Evaporation from porous media saturated with salt solution is influenced by the interactions among the transport properties of porous media, thermodynamics of the evaporating solution and environmental conditions. To study the effects of salt concentrations on the evaporation dynamics, we conducted a series of evaporation experiments under constant atmospheric conditions using columns packed with sand particles saturated with various NaCl solutions differing in concentrations. Results show that the evaporation rate decreases as NaCl concentration increases only up to a certain level. When exceeding this level, any further increase of NaCl concentration results in higher evaporation rates which is described theoretically using the thermodynamics of the solution. Results also reveal a nonlinear relation between NaCl concentrations and onset of efflorescence which is described by the numerical solution of the classical convection-diffusion equation. Moreover, we found a strong correlation between the growth dynamics of precipitated salt at the surface and the evaporation rate such that the maximum rate of surface coverage by salt coincide with the end of stage-1 evaporation. This potentially offers a new method to nondestructively study the evaporation process from saline porous media.
 Fundamental understanding of the evaporation process from porous media in the presence of soluble salt is important in various environmental and hydrological applications such as soil salinization, rock weathering, terrestrial ecosystem functioning, plant growth and vegetation, microbiological activities and biodiversity in vadose zone. Also complex dynamics of salt precipitation patterns affected by the salt concentration in pores of rock, masonry, and porous building materials can generate stresses which may lead to severe damages [Scherer, 1999; Flatt, 2002; Scherer, 2004]. Thus it is important to understand the effects of salt concentration on evaporation process and general dynamics of the salt precipitation patterns.
 Several studies showed that the presence of salt lowers the evaporation rate from porous media [Nassar and Horton, 1989; Shimojimaa et al., 1996; Nachshon et al., 2011]. For instance, Shimojimaa et al.  reported that in the presence of water table, the evaporation rate from silica sands and glass beads saturated with NaCl solution of ∼0.3 molal (i.e., moles of salt per kilograms of water) was reduced 70% and 30%, respectively, compared to the evaporation rate from pure water. Nassar and Horton also reported reduction of the evaporation rate due to the presence of KCl in water. Despite the fact that areas such as salt-affected lands, salt marshes, and salt lakes may contain high salt concentrations, most of the previous evaporation studies focused on the situations in which salt concentrations were relatively low and very few studies attempted to quantify the evaporation process from porous media saturated with highly saline solutions.
 Along with the evaporation rates, the dynamics of salt distribution and precipitation patterns depend significantly on the salt concentration. During evaporation from porous media, dissolved salt is transported via capillary induced liquid flow toward the evaporating surface where it preferentially accumulates [Shokri et al., 2010]. When salt concentration exceeds the saturation level, precipitation starts. The process is called efflorescence when taking place on the surface [Scherer, 2004; Guglielmini et al., 2008].
 This paper was motivated by the important consequences of the presence of salt on many hydrological processes. The main objectives of this paper are to address the nonlinear effects of salt concentrations on the a) evaporation rate from porous media and b) the dynamics of salt precipitation at the surface. Using thermodynamics of the salt solution, we describe quantitatively the effects of salt concentration on the evaporation rate. Also we use the convection-diffusion equation to analyze the effects of salt concentration in the liquid water that is transported from the deeper depths towards the evaporation surface on the onset of efflorescence at the evaporating surface. All the theoretical predictions are evaluated experimentally by conducting a series of laboratory evaporation experiments.
2. Theoretical Considerations
2.1. Effects of Salt Concentrations on the Evaporation Rate
 Evaporation from porous media is characterized by a high evaporation rate at the early stage of the process when it is relatively constant and is close to that from an open pan, the so called-stage 1 evaporation [Scherer, 1990]. At this stage, the evaporation rate is limited by the atmospheric demand and under isothermal condition is proportional to:
with e the evaporation rate, and P∞ and Ps the partial vapor pressure in the bulk air and saturated vapor pressure at the ambient temperature (corresponding to the vapor pressure immediately above the surface), respectively. Ps can be found from thermodynamic tables for pure water at different temperatures; however for saline solutions it changes based on salt nature and concentration. Raoult's law is widely used to calculate the saturated vapor pressure for solutions using the salt concentration as:
with x the molar fraction of water in solution and Pssol the saturated vapor pressure of the solution. Equation (2) is valid only if the salt concentration is relatively low (dilute solution) in which the activity coefficient (indicating the deviation of the solution from an ideal solution) is close to 1. For high salt concentrations, Raoult's law is modified as [Smith et al., 2004]:
with φ the fugacity coefficient indicating the deviation of the gas phase from ideal gas and γ the activity coefficient. Equation (3) shows that estimation of Pssol requires predictions of γ as a function of salt concentration which may be approximated using virial expansion of Gibbs free energy [Pitzer et al., 1984]. Depending on the nature of salt and its concentration, the activity coefficient may increase or decrease as salt concentration increases [Pitzer et al., 1984; Guendouzi and Mounir, 2003]. Pitzer et al.  obtained the activity coefficient for NaCl aqueous solution at different temperatures and concentrations. Their results showed that the activity coefficient decreases when NaCl concentration increases up to ∼1.2 molal at 30°C. However, any increase above this threshold results in a higher activity coefficient (Figure 1a) thus higher evaporation rates (equations (1) and (3)). Note that the concentration for minimum evaporation rate is slightly higher than the one for minimum activity coefficient.
2.2. Salt Transport and Precipitation
 During evaporation from porous media, convection induced by the capillary liquid flow transports salt toward the vaporization plane, while diffusion tends to spread the salt homogenously in the space. The resulting interplay between convection and diffusion affects the dynamics of salt distribution in porous media commonly characterized by the dimensionless Peclet number Pe(indicating the relative importance of convective to diffusive transport). Under the assumption of negligible ion adsorption on the pore wall, the equation governing the ions transport in liquid is given by the convection-diffusion equation (CDE). Assuming a 1-D vertical solute transport, the CDE will be [Guglielmini et al., 2008]:
with C(z, t) the mass fraction of salt, ε the porosity, D* the effective diffusion coefficient of solute in porous media, ρ the density of the solution, z the depth below surface, U the average velocity of the liquid, t the time, and S the saturation.
 Using the analytical and numerical solutions of CDE, many researchers studied the dynamics of salt distribution in drying porous media. For example Huinink et al.  and Guglielmini et al.  illustrated that low Pe results in homogenizing salt concentration throughout porous media; while for high Pe salt is preferentially accumulated toward the evaporation surface. In the present study, we solve CDE numerically to study the onset of salt precipitation at the surface as a function of initial salt concentration. More details about the boundary conditions and assumptions we applied to solve the CDE will be presented in section 4.2.
3. Materials and Methods
 A series of laboratory evaporation experiments were conducted in an environmental chamber in which the relative humidity and ambient temperature were kept constant at 30% and 30°C, respectively during the experiments. Reagent grade NaCl (from EMD Chemicals, Inc. NJ, USA) was used to make saline solutions. Sand particles with an average particle size of 0.48 mm were used to pack the glass cylindrical columns (85 mm in diameter and 230 mm in height) saturated with various NaCl solutions of 0, 0.1, 0.5, 0.75, 1, 1.5, 2, 2.5, 3, 3.5 molal. All boundaries of the columns were closed, except the top boundary which was exposed to air for evaporation. The sand grains were immersed in water to ensure complete initial saturation. The resulting packing porosity was 0.4 and the bulk density was about 1.55 g/cm3. The columns were mounted on digital balances connected to a computer to record the evaporative water loss each 5 minutes. A camera was set vertically to take pictures from surface of sand columns automatically each 30 minutes for recording the general dynamics of salt deposition patterns on the surface. The same experiments were also conducted just with salt solutions (in the absence of sand particles) of 0, 0.1, 0.5, 2, 3, 4 and 5 molal using plastic pans (160 mm in diameter and 70 mm in height) to study the effects of salt concentration on the evaporation from saline solutions.
4. Results and Discussions
4.1. Evaporation Rates as a Function of Salt Concentrations
 The evaporation rate from each column was calculated using the data recorded by the balances. The stage-1 evaporation rates were determined following the procedure described byShokri and Or . Figure 1bdepicts the average evaporation rates measured during stage-1 evaporation from sand columns and also from the salt solutions as a function of initial salt concentrations. The rates were normalized with respect to the potential evaporation rate (i.e., the evaporation rate in the absence of salt).
 Results show that the evaporation rates decreased as the initial concentrations increased up to a certain concentration. Further increase of the salt concentration resulted in higher evaporation rates. The solid line in Figure 1b shows the predicted relative evaporation rate as a function of salt concentration calculated as:
with e0 the potential evaporation rate. The solution vapor pressure was determined using the modified Raoult's law (equation (3)) and considering ambient air as an ideal gas (i.e., φ = 1). The activity coefficients of various NaCl solutions were calculated using the initial salt concentration of each sand column following the model described by Pitzer et al. . Figure 1b shows that the predicted evaporation rates as a function of the initial salt concentration were in reasonable agreement with the measured evaporation rates from both salt solutions and sand columns.
4.2. Onset of Efflorescence
 The onset of visible salt precipitation at the surface was determined experimentally using the pictures taken from surfaces of the columns. The experimental results are presented in Figure 2 showing the onset of salt precipitation at the surface as a function of the initial salt concentration. We solved CDE numerically to describe this relation. For the numerical solution, at the boundaries, we assumed that the diffusive and convective fluxes are balanced, i.e., at z = 0, L(L is the length of the column). We assumed negligible change in water saturation through the space, and also since the initial precipitation takes place during stage-1 evaporation, as a first order of approximation, we estimated the velocity term in the CDE by averaging the measured evaporation rate during stage-1 evaporation. Temporal change in liquid saturation is accounted as [Huinink et al., 2002]. We also used D* = 10−9 m2 s−1 as a typical value for the effective diffusion coefficient in porous media according to Huinink et al. , Pel et al.  and Shokri et al. . More details about the numerical solution of CDE can be found in many previous studies describing the dynamics of salt distribution during evaporation from saline porous media such as Huinink et al.  and Guglielmini et al. , thus it is not repeated here. The result of the numerical solution is presented as the solid line in Figure 2. Considering the simplifying assumptions used for solving the CDE, the simulated non-linear relationship between onset of efflorescence and the initial salt concentration was in a reasonable agreement with the experimental data initial.
4.3. Surface Coverage Rate Versus the Evaporation Rate
 The images of the sand columns were segmented to determine the lateral dynamics of precipitated salt at the surface (i.e., the growth dynamics of the area covered by salt at the surface). A typical gray value image, its corresponding gray value frequency distribution denoted as histogram and the segmented image is depicted in Figure 3a.
 Typically each histogram consists of four zones (Figure 3a) indicating the background (i.e., the scale), the glass wall of the column, sand particles without salt on top and regions covered by salt (i.e., the last peak in the histogram). A similar methodology to the one described by Shokri et al.  was used to determine the threshold value to segment the gray value images (inset of Figure 3a) to the black and white. The area covered by salt was then computed by counting the white pixels. The same algorithm was applied to all images to determine the dynamics of lateral propagation of the precipitated salt at the surface during drying of each column. Results show that the coverage rate as a function of time could be represented by Gaussian distribution function unique to each initial salt concentration. The dynamics and evolution of the area covered by salt at the surface during evaporation may be affected by the atmospheric condition, transport properties of porous media, and the nature of salt, among other factors. Typical surface salt coverage rates, rsalt, versus time are illustrated in Figure 3bshowing the continuous increase of the coverage rate during stage-1 evaporation. This might be caused by the fact that during this period, salt is continuously transported to the evaporation surface via the capillary induced liquid flow. When the concentration at the surface exceeds the saturation limit, first salt crystal appears and the concentration will remain the same as the evaporation proceeds. Crystallization starts with a small crystal (Nuclei) which forms due to a quick change of the concentration in a part of the solution which is in a metastable state of equilibrium. Other crystals form due to the same reason as well as collisions with the previously formed crystals [McCabe et al., 2004]. Thus, having more crystals on the surface may result in a higher salt coverage rate. However, at the end of stage-1, the continuous liquid pathways connecting the receding drying front to the surface start to detach from the surface one after the other (i.e., the transition period from stage-1 to stage-2 evaporation, seeShokri and Or for more detail). This results in a decreasing salt deposition rate at the surface during the transition period which continues until all liquid connections are disconnected from the surface marking the onset of stage-2 evaporation [Shokri and Or, 2011]. At this point, the salt deposition rate at the surface goes to zero (since vaporization does not occur anymore at the surface).
 We have found a relatively strong correlation between the time at which the salt coverage rate at the surface is maximum (i.e., the peak of the Gaussian distribution) and the end of stage-1 evaporation determined from the drying curves. For example,Figure 4a shows a typical result illustrating the measured evaporation rate from the sand column saturated with a solution of 2.5 molal of NaCl and the corresponding salt coverage rate at the surface.
Figure 4b shows the time at which the salt coverage rate at the surface is maximum, tsalt, delineated by image analysis for each sand column, versus the prolongation of stage-1 evaporation,tstage−1, determined from the drying curves following the procedure described by Shokri and Or . Except for the column saturated with the salt solution of 0.75 molal, the other points indicate a linear 1-1 relation between the end of stage-1 evaporation and the time at which the surface salt coverage is the maximum. To the best of our knowledge, such a correlation was never reported in the past. This may potentially offer a new tool to non-destructively study the evaporation process from porous media by quantifying the dynamics of the salt coverage and deposition patterns at the surface. Further research is required to explore this possibility in more details.
 In this work, we have studied the effects of salt concentration on the evaporation rate from porous media and also the dynamics of salt deposition at the surface. We predicted the effects of salt concentration on the evaporation rate by considering the thermodynamics of the salt solution evaluated by a series of experiments. Our theoretical and experimental results show that increasing initial NaCl concentration up to ∼1.5 molal reduces the evaporation rate from porous media, but any further increase of NaCl concentration results in higher evaporation rates, a conclusion which may not seem trivial at first glance. Besides, we studied the nonlinear effects of NaCl concentration on the onset of efflorescence using the numerical solution of CDE and as expected, higher initial salt concentration leads to earlier salt precipitation at the surface which was confirmed by the experiments. We have also studied the growth dynamics of the area covered by precipitated salt on the evaporating surface under various initial salt concentrations. Our results showed that the surface salt coverage rate can be described reasonably by a Gaussian distribution function. We have found that the maximum rate of lateral deposition of precipitated salt at the surface occurs at the end of stage-1 evaporation. This result may offer new tools and also future research lines for nondestructive analysis of the evaporation from porous media.
 The Editor thanks the anonymous reviewer for his or her assistance in evaluating this paper.