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a Dep. of Land Resources and Environmental Sciences, Montana State Univ., Bozeman, MT 59717-3120 USA
b Dep. of Soil and Water Science, Univ. of Alexandria, El-Shatby, Egypt
c Dep. of Soil Science and Soil Geography, Univ. of Bayreuth, Bayreuth 95440, Germany
hlangner{at}montana.edu
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMaterials and methodsResultsDiscussionREFERENCES |
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-10 cm. Experiments at h 
-5 cm consistently exhibited PNE conditions, indicating the presence of preferential flow. These results suggest that soil pores with effective radii of 150 µm and smaller (water-filled at h = -10 cm) do not contribute to preferential flow. Observed pore water velocities were not indicative of the presence or absence of preferential flow conditions. Continuous measurements of soil water content (
) using time domain reflectometry (TDR) revealed that at h = -10 cm, <2% of the soil volume (1–5% of at saturation) had drained.
Abbreviations: ADE, advection–dispersion equation • BTC, breakthrough curve • LE, local equilibrium • PFBA, pentafluorobenzoic acid • PNE, physical nonequilibrium • PVC, polyvinyl chloride • TDR, time domain reflectometry
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMaterials and methodsResultsDiscussionREFERENCES |
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Due to its potential importance in affecting the fate of chemicals, preferential flow has been studied intensively during the past two decades. The dependence of preferential flow on soil macroporosity (Germann and Beven, 1981; Luxmoore et al., 1990; Li and Ghodrati, 1994) or on management practices (e.g., tillage, application of manure) that influence soil macroporosity has been evaluated (Singh and Kanwar, 1991; Wu et al., 1995; Munyankusi et al., 1994). Results indicate that preferential flow is generally correlated with the number or volume of soil macropores. Although it is well recognized that the potential for preferential water and solute transport may increase with greater macroporosity, it has been difficult to determine relationships among specific physical soil properties (especially pore sizes) and the susceptibility to preferential flow. What constitutes a macropore is related to the processes being considered. In our discussions we use the term macropore to indicate those pores potentially forming preferential flow paths for soluble chemicals.
Germann and Beven (1981) suggested that the minimum radius of macropores is 1.5 mm, while Luxmoore (1981) defined macropores as pores >0.5 mm. In one transport study using undisturbed cores of an aggregated tropical soil, Seyfried and Rao (1987) observed significant preferential flow at matric heads (h) of 0 and -1 cm; when h was lowered to -10 and -20 cm, no preferential flow was observed. This suggests that pores with equivalent radii smaller than 0.15 mm (water-filled at h = -10 cm according to the capillary model; Jury et al., 1991, p. 41) did not contribute to preferential flow in their soil columns. In a field study using disk infiltrometers, Angulo-Jaramillo et al. (1996) observed a transition from capillary-dominated to gravity-dominated flow between h = -6 and -3 cm, suggesting that the minimum pore radius for preferential flow might be smaller than 0.25 mm. Other suggestions of macropore sizes range from >0.005 to >1.5 mm (see reviews by Beven and Germann [1982] and Luxmoore et al. [1990]). Although related factors such as pore geometry and pore continuity undoubtedly influence the potential for preferential flow (Bouma, 1990; Logsdon et al., 1993), the wide range in estimated macropore radii is due partly to our inability to identify water-conducting pore sizes responsible for observed preferential flow events. To narrow this range, experiments are necessary where (i) the water status (drained or filled) of various pore-size fractions in the soil can be effectively controlled and (ii) the transport behavior of solutes can be evaluated simultaneously for the presence of preferential flow conditions.
Preferential flow may be interpreted as a nonequilibrium transport process, with the soil profile exhibiting discrete water domains or regions. While one-region models assume a homogeneous mean pore water velocity (v) throughout the porous medium at steady state, two-region models divide the medium into a mobile domain, where solute transport occurs by advection and dispersion, and an immobile domain, in which there is no advective flow (van Genuchten and Wierenga, 1976). Advective–dispersive transport in the mobile domain is accompanied by diffusive mass transfer of solutes between mobile and immobile regions. If diffusive mass transfer rates prevent equilibrium between the immobile and mobile domains, solutes in the system may be considered to be in a state of nonequilibrium. This phenomenon has been termed transport or physical nonequilibrium (Brusseau and Rao, 1990; van Genuchten and Wierenga, 1976). When preferential flow conditions are present, a two-region (or PNE) model will generally fit the observed solute breakthrough data better than a one-region (or LE) model. In the absence of preferential flow, the PNE model reduces to an LE model.
The primary objective of this study was to examine the relationship between soil matric heads (and corresponding pore sizes) and nonequilibrium transport in a naturally structured soil, in smaller head increments than previously shown. Miscible displacement experiments were performed using two tracers (3H2O and PFBA) at several matric heads in large intact soil cores with an apparatus especially suited to maintain constant head and collect large effluent volumes. The observed BTCs were evaluated for PNE using a comparison between fitted LE and PNE models.
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Materials and methods |
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TOPABSTRACTINTRODUCTIONMaterials and methodsResultsDiscussionREFERENCES |
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Experimental Setup
Preparation of the soil cores and the experimental column apparatus were described in detail in Langner et al. (1998). Briefly, the soil columns were used to generate soil water characteristic relationships [(h)] and to perform unit gradient miscible displacement experiments. Soil cores were equipped with transducer tensiometers (to measure h) and TDR waveguides (to measure ) at depths of 
8 and 20 cm. A modified disk permeameter was used to deliver eluent solutions to the top of the column. The radius of the permeameter disk was 0.5 cm smaller than the radius of the column, allowing gas exchange as the column was wetted or drained. The permeameter was designed to allow rapid switching between eluents without changing h and without mixing the eluent solutions. Eluent switching by physically exchanging the permeameters (Jaynes et al., 1995; Angulo-Jaramillo et al., 1996; Casey et al., 1998) was avoided because it would have led to partial destruction of the surface pore system. Shortly before the planned switching of eluents, the valves to the eluent reservoirs were closed and a slightly more negative pressure than set by the Mariotte Device was applied to the flushing port (Langner et al., 1998). This accelerated the draining of the headspace in the permeameter base while h was held constant by the Mariotte Device. The moment when the permeameter headspace was effectively drained, the valve to the reservoir containing the new eluent was slowly opened while a slight negative pressure was maintained at the flushing port. When the air in the headspace was replaced with new eluent, the valves were closed again and the flushing procedure was repeated to ensure complete replacement of eluents in the permeameter. The column bottom rested on a porous stainless steel plate allowing uninterrupted application of constant negative pressure as well as collection of large effluent volumes (Langner et al., 1998).
Miscible Displacement Experiments
A series of two to four transport experiments was performed with each of four intact soil cores, under steady-state flow conditions. The matric head was varied between experiments with each soil column. The primary goal was to obtain BTCs of 3H2O and PFBA at a minimum of three h values per column. Across all columns, h ranged from 0 cm (ponding, Exp. III-p and IV-p) to -24 cm (I-24). Roman numerals I to IV indicate the four soil columns and arabic suffixes correspond with the imposed h (Tables 1 and 2) .
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After steady-state hydraulic conditions were established, the eluent was switched to a pulse solution containing 3 mM CaCl2, 3H2O (specific activity, 1.67 x 105 Bq L-1; Sigma Chemical Co., St. Louis, MO), and 0.1 g L-1 PFBA (Sigma Chemical Co.). Eluent was switched back to 3 mM CaCl2 when 0.7 pore volume of pulse solution had been applied. Experiments were continued for about four pore volumes, after which the column was wetted to saturation and reconditioned for subsequent experiments at different h. Two to four transport experiments were generally possible with a single soil column before significant changes in measured flow rate and (h) indicated changes in the soil pore systems (Langner et al., 1998).
Effluent fractions were analyzed for 3H2O using liquid scintillation analysis and for PFBA using ion chromatography (Pearson et al., 1992).
Modeling Approaches
Measured solute BTCs were evaluated using the LE and the PNE forms of the advection–dispersion equation (ADE) as a mechanism to identify the presence or absence of physical nonequilibrium (Toride et al., 1995). The ADE used to describe one-dimensional transport of a sorbing solute under steady-state fluid flow conditions through homogeneous porous media is given by (Lapidus and Amundson, 1952):
 | (1) |
is soil bulk density (M L-3), is volumetric water content (L3 L-3 ), s is sorbed-phase solute concentration [M M-1], D is the hydrodynamic dispersion coefficient (L2 T-1), x is distance from solute application (L), and v is average pore water velocity (L T-1). Assuming sorption–desorption equilibrium throughout the soil profile and isotherm singularity and linearity [s = Kdc, where Kd is the linear equilibrium sorption coefficient (L3 M-1)], the 
s/t term becomes Kd c/t, and Eq. [1] may be simplified and expressed in nondimensional form (LE model; Brusseau and Rao, 1989):
 | (2) |
is the retardation factor, and the dimensionless parameters are defined as follows:
, where C is the relative solute concentration, c0 is the eluent solute concentration (M L-3), P is the Peclet number describing the relative magnitude of dispersion, L is column length (L), T is dimensionless time (pore volumes), and X is dimensionless distance.
The LE model (Eq. [2]) does not appropriately describe solute transport under conditions where preferential flow paths result in significant heterogeneity in v. Substantial spatial variation in v can affect the transport of sorbing and nonsorbing solutes, and its results have generally been described as PNE or transport-related nonequilibrium (van Genuchten and Wierenga, 1976; Brusseau et al., 1989). van Genuchten and Wierenga (1976) modified the ADE to explicitly differentiate two soil water regions, with all advective–dispersive transport occurring in the mobile region, and diffusive transport into the immobile region. Sorption–desorption is again assumed as an equilibrium process following a singular linear isotherm. The governing differential equations for this PNE model in nondimensional form are given as:
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 | (4) |
 | (5) |
m is the mobile-phase volumetric water content (L3 L-3), f is the fraction of sorption sites that equilibrate with the mobile region, vm is the average pore water velocity (L T-1) in the mobile region, and 
is the first-order mass transfer coefficient (T-1) between the two regions. The variable ß is a partition coefficient describing the fraction of solute present in the mobile region (Brusseau and Rao, 1989). For nonsorbing solutes
, ß reduces to the fraction of mobile water (m/). The parameter 
is a dimensionless rate coefficient describing mass transfer between the mobile and immobile regions. Values of ß and can be used to evaluate potential contributions from PNE. Physical equilibrium conditions are approached when m and f (sorbing solutes only) approach and 1, respectively, and ß approaches 1 (Eq. [5]). When ß = 1, the PNE model reduces to the LE model. Similarly, if the mass transfer parameter in Eq. [4] increases, the rate of convergence of Cm and Cim increases. In the limit 
, Cm = Cim because solutes in each domain mix instantaneously, and the PNE model again reduces to the LE model. Several researchers have shown that optimized values of 100 indicate absence of nonequilibrium conditions (Valocchi, 1985; Bahr and Rubin, 1987).
To distinguish between LE and PNE conditions, measured 3H2O and PFBA BTCs from miscible displacement experiments were analyzed using both LE and PNE models. Model parameters L and v (= q-1) were obtained from direct measurement. The steady-state water flux density, q (L T-1), was calculated for each experiment from the effluent flow rate, and was determined by averaging the measured (TDR) water contents at both sensor positions. Measured tracer BTCs were fitted to the LE model under flux type boundary conditions using CXTFIT2 (Toride et al., 1995), a least squares parameter optimization method. Batch experiments performed to assess sorption of 3H2O to the Amsterdam soil suggested that 3H2O was not sorbed (15 samples with 50–750 Bq 3H mL-1, sorption of 0 ± 0.5% at a soil/water ratio of 1:1), providing justification for fixing Rf = 1 in the transport model optimizations. However, model fits using Rf = 1 did not yield reasonable agreement between observed and fitted data. Some retardation of 3H2O (Rf between 1.0 and 1.5) has been observed in a number of previous studies (e.g., Mansell et al., 1973; Wierenga et al., 1975; van de Pol et al., 1977; Seyfried and Rao, 1987; Jacobsen et al., 1992; Gaber et al., 1995); and has been explained as isotopic exchange of 3H2O or adsorption (Stewart and Baker, 1973; Wierenga et al., 1975; van de Pol et al., 1977). Furthermore, considerable discrepancies between batch and transport-derived Rf were also reported by Seyfried and Rao (1987). Therefore, Rf was optimized for the lowest-h experiment performed (Exp. I-24, h = -24 cm, Fig. 1)
where no PNE was observed. The resulting estimate of Rf (1.18) was used as a fixed parameter in fitting tracer effluent concentrations of all other experiments. Other modeling approaches, such as fitting Rf values for individual soil columns yielded the same conclusions regarding identification of PNE as a function of h. The uniqueness of the optimized parameters (ß, , D) was verified for each experiment by repeated CXTFIT2 runs with various initial parameter guesses to minimize chances of model conversion at local minima. We also investigated model sensitivity to possible inaccuracies of measured parameters (e.g., ) by conducting a series of model fits by systematically varying input parameters (e.g., testing for sensitivity to involved model input parameters like T, v, and pulse width). Based on these verification techniques we are confident that the fitted parameters reported in Table 1 are representative of our data set. The same approach was used to test for the presence of PNE in PFBA BTCs making use of the Rf (0.83) optimized for Exp. I-24. A value for Rf < 1 was expected for PFBA due to anion exclusion.
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were 1 or 100 (upper limit for in CXTFIT2), respectively. When these criteria were met, optimized values of P were not statistically different (95% confidence interval) for the PNE and LE models. Conversely, PNE conditions (preferential flow) were assumed when higher r2 values were obtained with the PNE model, which was the case when ß < 1 and < 100.
Soil Water Characteristic and Pore-Size Distribution
The procedure for obtaining (h) for wetting and drying from paired TDR and tensiometer readings was described previously (Langner et al., 1998). Since repeated wetting and drying cycles shortened a column's usability for tracer transport studies, (h) was determined only for a subset of columns (not for Column IV). Volumetric water contents measured at h between 0 and -70 cm were fitted to a parametric model (van Genuchten, 1980):
 | (6) |
s represents measured at saturation, r is residual water content (fitted), and a, n, and m are fitting parameters describing the shape of the (h) relationship. The pore-size distribution was estimated by relating the drained porosity [s-(h)] to the minimum drained pore radius r as a function of h. Values of r(h) were obtained from the capillary equation (e.g., Jury et al., 1991, p. 41):
 | (7) |
is surface tension of water (0.073 N m-1 at 23°C), 
is the contact angle between soil water and solids (assumed = 0°), w is the density of water (103 kg m-3), and g is the gravitational constant (9.8 m s-2). The drained porosity at any h is assumed to consist of soil pores having effective radii larger than r. |
Results |
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TOPABSTRACTINTRODUCTIONMaterials and methodsResultsDiscussionREFERENCES |
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, respectively. Curve-fitting results were similar for PFBA, suggesting LE conditions at h = -11 cm and PNE transport at h = -5, -3 cm, and ponding (Table 1).
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-5 cm, fitted values of ß and were <1 and <100, respectively, suggesting the presence of PNE.
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(h)] in the range of h = 0 to -70 cm were generated for Columns I to III during wetting and drying cycles, and the measured (h) data were fit using Eq. [6] (Fig. 4
, Table 2). As expected, the model fit the observed data reasonably well, although optimized parameters may not be representative for the drier range of the Amsterdam soil. Drained porosities as a function of h or corresponding minimum drained pore radii (Eq. [7]) were obtained from the fitted (h) (Fig. 5)
. The magnitude of drained porosity as a function of h varied substantially not only among columns, but also within individual columns depending on the instrument position and the extent of hysteresis between wetting and drying cycles. For example, drained porosities at h = -10 cm ranged from 0 to 6% of the total soil volume and at h = -5 cm from 0 to 3% depending on which (h) curve was selected to obtain pore-size distribution (Fig. 5).
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Discussion |
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TOPABSTRACTINTRODUCTIONMaterials and methodsResultsDiscussionREFERENCES |
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-5 cm, which do not participate in advective flow. Results obtained in our study are generally consistent with recent attempts to correlate immobile water fractions with h under field conditions (Casey et al., 1998). However, in our column studies no relationship was observed between h and the mass transfer coefficient (, Eq. [5]) obtained from PNE model fits to tracer BTCs.
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We found no evidence of increased PNE when h was further decreased to -24 cm. This observation agrees with the results of Elrick and French (1966) and Seyfried and Rao (1987), but differs from results of other studies (e.g., Biggar and Nielsen, 1960; DeSmedt and Wierenga, 1984), which reported increases in transport nonideality with decreasing values of h in homogeneous porous media. Apparently, the pore networks in the intact soils used by Seyfried and Rao (1987) and in the current study were sufficiently interconnected that drainage of larger pores did not result in the isolation of immobile water regions. The pore systems of more homogeneous porous media with a narrow pore-size distribution (e.g., sand or glass beads) may be more susceptible to isolation of immobile regions when decreases because of the lack of continuous pores with smaller radii (Brusseau and Rao, 1990).
Identical results were obtained with both 3H2O and PFBA tracers regarding the identification of LE or PNE transport conditions. However, it should be noted that optimized P values generated using the PNE model were generally lower for PFBA than for 3H2O, suggesting greater dispersivity (inversely related to P) of PFBA than of 3H2O in our experiments. According to modeling predictions by Brusseau (1993), PFBA may exhibit greater overall dispersivities than 3H2O at higher v because of the increasing importance of intraparticle diffusion. In the aggregated medium examined by Brusseau (1993), dispersivities of PFBA and 3H2O were predicted to be approximately equal between v = 0.1 and 1 cm h-1, while at v >1 cm h-1, the slower film and intraparticle diffusion of PFBA caused higher dispersivities of this tracer compared with 3H2O. Morphological differences between our soil and Brusseau's model aggregated medium may have caused deviations in the v ranges where differences between the tracers become apparent; however, a variety of other factors potentially affecting optimized P values should be considered before drawing further conclusions, for example, effects of anion exclusion, PNE, or sampling frequency.
Observed pore water velocities could not be used to predict the presence or absence of PNE. Although for each column tested the onset of PNE conditions was also associated with increases in v (Table 1), absolute values of v as a function of h differed among columns. Our data set allowed selection of BTCs that exhibited similar average v (0.82–1.06 cm h-1) but varied between LE and PNE transport conditions as a function of h (Fig. 3). Variations in pore-size distribution and continuity among different soils will affect the relationship between h and v; for example, values of v between h = -10 cm and ponding varied about threefold (between 0.82 cm h-1 for Exp. II-3 and 2.64cm h-1 for Exp. III-p) in cores of the Amsterdam soil, while other authors have reported 20- or 100-fold changes in v for the same h range (Seyfried and Rao, 1987; Germann and Beven, 1981). These results suggest that easily measurable v-related parameters, such as infiltration rates or water flux densities, may not be good indicators of preferential flow in soils.
Estimates of the fractional soil volume responsible for preferential flow in the Amsterdam silt loam were obtained using measurements of during transport and from the (h) relationship. Continuous TDR measurements of during the transport experiments indicated that <1 to 2% of the soil volume (1–5% of maximum soil water content) was drained under LE conditions (h = -10 cm, Table 1). Drained porosities corresponding with h = -10 cm were estimated using the (h) relationship determined during wetting and drying cycles (Fig. 5) and varied between 0 and 6% of the total soil volume. Our results represent an additional example of the difficulties in accurately defining the (h) relationship in the wet range, where PNE may be expected (Beven and Germann, 1982; Luxmoore et al., 1990). To generate more reproducible pore-size distribution data with our apparatus, the method of determining would have to be modified to obtain measurements of representative of a larger soil volume. This could be accomplished by modifying the dimensions, orientation, or number of TDR waveguides or perhaps via gravimetric measurements.
In summary, 3H2O and PFBA transport experiments in undisturbed cores of Amsterdam silt loam soil demonstrated a transition from physical equilibrium to nonequilibrium flow conditions between h = -10 and -5 cm as determined using a two-region form of the ADE. This transition range has been found for other intact soil cores, further suggesting that soil pores with effective radii <150 µm do not contribute to PNE. In the Amsterdam soil, the fractional soil volume responsible for PNE appeared to be <2%, as determined during the transport experiments. However, fractional soil volumes contributing to PNE could not be verified using (h) relationships due to a high degree of variability and hysteresis at high water contents.
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ACKNOWLEDGMENTS |
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Received for publication November 16, 1998.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMaterials and methodsResultsDiscussionREFERENCES |
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