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Modeling Water Movement in Heterogeneous Water-Repellent Soil: 1. Development of a Contact Angle–Dependent Water-Retention Model

^a Institute of Soil Science, Univ. of Hannover, Herrenhaeuser Str. 2, 30419 Hannover, Germany
^b Sustainable Land Use Group, HortResearch, Tennent Dr., P.O. Box 11030, Palmerston North, New Zealand
^c Dep. of Environmental Sciences, Univ. of California, Riverside, CA 92521, USA

View larger version (19K): [in this window] [in a new window]   FIG. 1. Dispersive sD (circles) and nondispersive sND (squares) surface free energy components as a function of the gravimetric water content (Fig. 1a) for a clay mineral (data from Chassin et al., 1986) and for a peat soil as a function of the water vapor humidity (Fig. 1b; data from Michel et al. 2001). Schematically shown is the equilibrium film pressure component as a function of moisture content.

View larger version (25K): [in this window] [in a new window]   FIG. 2. Relation between the advancing contact angle a and the common logarithm of the water drop penetration time, WDPT (a, m, n, t, tt, and c are empirical fitting parameters). Data from Bachmann et al. (2003) and Woche et al. (2005).

View larger version (28K): [in this window] [in a new window]   FIG. 3. Water drop penetration time (WDPT) as a function of water content and organic matter content (SOM) in a sandy soil (top). Figures at bottom show the corresponding data after conversion of WDPT to contact angle with the function displayed in Fig. 4. Plot recalculated after data presented in Täumer et al. (2005).

View larger version (18K): [in this window] [in a new window]   FIG. 4. Advancing and receding CA of air dry silt hydrophobized with dichlorodimethylsilane. Also shown are time-dependent contact angles (CAs) measured in a constant immersion depth. Soil was dried after wetting for 10 d in water, and CAs were measured with the Wilhelmy plate method (WPM).

View larger version (16K): [in this window] [in a new window]   FIG. 5. Cosine of the contact angle of a humus sand from a topsoil of a forest stand after three repeated wetting–drying cycles. In each cycle samples were remoistured to approximately field capacity and dried either to oven-dryness, to air-dryness, to pF 4.2, or to freeze-dried. Contact angles (CAs) were measured with the capillary rise method. Average standard deviation of CA determinations approx. 4 to 5°.

View larger version (25K): [in this window] [in a new window]   FIG. 6. Water entry pressure as a function of the cosine of the contact angle for three different soils.

View larger version (24K): [in this window] [in a new window]   FIG. 7. Schematic representation of the contact angle (CA) model. Location of node is indicated by i and j, time by t, contact angle by ; is the water retention parameter of the van Genuchten equation, and WP indicates the water content at the permanent wilting point. REV = representative elementary volume.

View larger version (18K): [in this window] [in a new window]   FIG. 8. Schematic representation of the dynamic decrease of the water content-dependent contact angle with time t (Fig. 7a) and positive pressure h (Fig. 7b) in the vicinity of a wetting front. Parameters used were crit = 2 Vol.-%, FK = 18 Vol.-%, max = 110°, min = 0, characteristic rewetting time to = 30 d, breakthrough pressure ho = 30 cm.

View larger version (38K): [in this window] [in a new window]   FIG. 9. Water tension–saturation relations (imbibitions) for a wettable soil ( = 0) used as reference soil (Ref. soil) to calculate the contact angle (CA) for hydrophobic soils with various contact angles. The 3.1% and 5% are the ratio of mixing of a bulk artificially hydrophobized quartz sand (100% hydrophobic) with a pure wettable quartz sand ( = 0) (Recalculated after data from Bauters et al., 1998). The ORC and EQL soils are naturally occurring hydrophobic sandy soils located under orange orchard and eucalyptus cover, respectively. Ignition of these soils (400 °C for 8 h) was used to establish a completely wettable reference soil (data taken from Arye et al., 2007). (VG function = van Genuchten function.)