Water Resources Research

Reply to Comment by Philippe Baveye on “Physicochemical controls on adsorbed water film thickness in unsaturated geological media”

Authors

  • Tetsu K. Tokunaga

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    1. Earth Sciences Division, Lawrence Berkeley National Laboratory,Berkeley, California,USA
      Corresponding author: T. K. Tokunaga, Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA. (Tktokunaga@lbl.gov)
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Corresponding author: T. K. Tokunaga, Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA. (Tktokunaga@lbl.gov)

1. Introduction

[1] I thank Dr. Baveye for his interest and comments [Baveye, 2012] (hereafter B2012) on my recent paper [Tokunaga, 2011] (hereafter T2011). Adsorbed films are indeed important in controlling flow [Lebeau and Konrad, 2010], straining of colloids during transport [Wan and Tokunaga, 1997], and retarding chemical transport [Hu et al., 2004] in unsaturated media. The main issue raised by B2012 is that films predicted in the work of T2011 and in other recent publications [Lebeau and Konrad, 2010; Tokunaga, 2009] are believed by Dr. Baveye to be too thick. This position presented by B2012 is based on questioning the experimental method used by Read and Kitchener [1969], a lack of referencing studies based on “much more sophisticated” experimental techniques, and uncertainties associated with the Hamaker constants presented by T2011. These points will be addressed in turn to show that the Derjaguin-Landau-Verwey-Overbeek (DLVO)-based predictions developed by T2011 are consistent with film thickness measurements obtained using suitable controls of the matric (disjoining) potential, including those cited by B2012.

[2] Read and Kitchener used a trapped bubble method for controlling the disjoining pressure of aqueous films in contact with a silica surface, and laser reflectivity for determining film thicknesses [Read and Kitchener, 1969]. This combination of control and measurement methods permitted Read and Kitchener to obtain high resolution in both the disjoining pressure and film thickness. The uncertainty in the disjoining pressure is associated with uncertainties in the trapped bubble's excess pressure calculated with the Young-Laplace equation. For a trapped bubble geometry,

display math

where σis the gas-water interfacial tension,r is the harmonic mean interfacial curvature of the bubble, and Rb is the optically measured bubble radius. Thus, for a reasonable choice of σ, and fairly accurate measurement of Rb, the relative uncertainty in the ΔP will be fairly small (less than 10% of the calculated value), and absolute uncertainties will be a fraction of the calculated disjoining pressure. Based on information presented by Read and Kitchener, uncertainties in film thickness determined by interferometry appear to be <5 nm. Thus, the experimental approach used by Read and Kitchener appears sufficiently accurate for characterizing adsorbed films under their reported conditions. Similar and even finer resolution has been obtained in related experimental methods utilizing trapped immiscible fluid phases, including more recent publications by others [Aronson and Princen, 1978; Somasundaran et al., 2000; Vazquez et al., 2005; Ward et al., 1999]. As shown later, compared to methods relying on controlling relative humidity such as those cited by B2012, the trapped bubble approach is particularly well suited for establishing accurate, low-magnitude disjoining pressure conditions associated with the drainage of larger pores.

[3] Another objection raised by B2012 to Read and Kitchener's method is “These films are not the result of a traditional adsorption process. Rather, they are produced ingeniously by trapping some solution between a gas bubble and the silica surface.” Indeed, the gas phase is not at atmospheric pressure. However, the slightly elevated gas phase pressure (145 Pa) is less than a 1% departure from standard atmospheric pressure. Moreover, the practical equivalence of gas phase pressurization methods to aqueous phase “suction” methods is the basis for routine use of pressure plate methods for determining moisture characteristic curves with gas phase gauge pressures up to 1.5 MPa [Dane and Hopmans, 2002]. Variations on the pressure plate method have been developed to investigate aqueous films on variably rough surfaces using synchrotron X-ray fluorescence of ionic tracers, for equilibration with atmospheric air [Tokunaga et al., 2000] and with high total pressure (7.8 MPa) supercritical CO2 [Kim et al., 2012]. Results from those experiments indicate enhancement of film thicknesses on rough surfaces attributable to surface capillary retention.

[4] The experimental studies cited in the work of B2012 address water film thicknesses under disjoining potentials that are beyond the range of most unsaturated zone conditions, but nevertheless are remarkably consistent with predictions presented by T2011. Two of the more sophisticated methods for investigating adsorbed films cited by B2012 used either attenuated total reflection infrared spectroscopy [Asay and Kim, 2005] or synchrotron X-ray reflectivity [Bohr et al., 2010] on systems in which relative humidity (RH) as RH = p/po, where p and poare the partial and saturation vapor pressures of the water phase, was equilibrated with solid surfaces. These techniques certainly do permit probing of water-solid interfacial interactions. However, the use of relative humidity to control water potentials (ψw) and matric potentials (ψm) within the range commonly found in soils is problematic. This experimental limitation is evident upon considering the relation between the water potential, ψw, and p/po. On an energy per volume water basis,

display math

where R is the gas constant, T is the absolute temperature, and VM is the molar volume of water. The approximation for ln(p/po) is satisfactory for most soil and unsaturated zone conditions (ψw > −2 MPa). Note that p/po is directly related to ψw, which is typically the sum ψm + ψs, where ψs is the solute (or osmotic) potential. Thus,

display math

which at 20°C is approximately

display math

(with potentials in units of pascal). This relation shows that, because of the large magnitude of RT/VM, relative humidity must be controlled with extreme accuracy in order to regulate ψm at levels of common environmental interest. For example, assuming negligible ψs, controlling ψm at −103, −102, and −10 kPa (−10, −1, and −0.1 bar) requires p/po values of 0.9926, 0.99926, and 0.999926. The sophisticated experiments cited by B2012 do not have this level of p/po control. The study by Asay and Kim [2005]states “The adsorption of water onto this surface was accomplished by varying the ratio of dry argon flow to water-saturated argon stream.” Accuracies associated with mixing the gases and how the water-saturated argon was prepared were not stated. However, the error bar associated withp/po = 0.994 in their Figure 2 appears to range from 0.97 up to 1.000. With negligible ψs, this range of p/po corresponds to a ψm range from approximately 4 ×106 up to 0 Pa; i.e., practically the full range of ψm encountered in the subsurface. The large uncertainty in ψm obtained at high p/po with even the best available vapor pressure control technology is partly why humidity control is not relied upon for regulating unsaturated flow experiments. In discussion of their results, Asay and Kim did not imply that the thickness of 2.8 nm represents a limit as the p/po approaches 1.000. Rather, they stated “The thickness of the adsorbed layers starts increasing exponentially with RH, and bulk condensation occurs at near saturation vapor pressure” [Asay and Kim, 2005]. If the “water-saturated argon” had ap/po of 0.999, the resulting ψm would be approximately −105 Pa. At this potential the film thickness is in the range of 2 to 3 nm in the example calculations presented by T2012.

[5] Further discussions on relating p/po values to subsurface conditions and the importance of accurately controlling p/po and T appear warranted. The conditions prepared by Bohr et al. [2010] have a large p/po uncertainty of 0.02 (relative humidity uncertainty of ±2%) and an upper limit p/po of only 0.90, which corresponds to ψm approximately −14 MPa. Such conditions are well beyond (drier than) the typical range of unsaturated zone ψm, and beyond the range considered by T2011. Moreover, very minor fluctuations in T result in condensation and macroscopic droplet formation when relative humidity control is employed at p/po ≥ 0.99. Thus, lacking independent confirmation of ψw within the experimental device, wide ranges of ψw can be associated with the “close to 100%” relative humidity conditions referred to by B2012. The “near saturation” relative humidity condition for water vapor adsorption on mica [Beaglehole et al., 1991] is described by B2012 as “tended to a finite thickness of about 2 nm.” However, the graphs in that paper showing adsorption results on mica indicate continued increase in film thickness as p/po approaches 100%, and the text describes p/po ranging from 0 to 0.99 without providing uncertainties [Beaglehole et al., 1991].

[6] A more complete picture of adsorbed water film thicknesses under a wide range of environmental conditions emerges upon examination of the various experimental studies considered here. Representative data on film thicknesses from the cited sources are plotted in Figure 1, which is a modification of Figure 9 by T2011. Experiments on the basis of captive bubbles (droplets) and on vapor pressure control clearly address complementary ranges of water potentials. The experimental methods relying on confining films between bubbles (or droplets) and mineral surfaces are clearly limited to a narrow range of low-magnitude potentials, wherein aqueous films are typically in the tens of nanometers in thickness. In contrast, films investigated through controlling water vapor pressure are at most a few nanometers in thickness, and are equilibrated at much lower (more negative) potentials. The wide uncertainty bar on the thickest film reported by Asay and Kim reflects the uncertainties resulting from attempting to control water potentials asp/po approaches unity (note the p/po scale on the upper x-axis inFigure 1). The two curves included in Figure 1show predictions of the Langmuir model and the Derjaguin-Landau-Verwey-Overbeen (DLVO) calculations described previously by T2011. The measurements of film thicknesses obtained over many orders of magnitude in water (matric, disjoining) potential are roughly consistent with calculations based on these fairly simple continuum models. It is also evident fromFigure 1 that experimental methods for investigating film thickness relations are still needed in the environmentally important energy range of 103 to 106 Pa, where neither captive bubble or vapor pressure control techniques are suitable.

Figure 1.

Comparisons between experimental determinations of water film thicknesses (points) and model predictions (curves). The Langmuir model describes disjoining pressures in dilute aqueous films on surfaces with high electrostatic potentials. The DLVO calculation was done for a 1 mM ionic strength aqueous film adsorbed on a substrate with a surface electrostatic potential equal to −50 mV, and with an air-water interfacial electrostatic potential equal to −25 mV [Tokunaga, 2011]. The data points identified as “Campbell & Shiozawa, w. Tuller & Or” are based on data from both sources [Campbell and Shiozawa, 1992; Tuller and Or, 2005] as described in the work of T2011.

[7] Other studies referenced by B2012 also address the orientation of water molecules within 1 to a few monolayers at mineral-water and air-water interfaces. Short-range ordering certainly occurs at interfaces, over the full range of matric or disjoining potentials. However, these remaining studies do not address the issue of matric (disjoining) potential-dependence variation in overall (structured and bulk) water film thickness, nor do they include the control of matric (disjoining) potentials.

[8] While the DLVO approach has its limitations and uncertainties, it is not clear that a model based on the Sogami and Ise theory would better predict the thicknesses of water films confined between water-solid and water-air interfaces. Given the predominance of the electrostatic component in our calculations, and the requirement of interfacial charge balance, it is not clear how the Sogami and Ise theory could yield predictions that are significantly different from those based on the DLVO model. Finally, it is noted that the Hamaker constants used in the T2011 calculations of the dispersion contribution are estimates based on literature values, hence they are not adjustable parameters. In closing, the DLVO-based film thickness estimates presented by T2011 are generally consistent with available measurements obtained under well-controlled conditions, including the examples raised by B2012 when the uncertainties associated with vapor pressure control are recognized.

Acknowledgments

[9] I thank the anonymous reviewers for their very helpful comments and suggestions. This work was carried out under U. S. Dept. of Energy (DOE) contract DE-AC02-05CH11231. Funding provided by the DOE, Basic Energy Sciences, Geosciences Research Program is gratefully acknowledged.

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