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 We provide a unified model for the soil-water retention function, including the effect of bound and capillary waters for all types of soils, including clayey media. The model combines a CEC-normalized isotherm describing the sorption of the bound water (and the filling of the trapped porosity) and the van Genuchten model to describe the capillary water sorption retention but ignore capillary condensation. For the CEC-normalized isotherm, we tested both the BET and Freundlich isotherms, and we found that the Freundlich is more suitable than the BET isotherm in fitting the data. It is also easier to combine the Freundlich isotherm with the van Genuchten model. The new model accounts for (1) the different types of clay minerals, (2) the different types of ions sorbed in the Stern layer and on the basal planes of 2:1 clays, and (3) the pore size distribution. The model is validated with different data sets, including mixtures of kaolinite and bentonite. The model parameters include two exponents (the pore size exponent of the van Genuchten model and the exponent of the Freundlich isotherm), the capillary entry pressure, and two critical water contents. The first critical water content is the water content at saturation (porosity), and the second is the maximum water content associated with adsorption forces, including the trapped nonbound water.
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 In clayey soils and rocks, there are two types of water, bound and capillary. Some of the water molecules correspond to hygroscopic or hydration water covering the mineral surface (bound water). The second type of water is the capillary (free) water in the pores, which can include drainable and nondrainable waters. The distinction between these two waters can be made on the basis of the main force acting on the water molecule (capillary forces versus adsorption forces). Many attempts have been made to develop a consistent soil-water retention curve working at a broad range of water saturations, from full saturation to oven dryness, including properties like water condensation [see Ross et al., 1991; Rossi and Nimmo, 1994; Tuller et al., 1999; Or and Tuller, 1999; Tuller and Or, 2003, 2005; and recently Lebeau and Konrad, 2010]. Based on film water in triangular pore geometries, some recent works [Tuller et al., 1999; Or and Tuller, 1999; Tuller and Or, 2003, 2005] have realistically described capillary condensation mechanisms at very dry or high matric suction conditions. One of the remaining challenges is to accurately describe bound water in clay-rich materials and to combine an adequate isotherm for the bound water with a capillary water retention curve.
 Recently, Woodruff and Revil  have introduced a normalized clay-water isotherm model based on Brunauer, Emmett, and Teller (BET) theory describing the sorption and desorption of bound water in mixtures of clays, sand-clay mixtures, and shales. We will see, however, that the BET isotherm is not suitable for use with a capillary water retention curve because it does not predict a finite amount of bound water at a very high relative humidity. Calvet and Prost  observed that the amount of adsorbed water decreases as the quantity of exchangeable cations decreases and they suggested that at low relative humidity, the sorption of the water molecules are mostly associated with the sorbed cations [see also Laird, 1999, and Montes-Hernandez et al., 2003]. This implies in turn that the influence of the cations sorbed on the mineral surface needs to be accounted for in such models.
 Following Krushin  and Woodruff and Revil  normalized the clay-water sorption isotherms (sorption and desorption) of clayey materials by their cation exchange capacity (CEC), accounting for a correction factor depending on the type of counterion sorbed on the mineral surface. With such a normalization, all the data collapse into two master curves, one for sorption and one for desorption. The model of Woodruff and Revil  was, however, not considering the capillary water.
 We propose below an extension of the model of Woodruff and Revil  to include the capillary water by combining the CEC-normalized isotherm with the van Genuchten model [van Genuchten, 1980] for capillary water to describe the complete water retention curve from saturation to oven dryness. Our model accounts for the pore size distribution, the clay mineralogy, and the type of counterions that are present on the mineral surface. Such an approach also follows a similar line of thinking as the modeling effort described recently in Lebeau and Konrad  by combining bound and capillary water into a single closed-form mathematical expression [see also Tuller et al., 1999; Or and Tuller, 1999; Tuller and Or, 2003, 2005]. Rather than using the normalized BET isotherm proposed by Woodruff and Revil , we show that the empirical Freundlich isotherm is more suited to be combined with the van Genuchten retention model.
2. Three Types of Water
 In a water-saturated porous material, there are actually three types of pore water (see Figure 1): (1) a bound water content, corresponding to the sorbed (bound) pore water (in red in Figure 1); (2) the capillary water content, (in blue in Figure 1a) that can be drained; and (3) the water content that is not bound and not drainable, (in yellow in Figure 1a). So the water content, , can be written as
 We assume from now the sum of the bound water plus the trapped water is equal to , the water content ascribed to the adsorption force. Therefore,
where denotes the suction potential.
 Assuming that the sorbed water corresponds strictly speaking to a maximum of p-layers of water molecules covering the surface of the minerals (assuming there are no hydrophobic minerals), we have,
where S denotes the surface area between the solid phase and the connected pore space, V is the total volume of the porous material, d denotes the thickness of a water molecule (0.29 nm), represents the specific surface area (surface per unit mass of grains), and denotes the mass density of the grains (typically 2650 kg m−3). The value of p can be determined though an analysis comparing the strength of the capillary force with the strength of the adsorption force (p is likely to be between 2 and 4, as discussed below). Some simple calculations for bentonite show that half of the pore water can be bound water. Consequently, in clayey materials, due to the strong value of the specific surface area, the volumetric fraction of bound water can be very substantial.
 Three points will need to be discussed more, later in this paper:
 1. The idea that the surface is uniformly covered by layers of water molecules is a simplification of reality in which an important fraction of the water molecules can be partly clustered around the cations sorbed in the Stern layer [see Woodruff and Revil, 2011, Figure 2b]. Our model will account explicitly for the amount of bound water sorbed on the counterions sorbed on the mineral surface.
 2. The first two layers of bound water molecules have distinct properties (dielectric constant and viscosity) that are different from the bulk water. However, the third layer of water molecules is known to have properties that are similar to the bulk pore water [Israelashvili, 1992].
 3. The capillary force dominates the adsorption forces only at very high relative humidities (>0.98). This implies that the bound water, from a force standpoint, includes more than two layers of water molecules.
 The situation for saturations below the irreducible water saturation is depicted in Figure 1b. The pockets of residual water (bound water excluded) would serve as source terms to generate flow along the surface of the minerals where the bound water molecules get desorbed when the relative humidity becomes lower and lower. If the kinetics of desorption is slow enough, the desaturation occurs first by emptying the pockets of residual (nonbound) water. When these pockets are totally empty, desorption occurs from the layer of remaining bound water molecules. During sorption, at the opposite, there is no physical mechanism to have film flow from the mineral surface to these pockets. Therefore the saturation/desaturation curves are expected to exhibit a hysteresis. We do not consider, in this model development, any spontaneous pore filling or emptying mechanisms (i.e., pore snap off) [see Tuller et al., 1999; Or and Tuller, 1999; Tuller and Or, 2003, 2005; Haas and Revil, 2009].
3. Water Sorption Desorption Isotherms
3.1. Extended van Genuchten Model
 To continue, we first need a model to describe the capillary pressure curve. We chose, in the following, the van Genuchten capillary pressure model described by the following function for the total water content θ [van Genuchten, 1980]:
(constrained form of van Genuchten's model) where was originally described as the residual water content. In the current model, corresponds to the volumetric water content ascribed to adsorptive forces, considering also the water molecules in the trapped porosity. The water content θs = ϕ denotes the water content at saturation (porosity), 1/α denotes the capillary entry pressure, and ψ represents the suction pressure (in m), which is defined as negative in soil physics. The exponent, n, called the pore size exponent, is a structural parameter used to characterize the effect of the pore size distribution (similar to the pore size index, λ, in the Brooks and Corey model). Therefore, equation (2) can be written as
 We choose the van Genuchten retention model, because according to Nimmo  and Ross et al. , among many other works, the van Genuchten model successfully describes the water retention curve at high and medium values of the water content. However, it may fail to describe the water retention curve at low values of water content. In our model, the low values of water content are partially explained by the sorption-desorption of the bound water, and the redistribution of the water molecules from the trapped porosity by film flow, as shown in Figure 1b. Other models could be used as well to describe the capillary pressure curve, for example the model developed by Assouline et al. .
 The suction pressure (in Pa) (here defined as a positive value) can be related to the relative humidity, hr, by the Kelvin equation [e.g., Or and Wraight, 2000; LuandLikos, 2004],
where (m3 mol−1) is the molar volume of water (1.8016 × 10−5 m3 Mol−1), R = 8.31432 J K−1 mol−1 is the universal gas constant, T is the absolute temperature (in Kelvin), and ≈ 137 × 106 Pa at 25°C. Connecting the two potentials, as done in equation (6), should only be considered as an approximation. Indeed, the adsorption isotherm we used describes adsorption to flat surfaces. In contrast, the Kelvin equation describes capillary condensation corresponding to the filling of pores at a given relative humidity due to the effect of water surface curvature on potential.
 Note that in this paper, we will not account for the effect of suction on the porosity change. For high porosity materials, we expect, however, that suction would change the effective stress of the material (see Revil and Mahardika  for a general theory) and therefore the porosity, which could be model through a constitutive equation between the porosity and the effective stress [e.g., Revil et al., 2002].
3.2. The CEC Normalized Isotherm Equations
 The second contribution associated with the bound water is determined using the approach developed by Woodruff and Revil . The relationship between the water content (volume of water per volume of material) and the gravimetric water content, , ascribed to adsorptive forces (mass of water ascribed to adsorptive forces per unit mass of solid) is given by
where and denote the mass densities of the water and solid phases, respectively. Using equations (6) and (7), the data can be either displayed in ( , hr), ( ψ), (θ, hr), or (θ, ψ) diagrams.
 In the approach of Woodruff and Revil , the relationship between the gravimetric water content and the relative humidity is given by the BET isotherm [Brunauer et al., 1938],
where represents the gravimetric water content (mass of water per unit mass of grains) when the first monolayer is fully saturated and C denotes the BET constant, which is related to the enthalpy of sorption for the first molecular layer of water. The BET isotherm can be rewritten explicitly as a function between the gravimetric water content and the relative humidity:
 To avoid having an exceedingly high sorption water content at high humidity (which creates a problem when we want to combine the isotherm with a capillary retention curve at high water content), we propose to use the Freundlich isotherm as an alternative to the BET equation [Freundlich, 1909]:
where k and m (both dimensionless) are the Freundlich adsorption isotherm coefficients corresponding to the adsorption capacity and the adsorption strength, respectively.
Woodruff and Revil  normalized the BET isotherm by the CEC (expressed in meq g−1 or C kg−1 with 1 meq g−1 = 96,320 C kg−1 and 1 meq g−1 = 1 Mol kg−1), which represents the number of active sites of the mineral surface per unit mass of grains. The CEC of various clay minerals is shown in Figure 2a, and the sorption of hydrated cations in Figure 2b. The CEC is grossly proportional to the specific surface area. The ratio between the CEC and the specific surface area corresponds to the charge per unit surface area of the clay minerals. The active sites on the mineral surface correspond to the silanol and aluminol surface groups at the edges of the clay crystals or to the basal planes where isomorphic substitutions exist in the crystalline framework (especially for smectite). The idea to scale the water sorption/desorption isotherms by the CEC is based on the observation that the scaled isotherms, , fall under two trends (one for sorption and one for desorption), whatever the type of clay (see Figure 3, Krushin , and Woodruff and Revil ). Normalizing the isotherms by the CEC yields the following scaled BET and Freundlich isotherm (see Appendix A):
where we have used the following normalized parameters , for the BET equation, and for the Freundlich isotherm. The units of and are both in C kg−1 (or meq g−1 with 1 meq g−1 = 96,320 C kg−1 in Si units).
 As an example, we show in Figure 4 how the normalized isotherms for illite and kaolinite can be fitted with the BET and Freundlich normalized isotherms, equations (11) and (12). For the BET isotherm, the best fit of the data yields = 4.2 × 105 C kg−1 and = 23.3 × 10−7 kg C−1. We will see later that such a high value for (equivalent to 12 water molecules per site for the first hydration layer) may be due to the presence of Ca2+, which is indeed observed by Hatch et al. . The best fit of the data with the Freundlich isotherm yields = 1.6 × 105 C kg−1 (1.7 meq g−1) and m = 2.3 ± 0.2. Note that the Freundlich isotherm provides a substantially better fit of the data for illite and kaolinite by comparison with the BET sorption isotherm (compare Figures 4a and 4b).
 In Figure 5, we use the data of Figure 4, but we represent them in terms of the water content and capillary pressure in a (ψ, θ) diagram. We see very clearly that the Freundlich isotherm implies that the water content reaches an asymptotic limit at low capillary pressures. The departure from the trends for a capillary pressure below 50 MPa may indicate the effect of water condensation in the porous material.
 Using equations (7), (11), and (12), we write the two isotherms for the water content:
 The charge per unit pore volume [e.g., Revil, 2012], defined by
which corresponds to a parameter that is used in a lot of petrophysical models of rock properties (see recently Revil [2012, 2013] for the complex conductivity of siliciclastic sediments, and Revil and Mahardika  for their seismoelectric properties). Equations (13) and (14) can also be rearranged to get the water saturation ascribed to adsorption forces (with the connected porosity):
 In all cases (gravimetric water content, water content, saturation), the isotherms can be written as
where denotes the scaled isotherm. This function does not depend on the cation exchange capacity, but just on the type of sorption mechanism on the surface of the mineral. We will see that different types of clay minerals may be characterized by different functions, . This is probably because for illite and kaolinite, most of the sorption occurs on the crystalline edges, while for smectite, most of the sorption takes place on the basal planes. The normalized isotherms are given by
where . The scaled isotherm is characterized by a single parameter (b or m).
 The first generalization is to extend the previous model to a set of different mineral phases. We will use the subscript/superscript j to describe the mineral phase j and we will assume that the water sorption on silica and carbonate minerals can be neglected, because their surface area would, in general, be much smaller than the surface area associated with the clay minerals. A generalization to a polymineralic soil or clay mixture is
where the sum is extended to the N mineral phases (typically, kaolinite, illite, and smectite), is the mass fraction of mineral j in the soil, denotes the cation exchange capacity of phase j, will be either given by the BET normalized scaled isotherms or the Freundlich scaled isotherm, and is a constant (in isothermal conditions). According to Caroll , the CEC of kaolinite is the range 0.03–0.10 meq g−1, the CEC of chlorite and illite are in the range 0.10–0.40 meq g−1, the CEC of smectite is in the range 0.70–1.5 meq g−1, and the CEC of vermiculite is in the range 1.0–2.0 meq g−1 (see Table 1).
Table 1. Sorption Properties of the Different Clay Minerals Using the Freundlich Isotherm
CECj (meq g−1)
 Two other effects need to be accounted for. The first is related to the type of cations populating the surface of the clay minerals, while the second is related to the difference between sorption and desorption.
3.3. Type of Cation and Hysteresis
 According to Laird , the water molecules are mostly located around the cation sites located on the mineral surface (see Figure 2b). This explains why the cation exchange capacity, rather than the specific surface area, is a better parameter to normalize water sorption isotherms and therefore why the mass fraction rather than the surface fraction is a better way to scale the isotherms for a polymineralic assemblage. Because the cation exchange capacity depends on the type of ion used, we need to find a way to scale the cation exchange capacity with the type of ions. Woodruff and Revil  proposed that the measured cation exchange capacity for a cationic species i and a mineral phase j, is scaled to the absolute cation exchange capacity of the phase, CECj (measured using a cation that has a very strong affinity with the clay surface like ammonium or cobalt), according to
where (therefore ) denotes a scaling parameter that is dependent on the type of cation populating the mineral surface. Woodruff and Revil  found δ(Li) = 0.4, δ(Na) = 0.5, δ(Mg) = 0.6, and δ(Ca) = 0.8. We will provide some different values later on. In summary, the CECj in equations (23) and (24) should be replaced by the scaled cation exchange capacity . Then the two parameters entering the sorption isotherm need to be scaled with the cation-dependent effective cation exchange capacity.
 The second point is related to the observation that water sorption in clayey soils exhibits hysteresis. Hysteresis can be due to a number of mechanisms. One of them is likely that the mechanisms described in Figure 1b are not reversible. Indeed, film flow from the trapped water pockets occurs during desaturation but not during saturation.
 If the two previous effects are accounted for, we obtain the following hysteretic function:
where bw denotes a parameter associated with the amount of water trapped in the pore space during desorption (bw is on the order of 100 mg of water per gram of dry clay according to Woodruff and Revil ) and denotes the value of for sorption.
 We now need to find the characteristics of the adsorption for the different clay minerals. For the sorption of a monolayer, a bilayer, or three layers of water molecules on the mineral surface, we have
for the BET and Freundlich isotherms, respectively, , and p represents the number of hydration layers. Newman  found that a complete monolayer of water is obtained at a mean relative humidity of 0.47, using a database of 62 smectitic soils from the UK. Taking yields C = 1.27. Using this value, the relative humidity for the saturation of the second layer is = 0.65, in agreement with Figure 3.
 For kaolinite and illite, we come back to Figure 4a. The parameter C is determined by = 50. Therefore, the BET isotherm yields = 0.12 (monolayer), and 0.51 (bilayer). If we use the Freundlich isotherm instead, and if we use = 23.3 × 10−7 kg C−1, and = 1.6 × 105 C kg−1 (see Figure 4), we obtain = 0.10 (monolayer), and 0.51 (bilayer).
 As discussed below in section 6, the capillary force dominates the sorption forces in clayey materials at very high relative humidity (around 0.98–0.99). Using the Freundlich isotherm with m =2.3, = 23.3 × 10−7 kg C−1, and = 1.6 × 105 C kg−1, such a high relative humidity corresponds to two to three layers of water molecules. At the opposite, the BET isotherm (with C = 50) predicts that the third layer is formed at a low relative humidity of 0.74.
 The normalized parameter is defined by the mass of water per unit mass of grains divided by the CEC, which is itself the charge per unit mass of grains. Consequently, is defined as the mass of water ( ) per unit charge on the surface of the mineral ( ), and is given by
where e and N are the elementary charge (1.6 × 10−19 C) and the Avogadro number (6.02 × 1023 Mol−1), respectively, denotes the number of water molecule per site (for a monolayer), Zi is the valence of i, NS represents the number of sites on the mineral surface, and Mw is the molar mass of water in kg Mol−1 (18.02 × 10−3 kg Mol−1). Equation (31) simplifies to
 For sodium (Ζ(Na) = 1), Michot et al.  found 4 ± 1 water molecules per Na+ site (for the first layer) for four synthetic Na saponites (a trioctahedral mineral belonging to the smectite group). Using (Na+) = 4 yields = 7.5 × 10−7 kg C−1. With C = 1.27, we obtain = 2.8 × 105 C kg−1 for sorption (2.9 meq g−1). These values can be compared in turn to the values given by Woodruff and Revil : = 0.08 g meq−1 (8.3 × 10−7 kg C−1) and = 6.9 meq g−1 (6.6 × 106 C kg−1) using 1 meq g−1 = 96,320 C kg−1. Note that for smectites, like Ca-vermiculite, Ca2+ in the interlayer porosity is characterized by 8 water molecules in total (n(Ca2+) = 8), and therefore forms a Ca(H2O)82+ solvation complex, consistent with X-ray diffraction studies [Sposito et al., 1999].
3.4. Unified Model
 In summary, our generalized isotherm, , takes the form given by equations (2), (5), and (24). The unified capillary and sorption isotherms are defined by six parameters: (1) the porosity (water content at saturation), (2) the CEC, (3) the type of cation defining , (4) the BET or Freunlich isotherm coefficient (b or m), and finally, (5) and (6) two parameters of the van Genuchten model (α and n). The value of is kept constant. The chart to determine the water sorption isotherm from the material properties and the environmental conditions is shown in Figure 6. One remaining issue is if we can combine either the BET or Freundlich sorption isotherms with the van Genuchten model. It will be shown that the BET isotherm leads to unrealistic water contents at high relative humidity. Therefore, in general, it cannot be combined easily with the van Genuchten model. In the following, we use a combination of the Freundlich and van Genuchten models and we will show that this leads to a reasonable unified water retention model.
4. Comparison With Experimental Data
4.1. End-Member Clay Minerals
 First, we test our model on bentonite and kaolinite before we test the model on a mixture of the two materials. Figure 7 shows the fit of the sorption data for bentonite and kaolinite. The Georgia kaolinite has an unusually high CEC for a kaolinite. It is in the range 0.20–0.25 meq g−1, according to the laboratory measurements made by Cason and Reed . BET isotherm represents the bentonite data well, while the Freundlich isotherm better fits kaolinite data; however, the BET isotherm also fits the kaolinite data as well (not shown here). In Figure 8, we fit the van Genuchten model to the experimental data for the bentonite and kaolinite. The good fit between the van Genuchten model and the data indicates that the van Genuchten provides a good capillary retention model for these clays.
4.2. Complete Sorption Isotherms for the End-Members
 As mentioned above, the BET sorption isotherm leads to unrealistic water contents at high relative humidity (Figure 4a). The unified isotherm is therefore based on combining the Freundlich sorption isotherm with the van Genuchten capillary model. This combination yields the following equation for sorption:
 The water content, , denotes the maximum water content ascribed to adsorption forces and is defined by
or when . Such limit is well defined for the Freundlich isotherm, but not for the BET isotherm as mentioned above. Equation (33) ensures a continuous function of the water content with the suction as well as its derivatives, as discussed by Lebeau and Konrad  and shown in Figure 9. In its simplest form, the model can be fitted to experimental data with five parameters. This model includes two critical water content parameters ( , the porosity) and the maximum water content ascribed to adsorption forces but including also the nonbound and nondrainable water ( ), the capillary entry pressure (1/α), the pore size parameter n, and the sorption parameter m.
 In Figures 10 and 11, we use the data from Likos and Lu  for smectite and kaolinite, respectively. These data are fitted with equations (33) and (34). The optimization is done with the least square method without regularization. The unknown parameters are α, m, n, , and . The water content, , is used to compute the CEC using equation (35). In this exercise, m should be considered to be an empirical parameter as the optimized values for kaolinite and smectite are below 1. Equation (33) is able to fit the data. The inverted effective CEC is 0.75 meq g−1 for smectite (consistent with the presence of sodium, we used = 2.8 × 105 C kg−1) and 0.38 meq g−1 for kaolinite (with = 1.6 × 105 C kg−1 for kaolinite). The CEC of kaolinite is somewhat high with respect to the range reported in Table 1, which indicates that this kaolinite may contain some mixed layer clay minerals.
 In Figure 12, we show that the desorption isotherm of a mixture can be predicted from the sorption isotherms of the two end-members using the weighted average justified above in our model. We use mixtures of kaolinite and smectite to demonstrate the model. First we fitted the two end-members separately (kaolinite and smectite), and then we used a simple mixing formula employing these two end-members and their mass fractions. This process is used to predict the isotherms for various mixtures of kaolinite and smectite. Subsequently, we obtained an excellent agreement between the model prediction and the experimental data, as predicted by equation (23).
4.4. Effect of the Type of Cation
 Now, we re-evaluate the data by Montes-Hernandez et al. , who studied the water sorption on various homoionic MX-80 bentonites. The CEC of the MX-80 bentonite is in the range of 0.70–0.80 meq g−1 [Koch, 2008]. We will use a mean of 0.75 meq g−1 in the following analysis. The normalization should be done with . The normalized isotherm can be written as
which we can be written as
 For this analysis, we use sodium as a reference, with δ(Na) = 0.5. Then we can use the δ(Na) to find the value of δ for the other ions by adjusting the data in such a way that they all fall on the same trend. We then determine the following scaling factors for taking into account the effect of the ion: δ(Li) = 0.4, δ(Mg) = 0.8, and δ(Ca) = 0.8, and δ(K) = 0.4 (see Figure 13). Note that the value of δ(Mg) is slightly higher than the one reported by Woodruff and Revil  (δ(Mg) = 0.6). Fitting the data of Figure 13, we obtain = 0.277 ± 0.011. Taking a CEC of 0.75 meq g−1 yields = 2.7 ± 0.1 meq g−1 for smectite (see Table 1). Therefore, for a given type of ion (i) and clay (j), the Freundlich isotherm can be written as
where the values of are reported in Table 1 for the main types of clay minerals.
4.5. Further Validations
 To evaluate the applicability of our model for different types of soils, we tested the model against five other soils from the database investigated by Lebeau and Konrad . We were especially interested in the clayey sands and loams, including the sandy loam of Pachepsky et al. , the Adelato loam [Mualem, 1976], the Gilat loam [Mualem, 1976], and the Shonai sand [Mehta et al., 1994]. The water retention curve fits for the data are shown in Figures 14 and 15.
 For desorption, the relationship between and the CEC is given by
where bw is the excess mass of water per gram of dry clay (see equation (28) above), and ≈ 1. The CEC are provided in Table 2. Inverting equation (40) yields
Table 2. Inverted Properties of Five Soil Samples and the Computation of the CEC Using Equation (40) and = 2.8 meq g−1
CEC (meq g−1)
 According to Feigenbaum et al. , the CEC of the Gilat soil is 0.096 ± 0.008 meq g−1 (Na+), in agreement with the CEC predicted from our model (see Table 2, 0.089 ± 0.010 meq g−1). Using bw ≈ 30 mg per gram of dry clay, ≈ 1, and the values reported in Table 2 for the Gilat soil yields 0.086 meq g−1 (Na+). This gives a value for bw that is not too far from the value suggested by Woodruff and Revil  (100 mg per gram of dry clay).
 In the literature, capillary forces have been proposed to dominate over the adsorption force at quite high relative humidity. For instance, according to Silva and Grifoll , adsorption should give rise to multilayer films with thicknesses in the order of nanometers, and capillary forces should prevail at relative humidities in the range of 0.98 to 0.99. In the case of a monodisperse close packing of spherical particles, Tokunaga  showed that capillary forces should dominate at a matric potential of approximately −26 γ d, where γ represents the surface tension between the vapor and liquid water phases, and d denotes the particle diameter. For kaolinite, with a diameter in the order of 2 μm, capillary forces should prevail at a matric potential of approximately −9.45 × 105 Pa (or a relative humidity of 99.3%). For illite and smectite, the relative humidity at which the capillary forces dominate would be even higher. Therefore, the water film on the clay surfaces may form several additional layers past the second hydration layer at a relative humidity of about 0.50. That said, these additional layers of water molecules will have properties that are very similar to the properties of the bulk water. Indeed, past the second hydration layer, the water molecules have the same viscosity and dielectric constant as the free water molecules [e.g., Israelashvili, 1992].
 A second point that will need to be explored is the expansion of the present model to compute the relative permeability for both capillary and film flow, and to compute the streaming current density associated with his flow. Such electrokinetic effects provide a powerful method to monitor pore water flow as discussed recently by Revil and Mahardika . In parallel, it will be interesting to monitor very low water contents using complex conductivity measurements expanding the model developed recently by Revil  to very low saturations.
 Based on this work, the following conclusions have been reached.
 (1) The normalization by the CEC of the sorption/desorption isotherm for single minerals leads to two master curves for sorption and desorption. We have extended the approach developed by Woodruff and Revil  to include the Freundlich isotherm. This isotherm is better suited to be combined with the van Genuchten capillary pressure model to provide a unified model of various types of soils.
 (2) For a mixture of various minerals, the sorption/desorption isotherms are given by the weighted sum of the sorption isotherms of the different minerals using the mass fraction of each mineral as weighting factor. This procedure is both justified from a theoretical point of view and conforms to the experimental data for mixtures of kaolinite and smectite.
 (3) We provide a way to compute a unified isotherm and capillary pressure curve combining the van Genuchten model and the CEC-normalized Freundlich model for a mixture of clay minerals and nonclay minerals. This new model includes two exponents, m and n, the capillary entry pressure (1/α), and two critical water content parameters, one being the water content at saturation ( , the porosity) and the second being the maximum water content ascribed to adsorption forces, including the trapped nonbound water. The maximum water content can be related to the cation exchange capacity of the material.
 (4) The new water retention model was tested through a few data sets of soils, indicating it is capable of describing water isotherms for clayey media.
Normalized Sorption Isotherms
 Normalizing the sorption isotherms with the cation exchange capacity yields
where . The units of and are both in C kg−1 (or meq g−1). Note that 1 meq g−1 = 96,320 C kg−1. After straightforward algebraic manipulations, we obtain
 Defining the following sorption parameter , we obtain
and is in C kg−1 (or meq g−1). In addition, we can easily show that . After some algebraic manipulations, and using (dimensionless), we obtain the following nonnormalized and normalized sorption isotherms
 The normalization of the Freundlich isotherm is straighforward. We start the normalization with the isotherm . Next the normalization is completed by replacing k by , where denotes a constant. The normalized isotherm can be written as
 We thank the National Science Foundation (NSF award CMMI 0926276) for financial support. A. Revil thanks also the Organics, Clays, Sands and Shales (OCLASSH) Consortium at the Colorado School of Mines. We warmly thank Marc Lebeau and Jean-Marie Konrad for sharing their database with us. We thank the Associate Editor, Denis O'Carroll, and three anonymous referees for their very constructive comments.