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a Dep. of Soil and Water Sciences, The Hebrew Univ. of Jerusalem, Rehovot 76100, Israel
b Inst. of Soil Science, Univ. of Hannover, Germany
* Corresponding author (yona.chen{at}agri.huji.ac.il)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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) at the solid–liquid–vapor interface. Aqueous ethanol solutions (AETS) are commonly used as testing liquids having different liquid–vapor surface tensions (
LV); however, measurements using AETS have rarely been performed on water-repellent soils (WRS). Measurements of in this study were conducted using both the Wilhelmy plate method (WPM) and the CRM (weight-gain capillary rise method) for three natural and four hydrophobized WRS (water-repellent soils). The values of the Young equation (solid–vapor and solid–liquid surface tension) were calculated, and correlated with the Goods–Girifalco interaction parameter, 
. The factor was found to be a linear function of the solid–liquid surface tension: = 1 – 0.011SL, with no significant differences between soils. This relation was then used to formulate an ESIT (empirical equation of state of interfacial tension), suggesting that from one universal constant, can be predicted as function of SV. The applicability of the ESIT approach to WRS was found to be inferior, in contrast to its successful use for ideal solid polymers. Nevertheless, it was found that for a water–WRS system, was 
0.6 rather than 1.0 as previously assumed. Applying = 0.6 was successfully used in predicting SV as well as the hydrophilic domain of vs. LV for water and AETS.
Abbreviations: AETS, aqueous ethanol solutions • CRM, weight-gain capillary rise method • EP, eucalyptus • ESIT, equation of state of interfacial tension • MED, molarity of ethanol droplet • OM, organic matter • OR, orange orchard • PN, pine • WPM, Wilhelmy plate method • WRS, water-repellent soils
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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Information about the solid–liquid contact angle () and the solid–vapor surface tension is essential to the understanding of the water flow mechanism and capillary saturation relations in unsaturated WRS. These two measures were used to characterize the magnitude of soil water repellency (Letey et al., 1962; Letey, 1969; Miamoto and Letey, 1971; Bachmann et al., 2003). The solid–vapor surface tension cannot be measured directly, so it is evaluated from measured data. As a result, most methods used to characterize the magnitude of soil water repellency consist of direct or indirect measurements of the initial advancing contact angle at the solid–liquid–vapor interface. Due to surface roughness and pore-size distribution in soils, however, a direct measurement of on WRS can yield, at best an "apparent contact angle," which has been found in some instances to equal the real plus the angle of pore divergence (Bond and Hammond, 1970; Philip, 1970).
Bachmann et al. (2000) proposed an alternative approach, the modified sessile drop method, which measures the apparent of hydrophobic soil particles optically, by placing a dry, one-grain-thick layer of uniform soil particles onto an adhesive tape and conducting the measurements using a microscope fitted with a goniometer scale.
A contact angle measured directly on a plane or quasi-plane surface can be described from the mechanical equilibrium of the solid–vapor (SV), solid–liquid (SL) and liquid–vapor (LV) interface, as defined by Young's equation (Young, 1805):
 | [1] |
(mN m–1) is the surface tension of the respective phase (as well, can also be viewed as the interfacial free energy, mJ m–2), and Y is the equilibrium at the solid-vapor-liquid interface and can be denoted as "Young's contact angle." Based on experimental considerations, Y can be defined as the experimentally measured contact angle (E), which can be inserted into Young's equation.
The basic experimental conditions under which E = Y are: (i) the solid phase is an ideal one, hence, it should be smooth, flat, rigid, chemically homogeneous, insoluble and nonreactive; (ii) the liquid phase is pure, hence, no mixture of liquids can be used; and (iii) vapor adsorption to the solid phase is negligible (Kwok and Neumann, 1999). Given these conditions as a starting point, when applying Young's equation to WRS, we can anticipate that deviations of E from Y will be the rule rather than the exception. Nevertheless, studies that employ E as a means of understanding soil water repellency use Young's equation as a starting point for the investigation of the surface properties of WRS. When using E in conjunction with Young's equation, however, it is essential to take into consideration the sources for deviations of E from Y resulting from the nature of WRS. As a consequence, some simplified assumptions have to be considered.
The physically and chemically heterogeneous nature of WRS prevent us from defining WRS as ideal solids for which E = Y. Therefore, it should be kept in mind that the measured values of E and, as a consequence, the energy compounds in Young's equation are only relative values (Chibowski and Perea-Carpio, 2002). Nevertheless, the initial advancing E was found to be a good approximation of Y (Kwok and Neumann, 1999). Therefore, care must be exercised to ensure that E being inserted into Young's equation is the initial advancing contact angle.
Nonideal WRS surfaces may also result from hydrophobic compounds from the soil surface dissolving into water during the measurements of E. As a consequence, LV could differ significantly from that of pure water. Measurements (Chen and Schnitzer, 1978; Anderson et al., 1995; Yates and von Wandruszka, 1999) revealed significantly lower LV values for soil extracts than for pure water, with the differences depending on their dissolved organic matter concentration, pH, ionic strength, and the valence of any metal ion(s) present in the solution. If indeed LV was lower, SV and consequently SL can change their values during the measurement. This change, however, would depend on the measurement method applied and on the duration of the measurements of the initial advancing E.
Since for WRS, AETS are commonly used as testing liquids providing different LV values, the second experimental condition, requiring the use of pure liquids, is contravened. Nevertheless, measurements with AETS were proven to be more suitable for measurements of E vs. LV in WRS than homologous series of pure organic liquids (Watson and Letey, 1970); however, during prolonged contact of AETS (or water), some specific interaction, which depends on the molar fractions of ethanol, may take place at the solid–liquid interface. As a consequence, the initial properties of the WRS surface may alter.
Such interaction may result from the ability of AETS (or water) to form H bonds with negatively charged functional groups, dissolution of soil constituents, preferential sorption of ethanol across the solid–liquid interface, and faster evaporation of ethanol than water across the liquid–gas interface (Chen, 1975; Roquerol et al., 1999; Roy and McGill, 2002). An additional important property of AETS is their significantly lower dielectric constant than water. A decline in the dielectric constant reduces the repulsive forces between charged particles (Chen, 1975), and therefore can cause the reorientation of functional groups at the solid surface. Since methods applied to measure the initial advancing E are usually fast, changes in E are limited (Roy and McGill, 2002).
Despite the fact that WRS are characterized by lower SV than wettable ones (Roy and McGill, 2002), water-vapor adsorption isotherms of WRS differ only slightly from those of the latter ones (Miyamoto and Letey, 1971). If the organic coating on a WRS surface area consists of humic substances, a monolayer of water can be adsorbed through H bonding. At high relative humidity, the water vapor can condense into clusters around COOH groups (Chen and Schnitzer, 1976). This, however, provides some evidence that vapor adsorption to WRS surfaces is not negligible. Therefore, SV = S – 
SV, where S (mN m–1) is the solid surface tension in vacuum and SV (mN m–1) is the spreading pressure. If SV 
0, vapor adsorption is considered to be negligible, and hence, SV = S. For WRS, however, it can be deduced that SV > 0 and thus changes the apparent SV. Therefore, neglecting SV can be justified only if measured values of SV are available (Siboni et al., 2004). Since for WRS SV is not routinely measured, the preferred option is to maintain SV at low and constant levels. This can be achieved by conducting measurements of E on air-dry soils after equilibration at constant temperature and relative humidity. This should ensure that the contribution of SV is at least normalized across soils (Roy and McGill, 2002).
The heterogeneous nature of WRS surfaces can cause deviations from the ideal behavior proposed by Young's equation, in particular when AETS are used as wetting liquids. In the absence of an accepted method for the determination of Y, or alternatively the real SV or SL in Young's equation, the initial advancing E can give useful information on wetting processes in WRS.
To the best of our knowledge, measurements of E vs. LV of AETS have rarely been published for WRS. For example, the data published by Watson and Letey (1970) report on E that was evaluated from the capillary-rise height after setting an arbitrary equilibrium time of 24 h. Hence, any interaction between the liquid and soil would have reached an apparent equilibrium and E cannot be considered to be the initial advancing one.
The primary purpose of this study was to report experimental data on E measured with water and AETS for a series of natural and hydrophobized WRS. These data were obtained via the use of two methods, recently modified for soils by Bachmann et al. (2003): (i) the Wilhelmy plate method (WPM); and (ii) weight-gain measurement of the initial stage of the capillary rise (CRM).
The specific objectives of this study were to: (i) apply well-known approaches of the critical surface tension to WRS; (ii) correlate the results with the interaction parameter, (Girifalco and Good, 1957) and, subsequently, to formulate an empirical ESIT; and (iii) analyze the sensitivity of the ESIT approach in predicting E vs. LV for WRS.
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THEORY |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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E vs. LV of a homologous series of liquids (the so-called Zisman plot), exhibits a linear relationship. Likewise, it was shown that AETS (Watson and Letey, 1970), or aqueous methanol solutions (Bachmann et al., 2003) could also exhibit linear relationship when applied to WRS. However, for WRS, linearity in a Zisman plot was observed only in the lower LV domain. At the domain close to the values of LV of water, the pattern was curvilinear rather than linear. Zisman (1964) suggested that extrapolating the straight line of cosE vs. LV to the point where cosE = 1 yields the "critical surface tension" (CR), i.e., the LV at which a liquid will cause a complete wetting of the solid surface (E = 0); however, when different homologous series of organic solvents such as alkenes or alcohols were used to achieve various LV values, the two lines could not be completely superimposed even though each of the series produced straight lines of the same plot (Spelt et al., 1992), leading to two different (though similar) values for CR.
Since the variation in values of CR for different solid surfaces showed the same qualitative behavior as one would expect of SV (in accordance with Young's equation), CR can be considered to be good approximation of SV (Siboni et al., 2004). Nevertheless, according to Young's equation, if cosE = 1, then SV = LV + SL and therefore the Zisman (1964) concept will lead to the result that SL = 0. This implies that SV = LV at the point where cosE = 1. Moreover, for WRS, SV > 0 and so the approximation of SV based on the experimental value of CR can be higher than Young's equation would predict. Since this has already been taken into account in the E measurements and thus will be expressed when SV is estimated from the Zisman (1964) plot (E vs. LV), further reduction due to SV should not be used. The contribution of SV will, however, be considered a normalized variability across soils.
Below, the assumption that SL = 0 when cosE = 1 is discussed. Using experimental data from eight solid polymers, it was shown by Spelt et al. (1992) that the term LV cosE changes smoothly with changes in the LV, i.e., LV decreases with increasing the product of LV cos(E). By curve-fitting a second-order polynomial function, P(LV) to the experimental data, they demonstrated that
 | [2] |
LV) approaches zero, E = 0, and, consequently, according to the assumption of Zisman (1964), SV can be estimated. Alternatively, the point at which E = 0 can be detected from the intersection of P(LV) with the 1:1 line (i.e., LV cos = LV).
It seems that only if a plot of cosE vs. LV can be described as a straight line for the whole LV domain (including LV when water is the wetting liquid), can a plot of LV cosE vs. LV be fitted with P(LV); however, a Zisman plot for WRS forms a straight line only in the hydrophobic domain of LV. Therefore the second-order polynomial function will not fit the experimental data in such soils.
Assuming that SV is a constant property of a given soil, we can deduce from Young's equation that
 | [3] |
 | [4] |
SL decreases as LV decreases, and from Eq. [4], it can be concluded that SL approaches its minimum when E = 0. Furthermore, from the understanding of the cohesive behavior of the liquid–liquid interface, Spelt et al. (1992) concluded that zero should be the minimum value for the solid–liquid interfacial tension when the E approaches zero:
 | [5] |
SV is known, SL can be calculated from Young's equation for any given pair of E and LV.
As neither SV nor SL in Young's equation is a measurable property, further information is needed. For that reason, an additional term referring to the unknowns in Young's equation has been introduced in the form of an ESIT:
 | [6] |
An ESIT that has been used in soil water repellency research is based on work reported by Girifalco and Good (1957). Their approach will be briefly discussed below. It should be noted, however, that ESIT needs to be distinguished from the "equation of state approach."
The definition for free energy of adhesion between the solid and the liquid phases (WSL) is:
 | [7] |
LV), and that of the solid phase, WSS (defined as 2SV), is expressed as follows: WSL = 
; however, this approximation was found to be valid only if LV SV. Girifalco and Good (1957) modified the geometric mean combining rule by introducing the "interaction parameter," , defined as
 | [8] |
 | [9] |
LV > SV), from the above it can be concluded that cannot be expected to equal one and therefore a value lower than one should be anticipated for WRS.
Introducing Eq. [9] into Young's equation results in
 | [10] |
LV is the liquid–vapor surface tension that results in E = 90° (ND), Eq. [10] yields
 | [11] |
ND is by the use of the MED (molarity of ethanol droplet) test (Watson and Letey, 1970; King, 1981). The procedure for the MED test consists of preparing a series of AETS, which produce various LV, and finding the LV at which a drop will penetrate the soil within 10 s. If the values of the MED test are reported in terms of LV (rather than molarity or volumetric percentage of ethanol), it can be considered as an approximation for ND. In the discussion below, the term ND will refer to the value obtained from a dataset of E vs. LV and the term MED will refer to the value obtained by the MED test.
Assuming that ND is the precise value for a given WRS, then a "deviant" value = 0.9 would result in an estimated SV 23.5% greater than the "true" value. Miyamoto and Letey (1971) proposed the same expression (Eq. [11]) for SV, but used the assumption = 1; however, by substituting Eq. [11] into Eq. [10], is being disregarded:
 | [12] |
= 1 is included in Eq. [12] since, when E approaches zero, the denominator in Eq. [12] is assumed to be equal to SV, which in turn equals ND/4. From our experience and data published for ND (in terms of MED), prediction of SV with ND/4 (or MED) results in very low and nonsensical values. Therefore, one of the scopes of this study was to examine whether Eq. [11] is valid for WRS, under the assumption of = 1 or any other constant value.
Carrillo et al. (1999) evaluated the validity of Eq. [12] assuming that ND = MED. They calculated E values for WRS (for water as the wetting liquid), using data from breakthrough pressure measurements, and compared them with predicted E evaluated by introducing MED into Eq. [12]. By plotting both predicted and calculated E in terms of cosE vs. (MED)1/2, they argued that the linear relation obtained from Eq. [12] was in good agreement with the calculated E (0.02 was the root mean square error).
Since measurements of E vs. LV are usually not available for WRS, the common practice is to use Eq. [11] or Eq. [12] (with MED) to predict E or SV, respectively; however, when E vs. LV data are available, the result is usually analyzed in conjunction with the Zisman method. An alternative method is the "equation of state approach", which can be interpreted as a further development of the Zisman (1964) approach. It is, however, essentially an empirical curve fit to E data, which results in derivation of an empirical ESIT. The formulation of the two empirical ESIT will be detailed below, and their applicability to WRS will be examined.
The formulation of the first empirical ESIT (Neumann et al., 1974) is based on assessment of the parameters in Young's equation from E vs. LV data followed by correlating the obtained results with the of Girifalco and Good (1957) (Eq. [9]). Applying this approach, Spelt et al. (1992) showed that could be described as a linear function of SL (i.e., = –
SL + 
). From the measurements of eight solid polymer surfaces, they suggested that the empirical values of = 0.0075 and = 1.0 can be used as representative for all low-energy surfaces.
The second empirical ESIT (Li and Neumann, 1990) is based on the consideration of modifying the geometric combining rule of the form:
 | [13] |
Combining Eq. [13] with Eq. [7] results in an empirical ESIT that can be written as
 | [14] |
 | [15] |
E vs. LV, an average value of ß = 0.000115 was obtained (Spelt et al., 1992).
Watson and Letey (1970) argued that plots of cosE vs. LV, as measured with AETS for WRS, suggest a curvilinear trend rather than a linear one, particularly at high LV. The same trend can be observed for WRS examined by Bachmann et al. (2003), who conducted measurements with aqueous methanol.
Since a straight line satisfactorily described the results at the lower LV domain and, as suggested, a curvilinear pattern best fitted the results at the higher surface tension domain, we suggest, for WRS, the entire domain be described with a logistic equation of the form
 | [16] |
w (w is the measured E when water is the wetting liquid, i.e., y0 = cosw), and constraining cosE not to exceed 1.0 (i.e., a = 1 – cosw), the resultant semiempirical equation is
 | [17] |
E vs. water and AETS LV. |
MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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E measurements and was further analyzed for particle-size distribution and organic matter (OM) content (Table 1).
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The extraction procedure included placing 70 g of leonardite or sphagnum peat in a thimble and wetting it with the solvent before placing it in the Soxhlet apparatus. The reflux time was set to 10 h, at which time no visible color of the reflux solution could be detected. The extract was filtered twice through a glass filter (Whatman GF/A). The extracts were added by first forming an 20-mm layer of 2000 g of quartz sand in a polypropylene box and then uniformly spreading the extract solution on the soil surface until its level reached 10 mm above the soil surface. Then the soil was slightly shaken for 15 min, left to dry in a hood for 48 h, and then passed again through a 0.5-mm sieve to remove the excess dry extract material that had accumulated on the soil surface. Finally, the soils were placed in an oven for 12 h at 65°C to remove solvent residues. The quantity of the adsorbed OM was measured gravimetrically by placing the soil samples for 8 h at 400°C (Ben-Dor and Banin, 1989) (Table 1).
Aqueous Ethanol Solutions
Aqueous ethanol solutions were produced with 99.9% absolute ethanol and distilled water at concentrations ranging from 0.2 to 6 M at 0.2 M intervals. These solutions were used for the MED test (Watson and Letey, 1970; King, 1981) following the detailed protocol of Roy and McGill (2002). For the MED test, the solution that infiltrates to a given soil within 10 s was identified and its LV was measured. As mentioned above, the term MED is used to distinguish it from ND. The results of both tests are reported in terms of surface tension. Measurements of LV were conducted with a dynamic tensiometer (DCAT 11, Data Physics, Filderstadt, Germany).
In a similar manner, AETS were prepared for the E measurements, which were also conducted with deionized water. To avoid erroneous results from possible changes in ethanol concentration with time, LV was measured immediately before the E measurements were taken.
Contact Angle Measurements
Measurements of E were conducted using two methods, the WPM and the CRM. First, the WPM was used to measure the entire range of E, including values >90°. Then, according to the results, the CRM method was applied for those AETS producing E < 90°. For the detailed underlying theory and a description of the methods and their adaptation to soils, see Bachmann et al. (2003). An operational short description is given below.
Wilhelmy Plate Method
A glass plate, 4 cm long, 2.55 cm wide, and 0.1 cm thick, was covered (on all sides) with a double-sided adhesive tape. The plate was then covered with an excess of the soil being tested and the excess was removed by gentle tapping, producing a plate covered with a one-grain-thick layer of air-dried soil. The soil-covered plate was attached to a dynamic tensiometer (DCAT 11, Data Physics, Filderstadt, Germany), with a data acquisition rate of 10 to 30 measurements s–1 and a mass resolution of 10–5 g. A glass vessel containing the wetting liquid was placed on a platform attached to a motor, which enabled lifting and lowering of the vessel at a constant rate. After the balance was tared, the vessel was lifted toward the plate, and the plate was slowly immersed in the test liquid. During immersion, the three forces acting on the plate are: gravity (Fg), buoyancy (Fb), and the meniscus force (Fw). The total force, Ft, as measured with the balance, is then
 | [18] |
l (Mg m–3) is the liquid density, a (Mg m–3) is the air density (negligible compared with l), lw (m) is the wetted length and g is the force of gravity. Taring the balance sets mass (m) equal to 0, so Eq. [18] can be rearranged to give
 | [19] |
E can be calculated from Eq. [19].
Weight-Gain Capillary Rise Method
The Washburn equation (Washburn, 1921) converted to a weight-gain (w) expression is
 | [20] |
(kg m–2 s–1) is the viscosity of the liquid, t (s) is the time, and c (m5) is a soil-specific constant depending on the effective capillary radius and porosity. If completely wetting liquids like n-hexane are used as a reference liquid, the geometry factor c in Eq. [20] can be obtained from the slope of the linear relation of w2 as a function of time at the initial time of wetting. Once the c factor is known, E can be estimated for water or AETS from the slope calculated using Eq. [20]. |
RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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E vs. LV results for water and AETS are presented in Fig. 1
for both WPM and the CRM data. The leftmost point in each graph, marked as a filled triangle, is a conceptual value added to demonstrate the assumption of E = 0 for pure ethanol. The agreement between the two methods in terms of evaluating cosE vs. LV was analyzed statistically by applying a covariance analysis to the linear regression lines using the statistical package JMP (JMP IN Version 5.0.1a, SAS Inst., Cary, NC). For the CRM measurements, the linear regression model was calculated from all data measured. For the WPM, the largest E for water and the following AETS with the highest LV were excluded from the regression analysis due to their nonlinear character regarding the entire data sequence. With respect to the slope, the covariance analysis showed no significant difference (0.15 < P < 0.98) between the two straight lines obtained for any one of the soils. The slope (
) and the intercept (
) given in Fig. 1, were obtained by combining data from both methods.
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E = 1 has no physical significance, an attempt to extrapolate the straight line to a higher LV, particularly to the LV where water is the wetting liquid, will result in unreasonable or incorrect values of w. As can be seen in Fig. 1, this argument is valid for both moderate and high WRS, regardless of the method used to measure E.
In summary, a straight line reasonably describes the results of all soils, excluding the point obtained with pure water as the wetting liquid; however, the domain in which the E approaches zero (i.e., cosE approaches 1.0) exhibits some uncertainty when attempting to detect the exact point at which cosE = 1. For both methods (WPM and CRM), this domain was found to be sensitive to measurement, since replicated measurements for a given soil often included both zero and nonzero values. Furthermore, for all soils, WPM measurements approach cosE = 1 at lower LV values than the CRM-based values, thus suggesting slightly higher SV values when WPM is used.
A reasonable explanation for this trend can be explained by an advancing liquid film when measurements are conducted with WPM. Consequently, some liquid will flow in films up the soil layer, adding to the weight of the plate, which in turn will result in lower E values when the WPM is used. This explanation is valid only if the effect of the liquid film is more pronounced than a potential effect of entrapped air bubbles or time dependency of soil water repellency.
Since for WRS we found that a straight line can satisfactorily describe the results only at the lower domain of LV, Eq. [17] is suggested as an alternative method to account for all data sequences. Data from WPM and CRM were examined by fitting Eq. [17] using the numerical regression code of the SigmaPlot software (Version 8, Systat Software, Point Richmond, CA). The assumed point for ethanol (filled triangle) was not used for the curve fitting; nevertheless, it is accounted for as a constraint introduced into Eq. [17] (i.e., a = 1 – cosw). Values of the fitting parameters b and x0 (Eq. [17]) are given in Fig. 1. Mathematically, Eq. [17] was found to adequately describe the entire measured domain (the lowest R2 was 0.9). As can be seen, Eq. [17] fits the data with sufficient accuracy for the higher domain of LV as well as for lower one. Some deviation from linearity occurs, mostly near the inflection point. In the domain where cosE approaches one, Eq. [17] converged to this point always near the last point of the uncertainty domain.
Estimation of Solid–Vapor Surface Tension from Measured Data of Contact Angle vs. Liquid–Vapor Surface Tension
To evaluate SV from pairs of measured E and LV, one has to determine experimentally the exact position at which cosE approaches 1.0 (i.e., E = 0). The first approach taken to evaluate the point of E = 0 was the Zisman plot technique of fitting a straight line to the linear branch of the data. For these plots, the evaluation was performed separately for each method used to measure E (WPM, CRM, and WPM + CRM) and the values obtained for SV are presented in Table 2.
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The proposed method of evaluating SV consists of first plotting the product LVcosE as a function of LV (Fig. 2
). Results of solid polymers tested with pure liquids plotted in this manner exhibited a pattern that was well fitted with a second-order polynomial function (Spelt et al., 1992). As mentioned, only if a straight line can describe the entire data sequence of cosE vs. LV can a second-order polynomial function be fitted; however, this is not the case for WRS when E is measured with water and AETS. Therefore, a different fitted line should be used (Fig. 1 and 2). For this purpose, Eq. [16] was modified to account for presenting data in the form of the product LVcosE vs. LV. By setting y0 equal to wcosw and constraining LVcosE to be no greater than LV (i.e., cosE 
1) in the domain where the slope of the curve approaches zero (i.e., a = LV – wcosw), the semiempirical equation obtained is
 | [21] |
SV was accomplished from the maximum of the curve. At this point, which can be calculated from the first derivative of the fitted line, the slope of the curve approaches zero (i.e., cosE = 1).
The results obtained for SV according to the Zisman approach, applied to the CRM, WPM, and CRM + WPM, along with values obtained using Eq. [21], are presented in Table 2. From the 95% confidence intervals of the four regression lines used, we found no significant different between the values obtained for SV.
Theoretically, one can anticipate that the higher the value of w the lower will be SV. From the results obtained in this study, this is indeed the general tendency (including all hydrophobized soils and natural ones) with two exceptions, namely, the EP and PN soils. According to the w measurements for these two soils, the EP soil (w = 103.3°) was not expected to yield lower values of SV. On the other hand the PN soil (w = 83.9°), which exhibited only subcritical water repellency (w < 90°), was expected to yield higher SV. These observations are valid according to all four methods used to estimate SV, especially when the Zisman approach was employed. It seems to us that estimation of SV using Eq. [21] is more suitable for WRS, since all data sequences have been considered.
It should be noted, however, that EP and PN soils are natural, in contrast to artificially hydrophobized soils. Natural soils are chemically heterogeneous in nature and can contain different OM compounds mixed between soil particles and coating their particle surfaces. It could be that the wettability of certain compounds is more pronounced at lower LV than w and therefore can exhibit higher or lower E from the one expected according to w.
For several of the soils, replicate measurements of E included both zero and nonzero values at the lower domain of LV. It is therefore recommended that measurements be conducted at smaller LV intervals within this uncertainty domain by only slightly changing LV above and below the first LV producing E = 0.
From the above, it can be summarized that the increasing expected trend of w vs. SV is generally valid for WRS. Nevertheless, for natural soils, exceptions could be expected. Since using Eq. [21] to estimate SV yields a better agreement with an increasing tendency, (SV vs. w), further calculations were conducted with this value.
Formulation of Empirical Equation of State of Interfacial Tension from Measured Data
Using the two determinable parameters (LV and E) and subsequently derived estimates for SV, one can calculate SL straightforward from Young's equation (Eq. [1]). Therefore, it is now feasible to correlate the results with in Girifalco and Good's (1957) equation (Eq. [10]).
The results of vs. SL are plotted in Fig. 3
for the seven WRS used in this study. It can be clearly seen that can be described as a linear function of SL, with some systematic deviations when water is the wetting liquid (filled circle). These deviations are in agreement with observed deviations from linearity of cosw in the Zisman plots (Fig. 1).
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) and the intercept () of the calculated regression line were found not to be significantly different among the seven soils. The average values obtained for and were 0.010 ± 0.0006 and 0.98 ± 0.0067, respectively. The reported by Spelt et al. (1992) for eight systems of solid polymers with homologous series of liquids was 0.0075 and the intercept was set to be 1.0. The results of our study show that the intercept is indeed close to 1.0. Hence, the lower value for SL can be assumed to equal zero. The results obtained indeed exhibited negative values for SL, corresponding to values ranging from 1.007 to 1.04. Hence, these can be considered as experimental errors rather than being physically significant. Furthermore, we note that the literature shows no evidence of a negative solid–liquid interfacial tension. Rather, our results provide valuable evidence of zero being the lower limit of all solid–liquid interfacial tensions. Since does not significantly differ from one, however, we recalculated the linear regression line while setting = 1 for all soils. Accordingly, the average value obtained for was 0.011 ± 0.0007. For further calculations we used these values ( = 0.011, = 1).
Because is a linear function of SL, with a single slope and intercept applying to all soils examined, one empirical ESIT can be formulated for all WRS examined when the wetting liquids are water and AETS. Combining the relationship = 1 – 0.011SL with Girifalco and Good's (1957) approximation (Eq. [10]) provides the following empirical ESIT:
 | [22] |
E as a function of SV and LV:
 | [23] |
E are demonstrated below.
Prediction of the Solid–Vapor Surface Tension
The use of the ND as a means of predicting the SV (Eq. [11]) was evaluated in conjunction with the values obtained for w (the interaction parameter when the wetting liquid is water, filled circles in Fig. 3).
In contrast to the assumption that w = 1, the calculated values of w for WRS range from 0.33 to 0.78, with an average value of 0.6 ± 0.15. The sensitivity of the w values in estimating SV was tested for two cases: (i) under the common assumption that w = 1, and (ii) with the average value obtained in this study for all soils (w = 0.6).
The validity of Eq. [11] was then tested by substituting the different w values and the evaluated ND. When = 1, the value obtained for SV was nonsensical compared with SV values estimated from the measured data, regardless of the method used for the evaluation of SV. Values of SV evaluated using = 1 ranged from 11 to 14 mN m–1, suggesting that WRS were wetted with a E = 0 with LV lower than that of pure ethanol (22.4 mN m–1). On the other hand, the average value, w = 0.6, yielded a better estimation for SV for all soils; deviations from w = 0.6 resulted in high or even nonsensical values for SV.
To test our findings, namely, that w should be 0.6 for WRS, the results reported by Watson and Letey (1970) for two hydrophobized WRS (amine–sand and silane–sand) were reexamined. The SV and the ND were estimated from the reported linear regression line. The results (Table 3) clearly present a better estimation of SV when w = 0.6 rather than w = 1; however, since the E values reported by Watson and Letey (1970) were calculated from the maximum height of the capillary rise when the soil surface and liquid reacted for 24 h, SL and SV could not equal zero. Therefore, the calculated E could not be considered neither the initial advancing E nor an approximation for Y.
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SV. If the prediction of SV from Eq. [11], based on ND and , yields reasonable and satisfactory values, then, from independent measurements, one can predict the E for a given WRS with varying LV by using one of the equations presented here (i.e., Eq. [10], [12], [15] and [23]). If SV is assumed to be a constant quantity for a given soil, then the sensitivity of each equation can be examined with respect to (Eq. [10]), ND (Eq. [12]), ß (Eq. [15]), and (Eq. [23]).
The sensitivity analysis (Fig. 4
) was first performed using these considerations, and then by applying a ±10% error to the SV data evaluated from the measured data, thus reflecting the potential error in this evaluation. The results presented in Fig. 4 show the data obtained for the EP soil as a representative of the entire set of soils.
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w were examined: 1.0, 0.6, and 0.3 (Fig. 4a). Assuming w = 1 resulted in a very poor fit to the measured data, excluding the domain where cosE approaches 1.0. On the other hand, w = 0.6 provides a very reasonable estimation of cosE between the point where the wetting liquid is water and the point where cosE approaches zero. Therefore, ND is reasonably assessed as well. A further decrease in w to 0.3 yielded values that matched the measured data poorly. Assuming that w = 0.6, and the evaluation of SV for the EP soil resulted in a ±10% error, we still obtained a reasonable agreement with the measured data. It should be noted that a 10% error in the evaluation of the SV from the measured data resulted in only –1.4 to 3.0% error for w relative to its measured value.
In a similar manner, Eq. [12] (Fig. 4b) was found to be suitable for describing the domain of the relatively hydrophilic branch. In this case, a potential ±10% error in evaluating ND resulted in an error of –2.8 to 2.2% in predicting w.
Since in most studies ND is evaluated by MED (Watson and Letey, 1970; King, 1981), deviation from the actual value of ND should be expected. The MED values (Table 3) obtained in this study, which were found to be lower than ND, still resulted in good agreement with ND; however, for the PN soil (w = 83.9°), the obtained MED value (62.7 mN m–1) suggests that this soil can be defined as water repellent, whereas one would conclude from ND that it is not. Therefore, the sensitivity of the MED or ND values at subcritical water repellence could be misleading. If for natural WRS, however, w ranges from 90 to 109° (Roy and McGill, 2002), according to Eq. [12] the corresponding ND will range from 70 to 33 mN m–1. From the above, however, it seems that Eq. [12] is not suitable for the prediction of w at the higher values of ND.
The conceptual origin of both Eq. [15] and [23] is Young's equation (Young, 1805) and the Girifalco and Good (1957) ESIT. Their formulation, however, is essentially based on an empirical ESIT, which for both equations results in empirical constants (ß in Eq. [15], in Eq. [23]) that are assumed independent of SV. The first question arising in this context is whether these constants can be considered universal for all WRS. If the answer is no, the second question arises as to whether, for any varying constants, Eq. [15] and [23] are valid as a predictive tool in the assessment of w for WRS. According to the results of this study, as shown below, it seems that the answer to both questions is no.
In Fig. 4C and 4D, the sensitivity of Eq. [15] and Eq. [23], respectively, is analyzed for different constants ( and ß). The different slopes of vs. SL () in Eq. [23] were examined for the purportedly universal value for polymers (0.0075), the value obtained for WRS in this study (0.011), and two additional, arbitrary values.
Regardless of the actual value of , all lines are essentially equivalent at the point attributed to SV, which is in agreement with the basic assumption of the ESIT approach; however, it can be seen that, for any value of , Eq. [23] seems to be unsuitable for predicting E as a function of LV. Furthermore, at the higher value, Eq. [23] is subject to mathematical difficulties when the hydrophilic domain of LV is considered. In addition, cosE vs. LV tends to present a convex trend rather than a concave one, which is the tendency obtained for 
0.0075. Equation [15], however, which provided a concave trend regardless of the value of ß, is also subject to mathematical difficulties in the hydrophilic domain. Excluded was the curve for ß = 0.000115, which is the experimental value reported for polymers. Nevertheless, an increase in the value of ß resulted in a move toward the predicted line (Fig. 4C), which represents the more hydrophobic domain of LV.
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SUMMARY AND CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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E for WRS when measured with AETS is restricted. This argument is particularly valid when applying Eq. [15] and [23], which suggests that one universal constant is suitable for all soils. In contrast, Eq. [15] is widely and successfully used with polymeric substances. Nevertheless, Eq. [10] and [12] can yield a reasonable approximation in the relatively hydrophilic domain of LV, albeit with insufficient sensitivity for a potential experimental error on the one hand and small differences between soils on the other hand.
The derivation of the interaction parameter, w < 1.0, explains the differences observed in the literature between the values for the critical surface tension obtained with the Zisman plot technique and the considerably smaller values obtained with the classical MED test. According to our results, it seems that the value of w for WRS is 0.6.
When measurements of E vs. LV are available, the entire domain of LV should be separated into two sections: the hydrophobic one, which can be used to evaluate the SV by fitting the results with a straight line (Zisman plot), and the hydrophilic one, which can be described with the logistic curve (Eq. [17]). Extrapolations of the straight line to the point were water is the wetting liquid will result in overestimation of w. Further investigations should focus on the analysis of for more natural and artificial WRS with various textures, using a larger variety of pure liquids and aqueous mixtures.
Received for publication January 26, 2005.
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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