to the evaporation surface; each layer had a width of ∼1 to 2 mm (Figure 4a). The core was placed in a machined PVC cylindrical holder that was open at the top to the atmosphere. The gap between the core and the holder was filled and sealed with an epoxy material (Bolidt joint compound E/LP718, Netherlands) (Figure 4b). The core holder design permitted saturation of the sample from the bottom.
 The experiment was conducted as follows: The core was initially scanned dry, then saturated with 5% NaI solution while in the scanner without changing its position. The saturated sample was scanned and then left to evaporate within the scanner. The top 10 mm of the core were scanned every 24 h during the evaporation process. After 5 days, when changes were no longer observed and there was no additional salt accumulation at the top of the sample, the entire core was rescanned to map the salt distribution within it. A simple Klinkenberg air-permeability test [Klinkenberg, 1941] was performed on the scanned Berea sample before and after evaporation to estimate the effect of the precipitated salt on matrix gas permeability.
 For the Berea scans, a high-resolution scanner (Omni-X HD600 Universal Systems Inc., Solon, OH, USA) was used, which enabled observations at the pore scale. For these scans an energy level of 130 kV with lateral resolution of 1024 × 1024 pixels was used. Each voxel dimension was 10 × 10 × 11.5 m, along the x, y, and z axis, respectively. To analyze the CT scans, for both the large column and the Berea core, 3D image processing software was used (AVIZO 5, by Mercury, Burlington, MA, USA).
 This section compares mathematical model predictions to results from Exp 1. The model consisted of numerically solving equations (9) to (13) at 1 day intervals for 50 days. Physical parameters used in the model for the two sands and NaCl properties were: ; T = 30 °C; initial solution concentration was 5% (by weight); degree of supersaturation for NaCl crystallization was equal to 2 [Espinosa et al., 2008], corresponding to a concentration of cs = 52% (by weight); salt density was 2165 kg/m3 [Deer et al., 1966]; La = 0.1 m, and Lcap for fine and coarse matrices was 0.15 and 0.03 m, respectively. Lp was chosen as 0.01 and 0.04 for the heterogeneous and homogeneous media, respectively, to maintain Pe >> 1 (equation (3)). This difference in Lp values corresponds to differences in evaporation rates of the fine sand between homogeneous and heterogeneous columns. For these values of Lp Pe is in the range of 4 to 8, which is sufficiently high to force salt accumulation at the matrix surface [Pel et al., 2003]. The parameter , which adjusts for the laboratory-specific vapor concentration gradient between solution surface and atmosphere, was determined by fitting the model to a reference DI column and found to be equal to 8.5.
 Fitting the model to the Homo-fine-DI columns, corresponds to a mean value of 18% air-filled porosity, reflecting the partially moist drying zone. Fitting the model to the Homo-fine-saline column resulted in proportionality parameters related for vapor diffusion through matrix and salt that were found to be equal to 0.4 and 0.01, respectively. The highest cumulative evaporation values were observed for the Hetero columns, with both DI and saline fluids (Figure 5). These columns also had the longest S1 as predicted by Lehmann and Or , and the longest SS1 as predicted by our model. Lowest cumulative evaporation was observed for the Homo-coarse columns, with both DI and NaCl, as it shifted early into S2/SS2, because of the low air-entry value of this sand.
4.1. Homogeneous Columns
 Good agreement was observed between predicted (simulations) and measured results for the Homo-coarse columns (Figure 6). The dominant process governing evaporation for the Homo-coarse columns is the rapid recession (short S1) of the evaporation front below the matrix surface because of its low Lcap value. The short duration of S1 (∼1 day) did not allow formation of a massive salt crust at the surface; hence, no significant differences were expected, or seen, between DI and saline conditions. Once the evaporation front recedes into the matrix, Deff is the limiting parameter controlling evaporation rate.
 While the Homo-coarse columns showed no differences between DI and saline conditions, the Homo-fine columns showed significant differences between the two. The key distinguishing phenomenon (shown in both model and data, Figure 7) between DI and saline conditions is in the characteristics of S1: For DI the evaporation rate was constant during S1, whereas for saline conditions, the evaporation rate during SS1 gradually decreased. This is caused by the increasing osmotic potential. In addition, while Homo-fine S1 lasted 7 days because of the high Lcap value of the fine sand, SS1 lasted for less than 1 day. The significant reduction in evaporation rate after 1 day was caused by salt precipitation at the surface, which suppressed vapor diffusion.
 The model was used to elucidate the mechanism responsible for the dramatic difference between S2 (the second DI evaporation stage) and SS2 (the second saline evaporation stage). Under DI conditions S2 begins when the receding drying front disconnects from the matrix surface. By contrast, for saline conditions, transition to SS2 is caused by a salt effect that includes osmotic potential increase and salt-crust buildup. The arrow in Figure 7b indicates the time point when cumulative evaporation from the Homo-fine-saline column equaled the cumulative S1 evaporation for DI conditions; thus SS1 and SS2 occurred under hydraulic conditions of capillary connectivity to the evaporation surface.
4.2. Heterogeneous Columns
 The same mathematical model was applied to heterogeneous columns by separately calculating and then summing the evaporation from the fine and coarse segments, as well as the vertical interface (Figure 8).
 The DI column (Figure 8a) clearly shows that S1, which lasts for ∼18 days, is composed of two phases. The first phase, lasting for less than 1 day, occurs when the entire column is in S1. Since the air-entry pressure of the coarse sand is low, it shifts quickly to S2. At this point, the entire column enters the second phase of S1, where the fine sand continues to sustain a high and relatively constant evaporation rate (S1), but the contribution of the coarse sand is noticeably reduced, and the contribution of the interface begins. The first phase of S1 exhibited an evaporation rate of 60 g/d per column, decreasing to 40–50 g/d per column during the second phase. The total duration of S1, measured at ∼18 days, was in good agreement with the S1 duration predicted by the model and by equation (2).
 The model revealed an important contribution of evaporation through the vertical fine–coarse interface (dotted line in Figure 8). The relative contribution of the interface to evaporation increased progressively as the coarse-section evaporation rate dropped, because of the increasing surface area of the interface. Interface contribution to evaporation sustained its maximum value when the fine sand was in S1 and the coarse sand in S3. At that time, the vertical interfacial surface area is greatest while its distance from the matrix surface is low. Once the fine sand entered S2 and its water level receded, the contribution of the vertical interface decreased as its distance to the atmosphere grew.
 Saline evaporation from heterogeneous media exhibited the same phenomenological characteristics as for homogeneous media, with a SS1 stage composed of two phases, and shorter than the DI–S1 counterpart because of osmotic and salt crust mechanisms. Notably, because of the low air-entry pressure, the coarse segment contributes little directly to evaporation, whether DI or saline. The most significant reduction in evaporation is seen as the fine-sand section enters into SS2 because of salt-crust formation, indicating that the fine media is what controls the evaporation rate for a mixed-media system. While for the saline case the vertical interface also contributes to evaporation, its effect is also reduced by salinity. According to the model, under saline conditions, the interface contributes to evaporation of 47% of the total mass, and approximately 50% of the precipitated salt is accumulated at the fine–coarse interface, mainly close to the top of the column.
 During the third stage (S3 and SS3), the evaporation rate for the Hetero column (10–15 g/d per column) was significantly higher than for the Homo-fine one (5–10 g/d per column). The higher evaporation rate during SS3 is shown by the model to be provided by evaporation along the vertical fine–coarse interface followed by vapor transport via the (nonsalt-encrusted) coarse media.
4.3. CT Scans
4.3.1. Sand Column Scans
 The CT scans of the fine-textured sand columns (Figures 9a, 9b, and 9c) show that 80 ± 15% of the salt precipitated within the top 2.5 cm of the column. In the Hetero columns, more than 90% of the salt accumulated within the fine-textured portion (Figures 9b and 9c). This was also observed visually in the Hetero NaCl columns used for Exp 1 (Figure 10).
 For the Hetero half-divided column, a salt mass analysis was done along a vertical plane perpendicular to the fine–coarse interface, for the entire column length. Preferential salt precipitation was seen near the interface, with ∼2 times higher salt precipitating within the fine sand and within 15 mm of the interface compared to more distant locations (Figure 9c). This observation corroborates model results that show ∼50% of the salt accumulating within the fine sand near the interface.
4.3.2. Berea Sandstone Scans
 The CT scans of the Berea sample showed an initial NaI concentration in the saturated sample of 0.5 × 10-2 g per horizontal slice (each slice was 11.5 m thick). After evaporation, the top 1.5 cm of the sample was enriched to 0.19 g of NaI, representing 61% of the total salt in the 5.1 cm sample, whereas only 0.06 g (19%) of the salt accumulated in each 1.5 cm thick section below this upper region, showing a net reduction in NaI concentration caused by upward migration of ions (Figure 11).
Figure 12 displays horizontal and vertical cross sections of CT images showing salt accumulation in the upper section of the Berea pores, with preferential accumulation in the region with finer pores (< 0.2 mm) with the larger pores remaining open. The average porosity of the natural dry sample was 17%, calculated from both water content and CT-image analysis. Regions comprised mainly of small or large pores were differentiated by CT-image analyses and calculated to have initial porosities of ∼12 and ∼25%, respectively. After evaporation, more than 90% of the small pores and about 80% of the large pores were clogged. Salt deposition significantly reduced porosity in the top 7 mm of the sample to an average 2.5%, with porosities of ∼1% and ∼5% for the small- and large-pore regions, respectively. The coarse fraction of the Berea sample accumulated a higher proportion of the total salt than the coarse fraction of the large sand columns because its much higher air-entry pressure sustained a longer S1, which resulted in more salt precipitation prior to air entry. While the finer media acts as a wick to sustain a longer S1 and greater salt accumulation, the ratio of salt precipitation between coarse and fine fragments will be a function of both the air-entry value of the coarse fragment and the relative air-entry values of the two media.
 Klinkenberg air-permeability test indicated that salt precipitation has a small effect on mean matrix air permeability—a reduction of only 7% even though the top of the Berea was almost fully clogged with salt. The large-pore regions, which remained relatively open and ran parallel to the direction of the vapor flux, may have provided a preferential path for gas flow.
 The mechanistic and analytical model presented here for evaporation from saline porous media predicts the evolution of the evaporation process through its three stages. Model results are supported by our experimental results and concur with previously published studies which, in general, show suppressed evaporation rates (on the order of tens of percentage points) for saline solutions from a free surface [Salhotra et al., 1985], as well as from homogeneous porous media [e.g., Chen, 1992; Fujimaki et al., 2006; Nassar and Horton, 1999; Shimojima et al., 1996]. Here, we posit that salinity reduces evaporation rates by increasing solution osmotic potential and by the formation of a salt crust on top of the matrix that reduces vapor diffusivity.
5.1. Effect of Salinity in Homogeneous Columns
 Salinity of the evaporating solution leads to the development of three mechanistically controlled evaporation stages—SS1, SS2, and SS3—that are distinct from the three stages historically defined for DI evaporation (S1, S2, and S3). In contrast to the constant evaporation rate that defines S1, SS1 exhibits a continuous gradual reduction in evaporation rate resulting from increasing osmotic potential. Transition to SS2 begins with precipitation of the salt crust, which is evidenced by a sharp decrease in evaporation rate. Notably, while the transition to S2 occurs when the liquid becomes hydraulically disconnected from the surface, both SS1 and SS2, and even the early stages of SS3 occur while the liquid is still hydraulically connected to the evaporation surface. This indicates that the reduction in evaporation during SS2 and parts of SS3 is because of the salt effect only (osmotic potential and salt precipitation). As the solution disconnects from the matrix surface (S2 begins) salt will start to crystallize at the receding evaporation front within the matrix profile (Figure 11). In the case of high initial ion concentration, and very high permeability media, gravitational instabilities near the evaporation front may drive convection flows of the pore solution [Van Dam et al., 2009] which may postpone ion accumulation and affect salt precipitate distribution. In this study the good agreement between experimental results and the model indicate that these convection flows did not develop.
 The vapor-diffusion coefficient for the salt crust (Dcrust = D) was quantified by fitting the mathematical model (parameter in equation (9)) to the data from the Homo-fine-saline column. In that column had a value of 0.01, which corresponds to a 96% decrease in the diffusion coefficient through the salt crust relative to a dry, salt-free matrix, and which drives the sharp decrease in evaporation rate observed as soon as the formation of a salt layer is visually observed.
5.2. Effect of Heterogeneity
 Heterogeneity adds new mechanisms to the evaporation process from porous media. The fine-textured matrix acts as a wick, lengthening the duration of S1, and the vertical interface between coarse and fine sections enhances the evaporative flux. In this work, we expand on the work of Lehmann and Or  who described Hetero-S1 as a single stage with constant evaporation rate, which depends mainly on potential evaporation. Our results, both experimental and mathematical, show that S1 for a heterogeneous matrix is composed of two phases (Figure 8). The first phase exhibits a constant maximum evaporation rate while both fine and coarse sections are saturated and both contribute to evaporation. As the air-entry pressure of the coarse sand is exceeded, it enters S2 and its contribution to evaporation is reduced. This point marks the transition to the second S1 phase, where most of the evaporation occurs over the fine sand, with a significant contribution from the vertical fine–coarse interface. The second S1 phase lasts until the drying front of the coarse sand falls below Lcap, at which time the transition to S2 ensues. As an example, in Figure 8, the first S1 phase lasted for ∼1 day, followed by the second S1 phase which was sustained until around day 18.
5.3. Combined Effect of Heterogeneity and Salt Precipitation
 The most pronounced impact of heterogeneity on saline evaporation is the deposition of salt preferentially over the surface of the fine-textured medium (Figures 9 and 10), driven by evaporation occurring mostly from the fine sections. As a consequence, the impact of salinity in suppressing the evaporation rate was less pronounced for Hetero columns than for the Homo-fine columns. The formation of a pore-clogging salt crust over only the fine-sand section allowed unabated vapor transport from the coarse media and the vertical fine–coarse interface. As shown by the Klinkenberg test, the larger open pores sustain high air permeability. This is most evident during SS3, where evaporation rates for Hetero columns were ∼50% higher than for the Homo-fine one (10–15 versus 5–10 g/d per column), as seen in Figure 8b. High salt accumulation along the fine–coarse interface, an indication of evaporation from this region, was observed by the CT scans and was predicted by the model.
 Two parameters control the spatial distribution of salt precipitation in heterogeneous media: the air entry pressure of the coarsest portion and the difference in pore size between the two media (Lcap). While for the sand columns more than 90% of the salt precipitated within the fine-sand sections, for the Berea sandstone, the proportion exhibited less asymmetry because of the higher air-entry value of the coarse portion. Also, in the Berea sample, the higher air-entry value of the coarse segment caused the coarse media to sustain surface saturation for a much longer time, leading to much higher salt accumulation.
 The CT imaging also permitted the investigation of a question that has been discussed at length in the chemistry literature: Do crystals grow preferentially in the smaller or larger pores? Thermodynamic theory for salt precipitation in porous media predicts that crystals will grow mainly in the large pores. This is because growing in small pores requires a significant increase in surface area relative to a small increase in volume [Wellman and Wilson, 1965; Zehnder and Arnold, 1989]. However, that theory was developed for saturated conditions, where crystal formation responds only to interfacial energy of the solid matrix. In unsaturated media, crystals are limited to growing where liquid is present, and as the medium dries, growth is restricted to smaller and smaller pores.
Figure 13 summarizes the conceptual mechanism of salt precipitation in a heterogeneous matrix and its effect on evaporation, where parallel (to the flux) heterogeneity moderates the suppressive effect of salt precipitation on evaporation by controlling the spatial distribution of salt precipitation and by providing higher vapor diffusion through the coarser layers. A visual demonstration of this mechanistic model can be seen in Animation S1 of the auxiliary material. Animation S1 shows a long (260 days) evaporation process in a Hele-Shaw chamber packed with heterogeneous sand with a sharp interface (similar to the columns), saturated with 5% CuSO4 and allowed to evaporate freely.
5.4. Implications for Field-Scale Phenomena
 Structures like those studied herein are common in natural settings, mainly in sedimentary material that is characterized by the formation of layers in a depositional environment. Each layer may be relatively homogeneous, but the stacking of several layers generates a heterogeneous, layered structure. Regional deformation can expose such layered structures at the ground surface [Hyne, 2001]. In addition, horizontal sedimentary layers can be exposed to evaporation at the intersection with vertical fractures, animal burrows, or other cavities. As evaporation proceeds from the fracture, more salt will precipitate on the small-pore surfaces, while the large-pore surfaces remain open for gas flow.
 Previous studies [e.g., Adams and Hanks, 1964; Kamai et al., 2009; Nachshon et al., 2008; Weisbrod et al., 2009] have shown the potential for high evaporative losses from fractures and subsequent salt precipitation at and near the fracture walls [Weisbrod et al., 2000]. If the salt were to accumulate homogeneously on the fracture walls, the fracture would become sealed to vapor or gas flow. Here, however, we show that the natural layered heterogeneity of a matrix may decrease the salt sealing effect, maintaining pathways for vapor and gas fluxes between ground and atmosphere.
 In the case of passive gas extraction for remediation purposes (e.g., removal of volatile organic carbons—VOCs), the existence of a certain level of heterogeneity near land surface may be useful by decreasing ground-level pore clogging, thus facilitating diffusion of the volatile gases toward the atmosphere. On the other hand, the homogenizing effect of cultivation should, in saline soils, lead to a reduction in vapor and gas transport. Another application for improved understanding and quantification of this mechanism is in the suppression of haloclastic erosion of monuments, buildings, and other construction projects that are naturally exposed to saline conditions [Scherer et al., 2001]. Proper design can direct salts to accumulate in certain parts of the structure, leaving more sensitive locations salt-free. While further investigation is needed to understand the full implications of this mechanism on a field scale, the importance and potential benefits of understanding these processes are clear.
6. Summary and Conclusions
 This work explores the process of saline evaporation from a heterogeneous media. The heterogeneous porous media (sand columns) used for the study consisted of two layers of different grain sizes with a sharp vertical interface between them. Columns were saturated with DI or saline solutions (5% NaI or 5% NaCl) and allowed to evaporate and precipitate salt crystals in a controlled environment. Evaporation rates from homogeneous and heterogeneous media were quantified from mass loss, and the spatial distribution of salt precipitates was quantified by X-ray CT. In addition, a Berea sandstone core was used for NaI saline evaporation to investigate a different scale of heterogeneity, and the precipitation process at the pore scale was also quantified via X-ray CT. Three new stages of evaporation were defined for saline solutions: SS1, SS2, and SS3. SS1 exhibits a low and gradual decrease in evaporation rate because of increasing osmotic potential. During SS2, evaporation rate falls progressively because of salt-crust formation. SS3 follows SS2 with a constant low rate of evaporation. While phenomenologically, the saline evaporation stages may appear similar to the classical stages of pure water evaporation (S1, S2, and S3), they correspond to different mechanisms. The mechanisms controlling the transitions between S1, S2, and S3 are related to the ability of the matrix to deliver water to the evaporation front as well as its vapor-diffusion characteristics. On the other hand, in saline evaporation from porous media, the solution osmotic potential and resistance to vapor flow resulting from the development of a surface salt crust suppress evaporation and control the transition between SS1, SS2, and SS3. In fact, SS2 and SS3 began while there was still capillary liquid connected to the surface, a hydraulic condition that in pure water is considered to be S1.
 In addition to the work on saline evaporation, two new phases of S1 were identified as impacted by heterogeneity: the first phase exhibits a constant maximum evaporation rate, when both fine and coarse sections are saturated and contribute to evaporation; the second phase follows air entry into the coarse fraction and is supported mainly by evaporation from the fine-textured media and the vertical interface, with minimal contribution via vapor transport from the coarse section.
 In saline soil, heterogeneity provides two mechanisms that increase evaporation relative to a homogeneous matrix: (1) capillary forces divert pore water from the coarse sand through the finer pores toward the evaporating zone, resulting in extension of S1; (2) preferential evaporation over the fine sand leads to preferential salt accumulation in that region, resulting in the coarse section being relatively salt-crust free which allows for vapor flow through the open coarse pores. In essence, parallel heterogeneity forces the formation of two distinct hydraulic regimes: regions of high water permeability and regions of high air permeability. The first becomes a salt collector, and the second serves as a vapor-venting bypass. For the conditions studied, heterogeneity enhanced the evaporation rate by more than 50% during SS2 and SS3 relative to homogeneous media. The spatial distribution of salt precipitation depends on the range and ratio (finest/coarsest) of the air-entry pressures. This study explored both high and low air-entry values with the highest asymmetry salt distribution seen for high air-entry pressure ratio and low air-entry values of the fraction.
 Understanding the mechanisms controlling evaporation from heterogeneous saline soils is very important for management of natural systems. Nevertheless, the role of matrix heterogeneity in the evaporation-salinization process in soils and its subsequent impact on gas permeability of the crust of the Earth is still not well understood. This manuscript presents new experimental data and a mathematical model, shedding new light on these mechanisms.
 This work was funded by the Binational Science Foundation (BSF), contract 2006018 and the U.S. National Science Foundation (NSF) grant 0510825.