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a Dep. of Environmental Engineering, Aalborg Univ., Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark
b Dep. of Civil and Environmental Engineering, Faculty of Engineering, Hiroshima Univ., 1-4-1 Kagamiyama, Higashi-Hiroshima, 739, Japan
c Dep. of Crop Physiology and Soil Science, Danish Institute of Agricultural Sciences, Research Centre Foulum, P.O. Box 50, DK-8830 Tjele, Denmark
d Soils and Biogeochemistry, Dep. of Land, Air and Water Resources, Univ. of California, Davis, CA 95616
Corresponding author (i5pm{at}civil.auc.dk)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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. For use in the analysis, the relation between SA and the threshold water content where solute diffusion ceases due to disconnected water films was measured for eight soils (5–46% clay). The tortuosity analysis supported by measured Dp() data shows that SA governs and has a larger impact on liquid-phase tortuosity than PSD has on gaseous-phase tortuosity. At the same value of , the tortuosity is typically larger in the soil water than in the soil air phase, and the difference becomes more pronounced with increasing SA and at low . In the second analysis air permeability, ka, and gas diffusivity, DP,g, are linked in the Millington and Quirk fluid flow model to describe soil structure-forming potential and to establish a model platform to describe ka as a function of DP,g and . Measurements on repacked, nonaggregated soil support the ka(DP,g;) model platform, while measurements on repacked, aggregated soils and on undisturbed soils show that ka is greatly affected by soil aggregation and structure and DP,g is not. In the third analysis, a constitutive parameter model is applied to gas and solute diffusivities and air and water permeabilities in six soils along a soil texture gradient. This illustrates the different behavior of the four transport parameters with PSD and . The liquid-phase transport parameters show a steeper decrease with compared with the gaseous-phase parameters, in part due to the higher tortuosity in the liquid phase. Also, ka in undisturbed soil exhibited a less steep decrease with compared with DP,g, probably due to preferential air flow in larger pores during convective transport. Any attempt to develop a unifying and PSD-dependent model for transport parameters in the soil liquid and gaseous phases will require careful distinction between repacked and undisturbed soils.
Abbreviations: BET, Brunauer–Emmett–Teller • PSD, pore-size distribution • SA, soil surface area • WLR, water-induced linear reduction
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The diffusion coefficient by definition provides basic information about the effective, tortuous pathway of the liquid or gas phase (Currie, 1960; Millington and Quirk, 1964; Epstein, 1989). Thus, new insight into solute and gas diffusivity will also probably provide valuable new insight and understanding of tortuosity in the liquid and gaseous phases and possible links to water and air permeability in variably saturated soils. Recently, a number of conceptually based, predictive models for the solute and gas diffusion coefficients in soils have been presented (Moldrup et al., 2000a, 2000b; Olesen et al., 2001). The models have been developed with careful distinction between sieved, repacked soil and undisturbed soil, and, in the case of gas diffusivity, also between dry soil and wetted soil. Parameters included in the models have been degree of phase saturation (water content or air-filled porosity), total soil porosity and PSD, the latter represented by the Campbell (1974) PSD parameter (b) and volumetric content of large pores (represented by the air-filled porosity at -100 cm H2O of soil matric head, equal to the volume of pores with an equivalent pore diameter >30 µm). The new, predictive diffusivity models together with measured diffusivity data for different soil types enable a closer look into the tortuosity of the liquid and gaseous phases of unsaturated soil.
This study presents three analyses concerning diffusive and convective transport parameters in the soil liquid and gaseous phases. The analyses are based on the classical definition of porous media tortuosity (Epstein, 1989) where the pores are assumed to be tortuous capillary tubes of uniform and similar diameter. In the first analysis, the predictive solute and gas diffusivity models together with measured data for differently textured soils are used to compare tortuosities in the soil liquid and gaseous phases. In the second analysis, gas diffusivity and air permeability (ka) are linked together in a classical fluid transport model (Millington and Quirk, 1964) to establish a conceptually based model to describe soil structure-forming potential and to predict ka. In the third analysis, the Campbell type constitutive parameter model (Campbell, 1974) is applied for all four transport parameters considered (gas and solute diffusivities and air and water permeabilities) to illustrate differences between the diffusive and convective transport parameters in the soil gaseous and liquid phases.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Soil specific SA was measured on eight differently textured soils (Lundgaard, Ødum, L1–L6; see Table 1) by the N2 Brunauer–Emmett–Teller (BET) method (e.g., Pennell et al., 1995) using a Shimadzu Automatic Surface Area Analyzer (Gemini 2375, Shimadzu Scientific, Columbia, MD). Standard deviations for triplicate measurements were generally below 10%. Soils L1 through L6 had been sampled at six locations along a naturally occurring texture gradient identified in an arable field near Lerbjerg, Denmark (Schjønning et al., 1999; Olesen et al., 1999), with clay content ranging from 11 to 46%. Soils L1 through L6 therefore have the same mineralogy and have received the same soil management, including the type and quality of mineral fertilizers and organic manure (Schjønning et al., 1999), allowing a more straightforward evaluation of the impact of soil texture on other soil parameters. The other two soils (Lundgaard, Ødum) are also from arable fields. For all soils, sampling included the 0- to 20-cm plough layer soil. The eight soils have similar contents of soil organic matter (Table 1), and thus the possible effects of differing organic matter contents on N2-BET SA measurements (Pennell et al., 1995) can be disregarded in this study. To obtain the volumetric soil surface area, SAvol (m2 cm-3), the measured specific SA (m2 g-1) was multiplied by the soil bulk densities used in the previous solute diffusion studies for the eight soils (Olesen et al., 1996, 1999).
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Solute and Gas Diffusivity Models
Solute Diffusivity
In solute diffusion studies, it is typically observed that the ratio of relative solute diffusion coefficient (DP,l/D0,l) by volumetric soil water (
) increases linearly with (Porter et al., 1960; So and Nye, 1989; Olesen et al., 1996, 1999, 2000, 2001). This ratio
 | (1) |
Figure 1
shows the liquid-phase impedance factor, Eq. [1], derived from measured solute diffusion data for soils L1, L3, and L5 (Olesen et al., 1999). As expected, fl decreases linearly with decreasing soil water content and approaches zero at a certain threshold soil water content, th > 0 (Fig. 1). This is likely because the water films surrounding the soil particles become disconnected at a certain soil water content, the value of which will depend on the soil type (soil SA). In more clayey soils (e.g., L5 in Fig. 1), the high SA will result in lower water film thicknesses (compared with a sandy soil at the same water content) and thus in a higher value of th. Also, the soil water close to the soil mineral surfaces will exhibit higher viscosity (Kemper et al., 1964; Stigter, 1980), and this will lower the solute diffusion coefficient. The viscosity effect on solute diffusion coefficient should, at the same soil water content, be most pronounced for soils with high SA. Thus, both phenomena (water film discontinuity and increased water viscosity) would suggest an increasing th with increasing SA, in agreement with Fig. 2
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th and soil SA for the eight soils in Table 1. The value of th for each soil was found by linear interpolation of the fl() data as shown in Fig. 1. As the solute impedance factor and diffusivity are typically related to volumetric soil water content, it seems conceptually correct to use volumetric soil surface area, SAvol, instead of specific SA in the analysis. A highly significant (r2 = 0.98) but nonlinear relation between th and SAvol is observed (Fig. 2)
 | (2) |
The likely reason for the nonlinear behavior is that both viscosity and water film discontinuity play a role, and that water is mostly located in water films in clayey soils, while at a relatively higher water content, water will tend to be located in water menisci in sandy soils (Campbell and Mulla, 1990; Petersen et al., 1996).
Olesen et al. (2001) found, based on data for 23 differently textured soils, that fl can be predicted by fl = 1.1( - th). The term ( - th) can be interpreted as the effective water content available for solute diffusion and 1.1 is a factor describing the meandering of the diffusive pathway. Inserting Eq. [2] and fl = 1.1( - th) into Eq. [1] gives
 | (3) |
Gas Diffusivity
In dry (void of water), sieved and repacked porous media Moldrup et al. (2000b) found that gas diffusivity was best described by the Marshall (1959) model
 | (4) |
is the air-filled porosity (volumetric soil air content). In completely dry soil, will equal the soil total porosity, 
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Adding a linear reduction term to Eq. [4] (/, where is soil total porosity) to account for water-induced changes in air-filled pore shape and configuration in a wet compared with a completely dry soil, the water-induced linear reduction (WLR) model
 | (5) |
In the case of undisturbed soil, Moldrup et al. (2000a) found that both soil type and content of large pores apparently influenced gas diffusivity. At a soil water content corresponding to -100 cm H2O of soil water matric head, the following expression was found to describe well gas diffusivity for soils with different texture, from different soil horizons and representing different soil management
 | (6) |
100 is the air-filled porosity at -100 cm H2O (corresponding to the volumetric content of soil pores with an equivalent pore diameter >30 µm). Figure 3
illustrates the performance of the DP,g100(100) expression, Eq. [6], compared with the measured data for 144 undisturbed soils from Denmark, United Kingdom, and the Netherlands; see Moldrup et al. (2000a) for data references. The width of the 95% prediction interval is 0.09, and the coefficient of regression is r2 = 0.98. In Fig. 3, a mean value of DP,g100(100) measurements on between three and six closely sampled (within 0.5 m2) undisturbed soil cores was used for each soil, since the local-scale variability in the gas diffusion coefficient typically was small. Figure 3 also illustrates the level of 100 for most soils: 80% of the soils are within 0.1 < 100 < 0.3 m3 m-3, while some very sandy soils from Denmark and Holland have 100 values above 0.3 m3 m-3, and a few very clayey soils have 100 values below 0.1 m3 m-3. Hence, the common range for 100 is between 0.1 and 0.3 m3 m-3.
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) model for undisturbed soils was derived (Moldrup et al., 2000a),
 | (7) |
) data for 24 differently textured, undisturbed soils.
Diffusion-Based Tortuosity Analysis
Tortuosity (T) is here defined as the ratio of the average capillary tube length, Le, to the length of the porous media (soil sample), L, along the major flow (diffusion) axis, in a tortuous (sinuous) capillary tube of uniform diameter
 | (8) |
This definition follows Carman (1937)(1956), Currie (1960), Scheidegger (1974), Ball (1981), and Epstein (1989). As discussed by Epstein (1989), several definitions of tortuosity and tortuosity factor have been used in the literature, which contributes to a general confusion concerning use of the term tortuosity. Assuming diffusion in a porous medium with pores consisting of tortuous and nonconstricted tubes with uniform and similar diameter, the relation between diffusivity and Le/L becomes (Currie, 1960; Ball, 1981; Epstein, 1989)
 | (9) |
is the volumetric fluid-phase content (equals in the case of solute diffusion and in the case of gas diffusion). Combining Eq. [8] and [9] gives
 | (10) |
Combining Eq. [10] with the presented Dp/D0() models for soil liquid and gaseous phases, Eq. [3] through [7], enables a diffusion-based analysis of tortuosity. The tortuosity can also be considered to be the squareroot of (1/f), where f is the impedance factor (Eq. [1]).
Figure 4a shows T in the soil liquid phase as a function of soil water content and soil SA, based on the solute diffusivity model, Eq. [3]. As no significant difference in solute diffusion coefficients between sieved, repacked, and undisturbed soil has been observed (Olesen et al., 2000), the calculated tortuosity curves in Fig. 4a are assumed representative for both sieved and undisturbed soil. A large effect of both water content and soil type (SA) is seen for tortuosity in the soil liquid phase (Fig. 4a).
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values (high water contents), are evident from Fig. 4b. Data from literature (listed in Moldrup et al., 2000b) for gas diffusivity in completely dry soil is marked with open triangles in Fig. 4b. Data support the model and show that the tortuosity in the gas phase in completely dry soil is close to one. For wet soil, the tortuosity in undisturbed soil is larger than in sieved soil, probably due to local-scale zones with higher-than-average bulk density and/or water content that hinders the diffusive gas flux.
Varying the value of 100 (content of large pores) within the typical interval (0.1–0.3 cm3 cm-3; see Fig. 3) and with b = 6 (loam soil) gives minor effects on tortuosities. Varying both 100 and the Campbell PSD index (b) gave similar effects (not shown). The analysis implies that PSD (b, 100) has limited effects on gaseous-phase tortuosity; that is, the effects are minor compared with the water-induced effects on gaseous-phase tortuosity in a wet soil compared with a completely dry soil at the same soil air content (Fig. 4b), and also minor compared with the huge effect of soil type (SA) on liquid-phase tortuosity (Fig. 4a).
Measured solute and gas diffusion coefficients support the tortuosity analysis. Figure 5a
shows tortuosity, T, as a function of fluid-phase content, , in four differently textured sieved and repacked soils (Lundgaard sand, L1 loamy sand, L3 sandy clay loam, L5 sandy clay), obtained by inserting measured values of solute and gas diffusivities in Eq. [10]. No soil type effect on gaseous-phase tortuosity was seen, whereas there was a pronounced effect of soil type on liquid-phase tortuosity, in agreement with Fig. 4. Interestingly, the liquid- and gaseous-phase tortuosities became very similar for the more sandy soils (Lundgaard and L1). This implies that the effective diffusive pathways in coarser textured soils with low SA are quite similar in the liquid and gaseous phases. In contrast, a pronounced difference occured for more finely textured soils where the large soil SA will create a thin and tortuous liquid phase, while there still is a low tortuosity in the gaseous phase. Thus, the differences between the tortuosities in the liquid and gaseous phases of sieved, repacked soil becomes larger with increasing soil SA, especially at lower fluid phase contents (Fig. 4a, 4b, and 5).
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Another interesting question is at what soil water content the liquid- and gaseous-phase tortuosities become similar? Figure 6 shows the relative soil water content (/) where the models predict equal values of T in the soil liquid and gaseous phases of sieved, repacked soil. In this case, the gas diffusivity model, Eq. [5], was written with respect to soil water content using = - . Also shown in Fig. 6 are the actual values for soil L1 (sandy), soil L3 (loamy), and soil L5 (clayey) obtained from the measured DP() relations for solute and gas diffusivity in repacked soil. Good agreement between data-derived and model-predicted values for the point of equal tortuosity (/ value at equal tortuosity) in the liquid and gaseous phases is seen. The point of equal tortuosity will take place around half saturation (/ = 0.5) for the sandy L1 soil, whereas the point of equal tortuosity will be around / = 0.7 for the clayey L5 soil and thereby takes place in a much wetter soil. This is because a higher soil water content is needed in the clayey L5 soil to counterbalance the massive effect of the high SA on liquid-phase tortuosity (Fig. 4a). Hence, the higher water content will decrease the high liquid-phase tortuosity and at the same time increase the gaseous-phase tortuosity (due to a reduced soil air content), causing the tortuosities in the liquid and gaseous phases to approach each other.
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, where is soil air content), and Ball (1981) used the equivalent pore diameter
 | (11) |
Following Kirkham et al. (1958) and Moldrup et al. (1999), the equivalent pore diameter at -100 cm H2O of soil water matric head, d100, is suggested as a soil structure index. The value is obtained by using the measured air permeability and gas diffusivity at -100 cm H2O (ka100 and Dp,g100) in Eq. [11].
Figure 7 shows the values of d100 for six soils (L1–L6) sampled along a natural clay gradient, calculated from Eq. [11] using measured air permeabilities and gas diffusivities at -100 cm H2O. Three cases are considered, namely (i) sieved, repacked and nonaggregated soil (L3 and L5, measured in this study), (ii) sieved and repacked soil that have been standing in lysimeters for 17 mo exposed to freeze–thaw and dry–wet cycles as well as frequent tillage, and subsequently undisturbed soil samples were retrieved from the lysimeters (called structurally disturbed soil in Fig. 7; data from Schjønning et al., 1999), and (iii) undisturbed soil samples from the six field locations (data from Schjønning et al., 1999). The sieved, repacked and nonaggregated soil have a d100 value around 50 µm (49 for L3 and 51 for L5). The structurally disturbed soil has developed some structure during the 17 mo (new structure), probably in the form of aggregation due to biotic as well as abiotic mechanisms, and has d100 values between 100 and 250 µm. The d100 value is increasing with clay content, probably because larger clay content promotes formation of soil aggregates. For the undisturbed soil samples, d100 is even larger (250–500 µm) as more permanent and more continuous macropores will add to the overall soil structure (old structure). Only in the case of L6, d100 values were not significantly different (overlapping values of standard deviations for six closely sampled soil core, not shown) between structurally disturbed and undisturbed soil. The large difference between the three situations (repacked, structurally disturbed, and undisturbed) with respect to soil structure and air flow behavior is obvious from Fig. 7 (note logarithmic d100 axis).
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) values are well predicted by the WLR gas diffusivity model for sieved, repacked soil (Eq. [5]). Air permeability acts in an opposite manner to gas diffusivity and shows an increase in ka with decreasing soil air content, with the highest values of ka obtained at the lowest soil air contents (Fig. 8). At first sight, this appears illogical; however, the explanation is that at low soil air contents, the soil water contents were high and the mixing of the soil caused soil aggregation. This creates more continuous gas-phase pathways, causing pronounced higher air permeability as the convective gas flow is more likely to take place in the larger, more continuous pores (preferential gas flow effects). In accordance with this, the equivalent pore diameters (d) are increasing with decreasing soil air content for both soils, from 
40 µm at the highest values to d > 100 µm at the lowest values. Figure 8 proves that soil aggregation has little effect on gas diffusivity but dramatic effects on air permeability.
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) may therefore be derived from the Millington and Quirk (1964) fluid flow model. Combining Eq. [11] and [5] and isolating ka yields
 | (12) |
Figure 9c shows that Eq. [12] with d taken as a constant (50 µm = d100) describes the measured air permeabilities in the sieved, repacked and nonaggregated L3 and L5 soils reasonably well. In accordance with this, the WLR gas diffusivity model (an inherent part of Eq. [12]) describes well the measured gas diffusivity data for sieved L3 and L5 soil (Fig. 9a).
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The difference between transport parameters for sieved and undisturbed soil seems related to the magnitude of transport velocity. For the slowest process, solute diffusion, Olesen et al. (2000) found no difference between sieved and undisturbed soil. Some difference is evident for gas diffusion (compare Fig. 9a and 9b) and a pronounced difference is evident for convective gas transport (Fig. 9c and 9d). Figure 9 represents, to our knowledge, the first direct comparison of gas diffusivity and permeability for both undisturbed and sieved, repacked (nonaggregated) soil.
It is not immediately feasible to combine Eq. [11] with gas diffusivity models for undisturbed soil, for example Eq. [7], to derive ka() models for undisturbed soil. Besides the fact that d is very sensitive to small changes in soil structure including soil aggregation (Fig. 8 and 9), the rate of decrease in ka with in the case of undisturbed soil is not necessarily well described by the same term as used in the gas diffusivity model, 2 + 3/b (see Eq. [7]), because of preferential flow effects during convective gas transport. This can be shown by a constitutive function analysis for each transport parameter.
Constitutive Function Analysis of Transport Parameters
This analysis assumes the general validity of the Campbell (1974) constitutive parameter model
 | (13) |
as before is the fluid-phase content (soil water content, , for solute diffusivity and water permeability, and soil air content, , for gas diffusivity and air permeability). In a log(p/p*)–log(/*) coordinate system, Eq. [13] will yield a straight line with slope 
. The dataset (p*, *) represents the parameter value, p*, at a chosen reference value of fluid-phase content, *. In the present analysis * is taken as the highest fluid-phase content where a parameter measurement was available.
Figure 10a
shows p/p*(/*) for gas diffusivity and air permeability in undisturbed L1 soil. Two things are evident. First, the Campbell constitutive function describes well the two gas transport parameters within the soil air content interval where measurements were available. This was generally the case for gas diffusivity and air permeability as well as for solute diffusivity in the Lerbjerg soils (L1–L6) with the coefficient of regression (r2) >0.97 in all cases. Second, the air permeability shows a smaller decrease with (smaller value of ) than does gas diffusivity, probably due to preferential air transport in the larger pores during convective air flow.
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, as a function of the Campbell PSD index, b, for air permeability (undisturbed soil), gas diffusivity (undisturbed soil) and solute diffusivity for the L1 through L6 soils. The value of for air permeability increases with b, in agreement with the model proposed by Moldrup et al. (1998). Based on data for mainly sandy and loamy soils, they suggested = 1 + 0.25b, but from the data on Fig. 10b, = 1 + 0.05b would better describe air transport in the six Lerbjerg soils. Hence, the model = 1 + 0.25b would predict too steep a slope of the air permeability relations, especially for the finely textured L4 through L6 soils. In agreement with this, Moldrup et al. (1998) noted that = 1 + 0.25b could not provide a satisfying description for across soil textural groups (see Table 1 of Moldrup et al., 1998). Both studies therefore imply that the (b) description for ka needs further improvement.
The value of is decreasing with b for gas diffusivity and, for the interval two to three, is in agreement with the model by Moldrup et al. (1996), = 2 + 3/b; the latter was also used in this study (Eq. [7]). For the more finely textured soils (high b values), the effect of local zones of varying bulk density or water content will probably be more pronounced, yielding a lower value. The different behavior of gas diffusivity compared with air permeability is likely because air permeability is greatly affected by soil structure while gas diffusivity is not (Fig. 8 and 9). For all six soils, for air permeability is smaller than for gas diffusivity, and the difference is increasing with decreasing b (more coarsely textured soils). For sieved, repacked soil (L3 and L5), however, the values for air permeability and gas diffusivity were similar and close to 2.5 (not shown in Fig. 10), in agreement with the model platform for nonaggregated soil, Eq. [12]. These observations also support the hypothesis of preferential flow in the larger pores (structural pores) in undisturbed soil during convective air transport.
For solute diffusivity, is increasing with b, in agreement with the model by Olesen et al. (1996). Rearranging the model by Olesen et al. (1996) to obtain a expression yields = 1 + 0.3b. This is in reasonable agreement with the data for the six Lerbjerg soils, especially for the more finely textured L4 through L6. The values for solute diffusivity is generally higher than for the two gas transport parameters (gas diffusivity and air permeability; Fig. 10b), again implying a much larger tortuosity in the soil liquid than in the soil gaseous phase. The difference is especially pronounced for the finely textured L4 through L6 soils with high SAs.
No measurements for water permeability were available for the L1 through L6 soils. However, Poulsen et al. (1998)(1999a) showed that for air permeability is typically well above the Alexander and Skaggs (1986) model, = b + 3, and is typically well predicted by the original Campbell (1974) model, = 2b + 3. These two models have been plotted in Fig. 10b to indicate a likely range of water permeability. It is seen that for water permeability is at a completely different and higher level than the three remaining transport parameters. This is caused by the effect of water retention (water adsorption) to the soil particles, creating a much steeper decrease in water permeability with than for the three other parameters. Comparing the functions for solute diffusivity and water permeability is interesting in that solute diffusivity reveals the basic effects of the soil liquid-phase tortuosity, while the difference between solute diffusivity and water permeability reveals the basic effect of soil water adsorption on the water permeability function. Thus, by measuring both solute diffusivity and water permeability as a function of soil water content, it should be possible to distinguish between the effects of liquid-phase tortuosity and water retention on water permeability.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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= 2 in Eq. [13] gave a good prediction for most soils (Moldrup et al., 1998). Air permeability becomes an increasingly important parameter in environmental soil studies, for example when modeling and designing soil vapor extraction–soil venting systems for cleanup of contaminated soils (Poulsen et al., 1999b). Development of predictive air permeability models for undisturbed soil is an important scope of future research. 100) and other water retention parameters, that is, from the Campbell, multiparameter Campbell, Brooks–Corey, or van Genuchten–Mualem type water retention models. Additionally, for highly structured soils with cracks, worm holes, or root channels, two- or multiregion flow models are needed to predict water and air permeability (Wilson et al., 1992; Chen et al., 1993; Durner, 1994). th, for the eight soils in Table 1 all correspond to a soil water matric head less than -3000 cm H2O. The cause of th for solute diffusivity, discontinuous water films and increased water viscosity close to soil particle surfaces, will logically affect water permeability in an analogous way. Hence, it is likely that th for solute diffusion will be related to the residual water content, r, where water permeability ceases, as defined in the Brooks and Corey (1966) and van Genuchten (1980) models. Thus, it seems promising to develop expressions for r based on soil SA. 100, new types of predictive models for unsaturated hydraulic conductivity were developed. The macroporosity, 100, together with PSD and soil SA may therefore provide a good platform for describing gas diffusivity, air permeability, and water permeability in unsaturated, undisturbed soil.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Liquid-phase tortuosity is strongly soil type dependent and related to soil SA and liquid-phase geometry, Gaseous-phase tortuosity is less soil type dependent and related to gaseous-phase connectivity (connectivity of air-filled pores). This has important implications towards understanding and modeling diffusive and convective transport in the gaseous and liquid phases of unsaturated soil.
The observed differences between transport parameters in undisturbed compared with repacked soil greatly depend on the velocity of the transport process. No significant difference between solute diffusivity in repacked and undisturbed soil has been observed. Gas diffusivity in repacked and undisturbed soil only differ a little, and it is typically lower in undisturbed soil, probably because of local-scale zones with higher bulk density or water content that hinders the diffusive gas flux. Air permeability in repacked and undisturbed soil is very different and is typically much higher in undisturbed soil, probably because of preferential air flow during convective transport.
Along a natural soil texture gradient, the Campbell constitutive function parameter () increased slightly with Campbell PSD index (b) for air permeability, decreased slightly with b for gas diffusivity, increased with b for solute diffusivity, and, in comparison, was estimated to strongly increase with b for water permeability. The analysis is in agreement with previous models developed for each of the four transport parameters and may suggest the possibility for developing a unifying and soil type dependent model concept for diffusive and convective transport parameters in the soil liquid and gaseous phases. Key soil physical parameters for this include pore size distribution, soil volumetric SA, and soil structure parameters (including 100 and d100). The observations in this study emphasize that careful distinction between repacked and undisturbed soil systems is required for such model development.
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ACKNOWLEDGMENTS |
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Received for publication July 6, 2000.
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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A. G. Hunt Comments on "Fractal Fragmentation, Soil Porosity, and Soil Water Properties: I. Theory" Soil Sci. Soc. Am. J., June 29, 2007; 71(4): 1418 - 1419. [Full Text] [PDF]
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K. Kawamoto, P. Moldrup, P. Schjonning, B. V. Iversen, D. E. Rolston, and T. Komatsu Gas Transport Parameters in the Vadose Zone: Gas Diffusivity in Field and Lysimeter Soil Profiles Vadose Zone J., November 20, 2006; 5(4): 1194 - 1204. [Abstract] [Full Text] [PDF]
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K. Kawamoto, P. Moldrup, P. Schjonning, B. V. Iversen, T. Komatsu, and D. E. Rolston Gas Transport Parameters in the Vadose Zone: Development and Tests of Power-Law Models for Air Permeability Vadose Zone J., November 20, 2006; 5(4): 1205 - 1215. [Abstract] [Full Text] [PDF]
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T. G. Poulsen, P. Moldrup, S. Yoshikawa, and T. Komatsu Bimodal Probability Law Model for Unified Description of Water Retention, Air and Water Permeability, and Gas Diffusivity in Variably Saturated Soil Vadose Zone J., October 3, 2006; 5(4): 1119 - 1128. [Abstract] [Full Text] [PDF]
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G. Liu, B. Li, K. Hu, and M. Th. van Genuchten Simulating the Gas Diffusion Coefficient in Macropore Network Images: Influence of Soil Pore Morphology Soil Sci. Soc. Am. J., June 21, 2006; 70(4): 1252 - 1261. [Abstract] [Full Text] [PDF]
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T. G. Poulsen, P. Moldrup, L. W. de Jonge, and T. Komatsu Colloid and Bromide Transport in Undisturbed Soil Columns: Application of Two-Region Model Vadose Zone J., May 26, 2006; 5(2): 649 - 656. [Abstract] [Full Text] [PDF]
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A. Tuli, J. W. Hopmans, D. E. Rolston, and P. Moldrup Comparison of Air and Water Permeability between Disturbed and Undisturbed Soils Soil Sci. Soc. Am. J., August 4, 2005; 69(5): 1361 - 1371. [Abstract] [Full Text] [PDF]
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J. S. Tyner, W. C. Wright, J. Lee, and A. D. Crenshaw A Dynamic Air Permeameter for Coarse-Textured Soil Columns and Cores Vadose Zone J., May 12, 2005; 4(2): 428 - 433. [Abstract] [Full Text] [PDF]
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A. G. Hunt Continuum Percolation Theory for Saturation Dependence of Air Permeability Vadose Zone J., February 1, 2005; 4(1): 134 - 138. [Abstract] [Full Text] [PDF]
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A. G. Hunt and T. E. Skinner Hydraulic Conductivity Limited Equilibration: Effect on Water Retention Characteristics Vadose Zone J., February 1, 2005; 4(1): 145 - 150. [Abstract] [Full Text] [PDF]
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A. G. Hunt Comparing van Genuchten and Percolation Theoretical Formulations of the Hydraulic Properties of Unsaturated Media Vadose Zone J., November 1, 2004; 3(4): 1483 - 1488. [Abstract] [Full Text] [PDF]
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C. Kjaergaard, T. G. Poulsen, P. Moldrup, and L. W. de Jonge Colloid Mobilization and Transport in Undisturbed Soil Columns. I. Pore Structure Characterization and Tritium Transport Vadose Zone J., May 1, 2004; 3(2): 413 - 423. [Abstract] [Full Text] [PDF]
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P. Moldrup, T. Olesen, S. Yoshikawa, T. Komatsu, and D. E. Rolston Three-Porosity Model for Predicting the Gas Diffusion Coefficient in Undisturbed Soil Soil Sci. Soc. Am. J., May 1, 2004; 68(3): 750 - 759. [Abstract] [Full Text] [PDF]
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B. V. Iversen, B. V. Iversen, P. Moldrup, P. Schjonning, and O. H. Jacobsen Field Application of a Portable Air Permeameter to Characterize Spatial Variability in Air and Water Permeability Vadose Zone J., November 1, 2003; 2(4): 618 - 626. [Abstract] [Full Text] [PDF]
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A. G. Hunt and G. W. Gee Wet-End Deviations from Scaling of the Water Retention Characteristics of Fractal Porous Media Vadose Zone J., November 1, 2003; 2(4): 759 - 765. [Abstract] [Full Text] [PDF]
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A. G. Hunt and R. P. Ewing ON THE VANISHING OF SOLUTE DIFFUSION IN POROUS MEDIA AT A THRESHOLD MOISTURE CONTENT Soil Sci. Soc. Am. J., November 1, 2003; 67(6): 1701 - 1702. [Abstract] [Full Text] [PDF]
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P. Moldrup, S. Yoshikawa, T. Olesen, T. Komatsu, and D. E. Rolston Air Permeability in Undisturbed Volcanic Ash Soils: Predictive Model Test and Soil Structure Fingerprint Soil Sci. Soc. Am. J., January 1, 2003; 67(1): 32 - 40. [Abstract] [Full Text] [PDF]
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P. Moldrup, S. Yoshikawa, T. Olesen, T. Komatsu, and D. E. Rolston Gas Diffusivity in Undisturbed Volcanic Ash Soils: Test of Soil-Water-Characteristic-Based Prediction Models Soil Sci. Soc. Am. J., January 1, 2003; 67(1): 41 - 51. [Abstract] [Full Text] [PDF]
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P. Schjonning, I. K. Thomsen, P. Moldrup, and B. T. Christensen Linking Soil Microbial Activity to Water- and Air-Phase Contents and Diffusivities Soil Sci. Soc. Am. J., January 1, 2003; 67(1): 156 - 165. [Abstract] [Full Text] [PDF]
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A. G. Hunt, A. G. Hunt, and G. W. Gee Water-Retention of Fractal Soil Models Using Continuum Percolation Theory: Tests of Hanford Site Soils Vadose Zone J., November 1, 2002; 1(2): 252 - 260. [Abstract] [Full Text] [PDF]
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