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a L. Wollesen de Jonge, Department of Crop Physiology and Soil Science, Danish Institute of Agricultural Sciences, P.O. Box 50, DK-8830 Tjele, Denmark
b Department of Environmental Engineering, Aalborg University, Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark
c Department of Social and Environmental Engineering, Faculty of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739, Japan
* Corresponding author (kirsten.schelde{at}agrsci.dk)
Received 17 December 2001.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONMODELINGCONCLUSIONREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONMODELINGCONCLUSIONREFERENCES |
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Several experimental studies have demonstrated transport of colloids in soil (for a review see Kretzschmar et al., 1999). A number of colloid transport experiments have been made in structured soils in the field (Bottcher et al., 1981; McKay et al., 1993; Ryan et al., 1998; El-Farhan et al., 2000) or in structured soil columns in the laboratory (Toran and Palumbo, 1992; Saiers et al., 1994). Most laboratory studies have involved saturated flow conditions; however, a few laboratory experiments have dealt with unsaturated flow in structured soil (Smith et al., 1985; Jacobsen et al., 1997; Seta and Karathanasis, 1997; Karathanasis, 1999; Lægdsmand et al., 1999).
Jacobsen et al. (1997) investigated the transport and leaching of natural colloids from nine undisturbed soil columns sampled from the plow layer of a sandy loam field. They tested the impact of flow rate on the leaching of colloids under conditions of steady irrigation with tap water. In all cases they found an initial high leaching of in situ particles, followed by a gradual decrease and a final low constant concentration of colloids in the effluent. The experiment showed no effect of irrigation intensity on colloid leaching normalized to outflow volume, implying that detachment of colloids due to hydrodynamic shear was not a dominant process in colloid mobilization. When plotting cumulative mobilization from the columns vs. square root of time, a near-linear increase was found. This linearity indicates that the colloid release kinetics are diffusion-limited (e.g., Kookana et al., 1992). Lægdsmand et al. (1999) examined colloid mobilization in cores of macroporous soil originating from the same site as those of Jacobsen et al. (1997). Lægdsmand et al. (1999) found that the source of leachable colloids during prolonged infiltration seemed unlimited. Further, they concluded that after long-term rain events the mobilization process was controlled by diffusion in the matrix or at the interface between macropores and the flowing water. Seta and Karathanasis (1997) leached intact soil columns with about five pore volumes of colloid suspension and then switched the input solution to deionized H2O. After switching, they found a steep drop in the concentration of colloids in the effluent, but the concentration apparently had not dropped below 10 mg L-1 when the experiment was halted. Conversely, Karathanasis (1999) stated that leaching intact soil columns with five pore volumes of deionized H2O caused colloid concentration in the effluent to become "near zero".
Filtration theory and modeling of colloid transport kinetics have focused on homogeneous porous media, based on studies of colloid deposition in model systems with glass beads or packed soil columns, yet these theories do not apply well to natural porous media characterized by wide particle-size distributions and complex pore geometry (Kretzschmar et al., 1999). In fractured or macroporous soils, the large pore size implies that sedimentation or filtration of particles is less important than particle detachment (Seta and Karathanasis, 1997). There will be less sedimentation in the larger pores since the generally high flow rates allow less time for particles to settle. Attempts to model colloid mobilization and transport have typically involved a first-order kinetic rate law for the colloid release from the surface of the matrix (Dahneke, 1975; Corapcioglu and Choi, 1996; Jacobsen et al., 1997). This approach predicts that the amount of colloids attached to the solid phase decreases exponentially with time.
Lægdsmand et al. (1999) adopted an advection–diffusion approach to model the leaching of species from their soil columns. Macropores were assumed to be full-flowing cylindrical tubes with a constant concentration of the diffusing species on the tube wall, and the flow was assumed to be laminar Poiseuille flow. The model predicted effluent concentrations of total organic C and total dissolved solids (ionic species, mostly salts) well. Nevertheless, model predictions of mobilized colloids did not agree well with experimental results, indicating that colloid concentration at the macropore walls was not constant throughout the experiment.
Colloid mobilization is enhanced by chemical perturbations. Release rates generally increase with increasing pH and with decreasing ionic strength in the soil solution (Ryan and Elimelech, 1996; Kaplan et al., 1996; de Jonge et al., 1998). However, in the present work we focus on mobilization from mature macropores exposed to irrigation water with a stable chemistry similar to that of tap water (i.e., a neutral pH and a low ionic strength).
The primary objective of our study was to further evaluate the possibly diffusion-limited colloid mobilization process in natural macroporous soil. Earlier experimental work has focused on colloid release dynamics primarily by varying the water flow rate; however, we took a novel approach in focusing on the effect of flow interruptions. We emphasized the time-dependence of the release process by exposing intact soil columns to the following cycle: (i) equal periods of steady infiltration, (ii) variable pauses in the infiltration (flow interruptions), and (iii) equal periods of resumed infiltration. Our second objective was to develop a simple equivalent-macropore model to simulate the effective mobilization and transport of natural colloids as observed in our macroporous soil columns. We used the model to test the hypothesis that colloid release to the flowing water is governed by two diffusion processes, one in a uniform water film lining the macropore and one in the crust of the macropore.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONMODELINGCONCLUSIONREFERENCES |
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We designed Exp. 2 to examine the effect of the duration of an intermediate flow interruption on colloid leaching. Soil sampling and initial laboratory procedures of Exp. 2 were similar to those described in detail in Jacobsen et al. (1997) and de Jonge et al. (1998), and only a summary of the procedures, including any differences between the two experiments, is given below. A total of 21 soil columns are included in the subsequent data analysis: nine columns originating from Exp. 1 (Jacobsen et al., 1997) and 12 columns from Exp. 2.
All 21 soil columns were collected at the depth of 2 to 22 cm at the Røgen field station in the northeastern part of Jutland, Denmark. The soil is a sandy loam developed from moraine deposits and is classified as a Typic Hapludalf. Clay, silt, sand, and organic C fractions of the soil amount to 15.7, 27.8, 54.1, and 1.5%, respectively (Laubel et al., 1999). In Exp. 1 the sampling cylinders were made of polyethylene (20 cm long, 18.3-cm i.d.) and in Exp. 2 they were made of steel (20 cm long, 20.0-cm i.d.).
In the laboratory the columns were saturated and drained to ensure identical initial conditions before infiltration. After saturation for 3 to 4 d, the columns were drained on a sandbox to a potential of -20 cm H2O relative to mid-column. The water used for saturation and subsequent infiltration was degassed tap water (conductivity 300 µS cm-1, pH = 7.0) in Exp. 1 and artificial rainwater (conductivity 22.4 µS cm-1, pH = 7.82; de Jonge et al., 1998) in Exp. 2.
The soil columns were irrigated at steady state using a peristaltic pump connected to an irrigation device equipped with 25 hypodermic needles at a 30-mm spacing. Infiltration rates in Exp. 1 were 30 mm h-1 (high intensity; Column 1–5) and 11 mm h-1 (low intensity; columns 6–9), while the infiltration rate applied to all columns in Exp. 2 was constantly low, about 11 mm h-1.
In Exp. 1, the soil columns were irrigated for 120 to 300 min until a steady state and low particle concentration was obtained in the effluent. In Exp. 2, all 12 soil columns were irrigated for about 270 min upon which infiltration was suspended, in four replicates, for 0.5 h (Columns 10–13) or 1 d (Columns 14–17) or 7 d (Columns 18–21). The soil columns that were to rest for more than 0.5 h were allowed to drain for 20 min and then stored at 2°C to prevent drying of the soil. After the flow interruption, infiltration was continued for another 150 min in all 12 columns.
The lower boundary condition of the soil columns was chosen as atmospheric pressure (free drainage), since this promotes macropore flow in the soil. In a macroporous soil there is not necessarily equilibrium in the pressure head across the soil column, and a positive pressure can easily build up just within and close around macropore tubes at the bottom of the soil column. Thus, water leaves the column even if the bottom of the column is not fully water saturated. The free drainage outflow ensures free passage of particles and, in comparison with a suction-type boundary condition, seems a more realistic representation of a natural soil system, where macropore drainage prevails.
The soil columns were placed on a coarse stainless-steel screen (2 by 2 mm grid) that allowed free migration of suspended particles in the effluent. The effluent was collected and weighed on a balance, and particle-size distribution (Exp. 1, Columns 1–9; LUMOSED photo-sedimentometer; Retsch GmbH, Haan, Germany) and particle concentration were measured on subsamples of the effluent. In Exp. 1, particle concentration was measured by light extinction at a wavelength of 400 nm using a Spectronic 2000 spectrophotometer (Bausch and Lomb Inc., New York, NY). In Exp. 2, concentration was measured using a Hach 2100AN turbidimeter equipped with an EPA filter, measuring at wavelengths 400 to 600 nm (Hach, Loveland, CO). A correlation function between light extinction and concentration of clay particles originating from the Røgen site was used for calibrating the spectrophotometer (Jacobsen et al., 1997). Turbidity data in Exp. 2 were converted to particle concentrations by using a correlation obtained from turbidity measurements made on several suspensions of Røgen clay particles. The clay-size separates had been obtained by dispersing Røgen soil in deionized water and isolating the particles <2 µm by repeated gravitational sedimentation (de Jonge et al., 2000). Two linear relationships between the nephelometric turbidity (NTU) and particle concentration (C; mg L-1) were used: For NTU < 200, C = 0.9082 x NTU 
. For NTU > 200, C = 0.5171 x NTU + 83.0 mg L-1 
. A pair of linear regressions was chosen over a polynomial regression to prevent a few turbidity measurements above the calibration range from converting into unrealistic concentrations as a result of the curvature of a polynomial.
The columns of Exp. 1 were finally irrigated for 1 h at a rate of 10 mm h-1 with a dye solution (Brilliant Blue R250, CI number 42660, 1 g L-1) and dissected into four layers of 5 cm. The shape of the dye-colored areas was drawn onto sheets of paper in order to estimate the flow patterns and the active macroporosity. The water content of the columns was measured before and after Exp. 1 by weighing of the total soil column and determination of the dry soil bulk density at the end of the experiment (Jacobsen et al., 1997).
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONMODELINGCONCLUSIONREFERENCES |
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A statistical test based on the results from Exp. 1 showed that the irrigation rate did not affect the total amount of mobilized particles leached after 10 mm of outflow, nor did it affect the particle-size distribution in the effluent (Jacobsen et al., 1997). These results imply that hydraulic stress was not a governing process in the release of particles from the macropore walls. In contrast, Kaplan et al. (1993) found, particularly for one of their reconstructed lysimeters, that particle concentrations in the effluent were directly related to the square of the flow rate, and hence to the kinetic energy of the flowing water. The findings of Kaplan et al. (1993) therefore suggested that shear stress of the flowing water mobilized particles. Ryan et al. (1998) did not find any correlation between infiltration velocity and particle concentration in the effluent from macroporous soil lysimeter plots. Ryan and Gschwend (1994) normalized the colloid release rates to the volume of water passing through their packed quartz bed columns and found an effect of flow rate on colloid release rate that does not support a shear stress detachment theory: release rate coefficients decreased with increasing flow rates. It is often observed that increasing the flow rate increases the colloid detachment evaluated as a function of time, but this does not necessarily imply that shear stress is important to colloid mobilization. Colloid release is therefore best evaluated as a function of accumulated flow (Ryan and Gschwend, 1994; Jacobsen et al., 1997; El-Farhan et al., 2000).
In Jacobsen et al. (1997) it was hypothesized, in accordance with Ryan and Gschwend (1994), that diffusion across a thin stagnant water layer at the macropore walls may be an important and rate-limiting mobilization process. A constant diffusive mass exchange between the stagnant water layer and the flowing water in active macropores would cause fewer particles to be leached in a given outflow volume at higher flow rates. However, high flow rates may promote a thinner stagnant water layer, equivalent to a shorter diffusion path, and thus counterbalance the effect of slow diffusion. This could explain our finding that there was no effect of flow rate on the amount of leached particles in a fixed outflow volume. Plotting accumulated mobilized particles vs. the square root of time typically showed a linear increase after a few minutes of leaching (Jacobsen et al., 1997) and such a linear relationship suggests, but does not prove, that release kinetics are diffusion limited (e.g. Kookana et al., 1992).
The leaching results of Exp. 2 supported and supplemented the findings of Exp. 1. For the soil columns subject to a 0.5-h flow interruption there was practically no response to resumed infiltration; particle mobilization continued at the rate prevailing before the flow stop (Fig. 1). Conversely, peak concentrations observed after the flow interruption were significantly higher for the soil columns exposed to a 1-d and 7-d interruption than for the soil columns with a 0.5-h flow interruption. This result confirms that particle release is not controlled by hydrodynamic shear due to flowing water, as such a control would have generated equal leaching regardless of the flow stop period. Instead, colloid mobilization is a time-dependent process: during flow interruption, a particle storage is gradually replenished for easy particle release when water flow is resumed.
Another process that may be considered when evaluating our colloid mobilization experiments is the possible effect of an air–water interface present in the macropores prior to any flow event. As Wan and Wilson (1994a)(b) observed, colloids or other particles may sorb to an air–water interface. This preferential sorption may involve both hydrophilic and hydrophobic particles and is fast and irreversible. In the macroporous flow system, therefore, the first peak of particles in the effluent may be interpreted as originating from flushing of the air–water interface present before flow initiation, and the colloids adhered to it. In our experimental system this effect would occur both at the first wetting front (first infiltration event) and any later wetting fronts. However, in Exp. 2 we saw that after a relatively short flow interruption of 30 min there was no peak of particles when water flow resumed. This indicates that the preferential sorption and subsequent flushing of colloids was not a dominant process in our experiments, or rather, that the time-dependent, rate-limiting processes dominated over any such interfacial processes. The interfacial sorption process has been suggested as a possible effect by many researchers but has not yet been examined in depth. Recent work (Chu et al., 2001) suggests that the effect depends on the types of particles (virus) and porous media involved.
The total in situ particle mobilization from each column of Exp. 2 is found as the area below the leaching curves in Fig. 1. In the first part of the experiment, during the 250 min following breakthrough, the 12 replicates typically leached 30 to 100 mg in total. However, three soil columns mobilized substantially more material. Columns 10, 14, and 19 leached 319, 207, and 632 mg, respectively. The differentiation of single columns with regard to total particle mobilization and breakthrough concentrations in the effluent may reflect a mechanism other than diffusion. Aggregate stability of the macropore walls may differ among soil columns, or sampling and preparation of soil cores prior to infiltration could cause particles to become detached from the macropore walls for easy and immediate release. The latter may be the case for Column 19, whose leaching decreased to a moderate level after about 10 mm of infiltration, whereas Columns 10 and 14 maintained a high, fluctuating, and probably diffusion-limited mobilization throughout the experiment, including after the flow interruption.
Breakthrough time was significantly shorter after the flow interruption than before the flow interruption for all columns of Exp. 2, and the calculated mean macropore velocity was correspondingly higher (Table 1). The breakthrough times after the short flow interruption (30 min) in Exp. 2 were difficult to determine since small amounts of water continued to drip from the columns during the flow interruption. The difference in breakthrough times was probably due to additional wetting of the already wet soil matrix during the first part of the experiment and less wetting during the final irrigation. This means that the observed breakthrough times of the first infiltration event probably overestimated the travel times in the macropores somewhat. Also, the network of preferential pathways may change during the flow interruptions as macropores clog up with particles or they reopen as a result of the ceased water flow. The network may change to promote faster macropore flow, as in our soil columns, or the opposite may occur, as when de Jonge et al. (1998) noted that one soil column ponded following a flow interruption of 17 h and attributed this to clogging of macropores.
The degree of wetting and the net transport of water from the macropores to the matrix of the soil can be evaluated through the changes in average water content observed from the start to the end of Exp. 1. The measured soil water content before the start of Exp. 1 was 0.358 ± 0.011 m3 m-3 (mean and SD of nine soil columns). The measured water content at the end of the total experiment, after 5 to 6 h of infiltration, was 0.364 ± 0.010 m3 m-3 (mean and SD). Thus, a change of 0.006 ± 0.005 m3 m-3 was observed during the experiment. De Jonge et al. (1998) reported similar changes in water content during leaching experiments in Røgen soil monoliths, of 0.007 ± 0.004 m3 m-3. These changes in water content indicate that only a small wetting of the already moist soil columns took place during our experiments. Even if comparative measurements of soil water content changes are not available for Exp. 2, we do not expect that any significant redistribution of moisture took place during the flow interruptions, because of the generally wet conditions throughout the matrix.
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MODELING |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONMODELINGCONCLUSIONREFERENCES |
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The macropore is assumed to be the only source and pathway of colloids in the soil column. Water flows along the rough walls of the macropore, and soil water flow in the matrix is ignored. Macropore transport is described by convection and dispersion of particles in suspension, and colloid release to the flowing water is limited by the diffusion rate from a stagnant water film lining the macropore wall. The concentration in the water film concurrently depends on the particle diffusion rate from the crust of the soil matrix (Fig. 2). The crust has a finite thickness and holds an infinite number of detachable particles in relation to the time span considered in the column experiments.
Thus, the equivalent-macropore model is a three-phase model comprising the phases of mobile water, immobile water, and the crust. The equations describing the transport within the compartments of mobile water (Fmo; vertical transport), immobile water (Jim; horizontal diffusion), and crust (Jcr; horizontal diffusion) are given as Eq. [1] to [3]:
 | [1] |
 | [2] |
 | [3] |
In Eq. [1] to [3], C is concentration in mass per volume phase water and u is the macropore water velocity. The dispersive flux (given as the last term of Eq. [1]) is determined by the hydraulic dispersion coefficient Dh, and Dim and Dcr are the diffusion coefficients of the immobile phase and crust, respectively. The flow area Amo is the cross-sectional area of the mobile water phase, calculated as the product of the soil column area and an estimate of the mobile water content of the column. The tube area (contact surface) between the mobile and immobile phases is Amo–im, and the tube surface area separating the immobile and crust phases is Aim–cr. Amo–im and Aim–cr are calculated for each vertical soil column segment (dz), using the radius of the equivalent macropore and the thickness of the immobile water film (xim). The thickness of the crust is xcr.
The concentration of particles in all three phases is given in relation to the water content (
) that is equal to 1.0 in the mobile and immobile water phases and less than 1.0 in the crust. The governing equation for each phase (Eq. [7]–[9] for mobile, immobile, and crust phase, respectively) is derived under consideration of phase mass balance (Eq. [4]–[6]) and assuming that exchange across the interfaces can be described as diffusion between fully mixed phases (Cussler, 1984, p. 21–23):
 | [4] |
 | [5] |
 | [6] |
 | [7] |
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The diffusion-specific terms (Dim/xim) and (Dcr/xcr) in Eq. [7] to [9] may also be expressed through single values, equivalent to mass transfer coefficients in a mass transfer model. Thus, replacing the diffusion-specific terms in Eq. [7] to [9] with mass transfer coefficients (
) for the immobile phase 
and the crust phase 
simplifies the model into a conceptual model that includes two mass transfer processes, without making assumptions on the processes behind the mass transfer. Using mass transfer coefficients to describe the colloid exchange between the phases is a convenient approach as it reduces the number of unknowns in the model system. As will be shown below, the diffusion layer thicknesses and diffusion coefficients are difficult to estimate independently.
Model Assumptions
The equivalent macropore model was developed to simulate the processes observed in our leaching experiments. The assumptions inherent in the model are quite valid for our soil column studies, but some assumptions render the model less generally applicable. Two aspects to be addressed are:
As already discussed, our soil columns formed a hydrological system where macropore flow largely dominated. The flow in the matrix can be neglected in this context since the unsaturated hydraulic conductivity as well as the gradients in pressure head in the matrix were small. Villholth et al. (2000) estimated the saturated hydraulic conductivity of the matrix to be 2 to 5 x 10-4 m h-1 in the upper 25 cm of the soil at a tile-drained field plot at the Røgen site. Their estimate was based on measurements of total saturated hydraulic conductivity and on model calibration. This estimate of maximum hydraulic conductivity should be compared with water flow rates in the macropores of 0.3 to 2.4 m h-1 (Table 1). The restriction of flow to the macropores also means that, once the surface of the soil columns had been wetted, the water advanced as more or less plug flow to the bottom of the soil column. Therefore, we observed that the effluent flow rate became stable (at a rate similar or lower than the inflow rate) very quickly or immediately after breakthrough, indicating that near steady-state conditions were soon reached. This was also the case after the flow interruptions in Exp. 2. Typical examples of the temporal development of effluent outflow rates were given in Jacobsen et al. (1997)(Fig. 2) and de Jonge et al. (1998)(Fig. 2, Treatment 3). On the basis of this, we found that a steady-state macropore flow model is a fair approximation to our experimental system.
Finally, since the macropore radius is a constant, the model cannot account for deposition resulting in pore clogging, or for detachment resulting in pore regeneration in the natural macropore system. This model simplification is dictated by insufficient knowledge of the actual distribution of preferential pathways in every soil column, both as a function of depth and as a function of time.
Boundary Conditions and Model Implementation
The upper model boundary condition is a specified water flux and a specified particle concentration of the irrigation water (Cin = 0 for our experiments). The lower boundary condition is really an unknown outflow particle concentration but is approximated by assuming a zero concentration gradient at the outlet of the column.
Initial conditions are characterized by an empty macropore, so concentration in the mobile phase is undefined. Particle concentrations in the two other phases are assumed to have reached equilibrium, resulting in equal initial concentrations (Cstart). An optional prolonged simulation (e.g., in flow interruption experiments) with different settings is made using initial concentrations equal to those obtained at the end of the previous simulation. A flow interruption is simulated by assigning the diffusion coefficient of the immobile phase an infinitely small value, thus effectively preventing particle exchange between the mobile and immobile phases.
The model was implemented in a Borland Delphi 5.0 (Object Pascal) programming environment using an explicit scheme with forward-time-central-space (FTCS) calculations for the vertical transport. Discretization of the 0.20-m soil columns was 0.005 m. Hydraulic dispersion in the macropore system was expected to be insignificantly low and therefore merely set equal to the numerical dispersion inherent in the FTCS scheme, given by D = 1/2u2
t, where t is the time step.
Parameter Estimation
A simulation requires the estimation of the equivalent macropore radius, the thickness of immobile and crust phases, and the water content of the crust. The above variables were assigned constant values as given in Table 2. The area of the equivalent macropore was estimated as 2% of column cross area from dye experiments in Exp. 1 and de Jonge et al. (1998). The thickness of the immobile water film was estimated to 30 µm from water film measurements made by Tokunaga and Wan (1997) in a porous rock. Tokunaga and Wan found that the average film thickness depended on the matric potential of the rock and measured thicknesses between 2 and 70 µm. Finally, the crust needed to be thick enough to contain a sufficiently large number of detachable particles in experiments where flow continues for more than 250 min, but then its size was also proportionately related to the diffusion coefficient of the crust (Eq. [9]). Therefore it was set to the minimum thickness that allowed crust concentration to remain constant through every simulation. The specific crust thickness subjectively estimated to match our experiments was 2 mm.
For each soil column to be simulated, the macropore water velocity was estimated as the column height divided by observed breakthrough time. The mobile water content was estimated as the ratio between Darcy velocity (mean observed outflow through column cross area) and macropore velocity.
Sensitivity analyses showed that simulation results were highly sensitive to the initial, equilibrated particle concentration of the crust and immobile phases (Cstart) and to the diffusion coefficients, Dim and Dcr. Further, these parameters were difficult to estimate a priori, so the three parameters Cstart, Dim, and Dcr were subjected to calibration. Fortunately they influence rather different parts of the simulated outflow concentration curve (see Fig. 3). Cstart primarily influences breakthrough peak concentration, while Dcr determines the tailing concentration. Dim influences peak concentration as well as the decay rate of peak concentration. An initial estimate of Dim was obtained from Eq. [10] (Cussler, 1984, p. 118)
 | [10] |
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Parameter calibration considered only those observations before any flow interruption. For the flow interruption experiments, simulations were continued after the flow interruption without changing any exchange process parameters; only macropore water velocity and mobile water content were calculated from the flow data observed after the interruption.
Model Application
Calibration demonstrated the capacity of the model to reproduce well the first leaching in most of the 21 experiments (see Column 7 in Fig. 4 and Columns 11, 17, and 18 in Fig. 5). The model does not consider any physical disruption of the macropore and therefore failed to simulate very high initial peak concentrations (Column 19, Fig. 5) that could be caused by detached colloids resulting from disturbance of the soil structure during sampling and preparation of the soil column. As expected, the model also failed to simulate deviations from an ideal outflow concentration curve such as multiple peaks (Column 5, Fig. 4 and Column 14, Fig. 5) since the model does not consider possible clogging or reopening of flow paths.
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The mean Cstart and the mean Dim were statistically equal between the two experiments at the 0.05 significance level (t-tests; two test samples with nonequal variances). The mean Dcr were not equal between experiments (t-test, two test samples with nonequal variances). The mean Dcr of the first experiment was higher than the mean Dcr of the second experiment (Table 1). The opposite trend could have been expected because pH was a little higher and ionic strength a little lower for Exp. 2 compared with Exp. 1, and this combination enhances colloid release (Ryan and Elimelech, 1996; de Jonge et al., 1998). It appears that the small chemical difference between experiments did not significantly influence leaching. Instead, differences in cultivation history of the field soil may be more important. The soil cores of Exp. 1 were sampled when the field was under permanent grass, while the cores of Exp. 2 were collected after the harvest of a grain crop. The age or maturity of the macropores could affect the equivalent pore radius or the thickness of the crust; these factors are not differentiated between Exp. 1 and 2 in our simulations.
The model results in Fig. 4 for two soil cores from Exp. 1 support the finding of Jacobsen et al. (1997) that irrigation rate does not have an impact on the total mobilization of colloids. Columns 5 and 7 represent high and low flow, respectively, and the model calibration resulted in diffusion coefficients that were comparable (Table 1), indicating that release kinetics were the same for both columns. The higher breakthrough concentrations obtained in the effluent of Column 5 compared with Column 7 are due to a random, high initial concentration of colloids (Cstart) at the macropore walls, related to the natural variability of the experimental soil.
The model was quite successful in simulating the outflow concentrations after flow interruption. For the shortest flow interruptions, simulated concentrations in all four cases showed a very small or negligible increase when resuming flow, in agreement with observations (Column 11, Fig. 5). For the intermediate and long interruptions, predicted concentrations after the interruption were in the same range as those observed, while the decrease in concentration was not predicted as well as before the flow interruption (Columns 17 and 18, Fig. 5). For all columns the constant low level was simulated well both before and after any flow interruption.
Model Predictions and Model Sensitivity
The successful calibration of the model allows an investigation of the development of colloid concentration in the immobile and crust phases, variables not measured in the experiments. This is particularly interesting in the flow interruption experiment. Figure 6 shows the particle concentration in the immobile phase before, during, and after flow interruption for Columns 11, 17, and 18 that represent the three different flow stop intervals. During flow, the immobile phase is quickly depleted and particle concentration reaches a low level where diffusion in and out of the immobile layer is the same. During flow interruption, the immobile phase is gradually replenished via diffusion from the crust. After some time (2–5 d) the concentrations in the crust and immobile phases have equilibrated. When flow is resumed, the immobile phase is drained again. The time needed to reach equilibrium between the crust and the immobile phase during no-flow conditions indicates that there would be no extra "gain" (in terms of achieving large peak concentrations after flow stop) in interrupting flow for more than a week.
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The value assigned to the macropore radius prior to model calibration (Table 2) is not very realistic. The model concept of one single macropore representing total macroporosity may not be credible, and to examine the problem we carried out separate model simulations where the total macroporosity was shared among three identical macropores. This means that macropore radius and the mobile water content were reduced in these simulations, while the pore velocity and the thickness of phases were maintained at their prior values. The resulting outflow particle concentration was consistently increased compared with the reference simulations because the reduced mobile water content left a smaller volume of flowing water for mixing with particles. Repeated calibration to the experiments showed that diffusion coefficients were not modified in the new setup. Instead, recalibration caused Cstart to be reduced in every case by approximately 40% compared with the results listed in Table 1. The same result, that is, no change in exchange parameters, would evidently be obtained if one wished to consider any other number of equivalent macropores.
Likewise, the thickness of the crust had been subjectively estimated to provide a semi-infinite source of particles during our experiments. To evaluate the influence of crust thickness on the model system and the parameterization we ran simulations using double crust thickness (i.e., 4 mm). Simulated outflow concentration was affected only with respect to the tailing concentration that was reduced. This was because the diffusion path in the crust had been increased, thus limiting the release of particles to the immobile phase. During recalibration of the model, the effect of double crust thickness could be counteracted simply by doubling Dcr (also consult Fig. 3 for the effect of changing Dcr). This reveals a simple interdependence between Dcr and crust thickness.
As a final point we made a sensitivity analysis with respect to the thickness of the immobile phase. The wide range of film thicknesses (2–70 x 10-6 m) reported by Tokunaga and Wan (1997) guided our reference estimate of 30 x 10-6 m (Table 2). We subsequently fixed the crust thickness while varying the water film thickness according to Table 3 and made a new model calibration for each case. Calibration was made to the first infiltration event of Column 13 whose concentration outflow curve was clearly consistent with our model concept (Fig. 7). The results of the simulations (Table 3) show that increasing film thickness by a factor of 2 increases Dcr by the same factor and increases Dim by the square of the factor. Hence, as film thickness increases, the ratio Dcr/Dim is diminished. For the simulation labeled "Max. film" in Table 3, the ratio Dcr/Dim is equal to 0.4. This is in better agreement with our expectation that Dcr should be smaller than Dim as a result of tortuosity effects in the crust.
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The success of the model in reproducing the characteristic results of our experiments shows that the release of colloids in macroporous soil columns can be described by two rate-limiting processes in a water film and a crust layer lining the macropore walls. However, the calibrated diffusion coefficients of the immobile and crust phases bear a weakness in being interrelated with the estimated phase thicknesses. The values of the diffusion coefficients are conceptually meaningful only when phase thickness is known a priori, and this condition is rarely met neither for the water film nor for the crust. On the basis of our analyses, we therefore do not have evidence to accept the hypothesis of two diffusion processes, and we are prompted to rely on the simpler mass transfer concept.
Mass Transfer Coefficients
It follows from the above analysis regarding phase thicknesses and from the bottom row of Table 3 that the ratio between the mass transfer coefficients of the immobile phase and the crust (im/cr) is a fixed quantity, however different between soil columns. The ratio of 51 for soil Column 13 (Table 3) is a typical value for Exp. 2. We calculated effective mass transfer coefficients (Table 1) using the calibrated diffusion coefficients of Table 1 and the phase thicknesses as given in Table 2. The resulting ratios between mass transfer coefficients (im/cr) show that mass transfer in the immobile phase was 13 (SD = 6.3) and 51 (SD = 27) times larger than mass transfer in the crust in Exp. 1 and 2, respectively. As discussed above, we attribute this variation between experiments mainly to differences in cultivation history of the field soil (permanent grass in Exp. 1 vs. arable–grain in Exp. 2), but maybe also to small differences in soil solution chemistry.
Describing the particle mobilization using the mass transfer concept allows different interpretations of the two rate-limiting processes that contribute to the colloid mobilization process. While we are still confident that the dominant process in the stagnant water layer is diffusion, the detachment process in the crust may be more dominated by effects related to the electrostatic interaction between particles (aggregate stability) (Kretzschmar et al., 1999, p. 161). Aggregate stability varies with the chemical composition of the water in the soil crust and therefore must be taken into consideration when modeling systems with a more variable chemistry than our present experiments. In extending the model to include a particle detachment process in the crust (governed by, e.g., local gradients in ionic strength) we may be able to obtain values of the diffusion coefficient Dim that agree better with our theoretical expectation.
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CONCLUSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONMODELINGCONCLUSIONREFERENCES |
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The equivalent-macropore model required no recalibration of exchange process parameters to simulate the characteristic differences in particle mobilization after variable flow stop intervals. The success of the model shows that the mobilization of natural colloids in macroporous soil columns can be described by two rate-limiting processes; one in a stagnant water layer and one in a crust layer lining the macropore walls. The test of our hypothesis that two diffusion processes control the mobilization showed that the calibrated diffusion coefficients of the immobile and crust phases bear a weakness in being interrelated with the phase thicknesses, the latter being rarely known a priori. On the basis of our analyses, we are therefore prompted to rely on the less process-specific mass transfer concept. Our model analysis of colloid leaching from 21 soil columns showed that mass transfer coefficients are about 30 times larger in the stagnant water layer than those of the crust.
In perspective, this study shows the need for further experimental and theoretical studies investigating the particle mobilization and leaching processes in structured soils, and especially the role of particle detachment and diffusion at the macropore walls.
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ACKNOWLEDGMENTS |
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONMODELINGCONCLUSIONREFERENCES |
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