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DIVISION S-1-SOIL PHYSICS

Quantifying the Influence of Intra-Aggregate Concentration Gradients on Solute Transport

^a CSIRO Land and Water, Davies Lab., University Rd., Townsville, Australia

claire.cote{at}tvl.clw.csiro.au

	ABSTRACT

TOP ABSTRACT INTRODUCTION Theory NOTES Materials and methods Results Discussion Conclusions Appendix REFERENCES

 
The physical nonequilibrium of solute concentration resulting from preferential flow of soil water has often led to models where the soil is partitioned into two regions: preferential flow paths, where solute transport occurs mainly by advection, and the remaining region, where significant solute transport occurs through diffusive exchange with the flow paths. These two-region models commonly ignore concentration gradients within the regions. Our objective was to develop a simple model to assess the influence of concentration gradients on solute transport and to compare model results with experiments conducted on structured materials. The model calculates the distribution of solutes in a single spherical aggregate surrounded by preferential flow paths and subjected to alternating boundary conditions representing either an exchange of solutes between the two regions (a wet period) or no exchange but redistribution of solutes within the aggregate (a dry period). The key parameter in the model is the aggregate radius, which defines the diffusive time scales. We conducted intermittent leaching experiments on a column of packed porous spheres and on a large (300 mm long by 216 mm diameter) undisturbed field soil core to test the validity of the model and its application to field soils. Alternating wet and dry periods enhanced leaching by up to 20% for this soil, which was consistent with the model's prediction, given a fitted equivalent aggregate radius of 1.8 cm. If similar results are obtained for other soils, use of alternating wet and dry periods could improve management of solutes, for example in salinity control and in soil remediation.

Abbreviations: SSA, Single Spherical Aggregate model • TDR, time domain reflectometry

	INTRODUCTION

TOP ABSTRACT INTRODUCTION Theory NOTES Materials and methods Results Discussion Conclusions Appendix REFERENCES

 
MOST SOILS have a variety of structural and textural heterogeneities that can greatly affect solute transport by creating different water flow velocities, and thus nonequilibrium of solute concentration within the soil. Such phenomena are usually referred to as "preferential flow", and they limit our ability to predict solute movement reliably using traditional mathematical models such as the advection–dispersion equation (ADE) (Beven and Germann, 1982; White, 1985; Bouma, 1991; McCoy et al., 1994).

In order to describe solute transport when preferential flow occurs, a two-domain approach is frequently used (Coats and Smith, 1964; van Genuchten and Wierenga, 1976; Rasmuson and Neretnieks, 1980; Rao et al., 1980b; van Genuchten, 1985). With such an approach, the soil is conceptually divided into two regions, one associated with the fraction of the soil that is highly permeable (e.g., the macropore network in a structured field soil) and the other with the less permeable pore system of the soil matrix. As a further simplification, water in the less permeable region is often regarded as immobile. For convenience, we will refer to the permeable region as preferential flow pathways, and the less permeable region as "aggregates", although this may be a grossly simplified description of real field soils. Solute transport in the preferential flow paths is commonly ruled by advection, while in the aggregates diffusive exchange with the flow paths is important. Transfer of solutes between the two regions can be accounted for in two ways: (i) by using a macroscopically defined mass-transfer coefficient, relating the rate of exchange to the mean concentration difference between the two regions (van Genuchten and Wierenga, 1976; Gerke and van Genuchten, 1993a), and (ii) by using Fick's second law of diffusion. This method requires a description of the geometry of the aggregates. The idealized case is a column of packed spherical aggregates, as studied by Rao et al. (1980a, 1980b).

Many models using either method have been developed to describe solute transport. However, they are difficult to extend from the column scale to the field scale. Fitting the model parameters to experimental data based on the first method often leads to nonuniqueness of the fitted values, so that different groups of values would give an equally good fit to data. Determination of the size and shape of the aggregates for the Fick's law method in a field soil is not viable under natural conditions. Another limitation to two-region models using the macroscopically defined mass-transfer coefficient method is that only the average concentration in the aggregates is determined. It is implicitly assumed that no concentration gradients develop within the aggregates but, in field situations, it is unlikely that solute concentration should remain homogeneous throughout the aggregates considering the variety of conditions to which a field soil is subjected. Consider for instance a strongly structured field soil subjected to rain. The preferential flow paths become saturated and exchange solutes with the aggregates. Because of nonequilibrium of solute concentration between the two regions, concentration gradients develop within the aggregates. When water application stops, the preferential flow paths drain, no exchange takes place, solutes redistribute, and concentration gradients within the aggregates even out. In this study, we explore and quantify the influence on solute transport of such variations in concentration gradients.

We first developed a simple theoretical Single Spherical Aggregate (SSA) model that calculates the distribution of solutes in a single spherical aggregate surrounded by preferential flow pathways and subjected to alternating boundary conditions. These boundary conditions represent either (i) an exchange of solutes between the aggregate and the flow paths, or (ii) no exchange between the two regions, but redistribution of solutes within the aggregate. This model system allowed us to calculate diffusive exchange under alternating boundary conditions, and thus to assess the influence of variations in concentration gradients. Real soil is much more complex, but we assumed we could use the simple model to describe the influence of variations in concentration gradients in a structured field soil.

To test the model validity and its application to realistic systems, we performed experiments reproducing the alternating boundary conditions of the theory by adapting the so-called flow-interruption technique, which is usually used to differentiate between diffusive and advective processes in column experiments. Flow-interruption experiments have been employed in chemical engineering to distinguish between intraparticle diffusion and film diffusion (Helferich, 1962). They have also been used in soil science to investigate immobile phase diffusion processes in soil columns (Koch and Fluhler, 1993; Reedy et al., 1996), and to identify the processes involved in nonideal solute transport (Brusseau et al., 1997). In our experiments, we saturated a soil column with a tracer, applied a background solution at a fixed flow rate for a given time, and then drained the column to stop diffusive solute exchange. This allowed solutes to redistribute so that concentration gradients changed within the aggregates.

We present here the simplified mathematical model, the experimental setup and procedure used to perform intermittent leaching experiments, and compare the experimental data with model predictions.

	Theory

TOP ABSTRACT INTRODUCTION Theory NOTES Materials and methods Results Discussion Conclusions Appendix REFERENCES

 
Single Spherical Aggregate Model
Consider a single spherical aggregate of radius a in which the movement of solutes is governed by the radial diffusion equation, written as

(1)

where C is the concentration of solutes, r is the radial coordinate, t is time, and D_a is the constant diffusion coefficient in the aggregate.¹ We assume that the void space surrounding the aggregate represents the preferential flow pathways and that when flow occurs, both preferential flow pathways and the aggregate are saturated and exchange solutes according to Fick's second law of diffusion. When flow is stopped, we assume that the preferential flow pathways drain instantaneously, but that the aggregate stays saturated and solutes redistribute within the sphere by diffusion. The boundary condition is either (i) a constant concentration C_s at the surface of the sphere (when flow occurs, i.e., during a wet period) or (ii) a zero flux across the surface (when flow is stopped, i.e., during a dry period). Figure 1 represents a succession of wet and dry periods to which we exposed the spherical aggregate. Each cycle j consists of a wet period of duration followed by a dry period of duration T. We solve Eq. [1] subject to the initial condition

(2)

and boundary conditions

(3)

when flow occurs, or

(4)

when flow is stopped, where q is the radial flux of solutes defined by

(5)

View larger version (12K): [in this window] [in a new window]   Fig. 1 Schematic diagram showing the sequence of wet and dry periods imposed on a single spherical aggregate

(6)

where and r' are dummy variables over which the integration takes place, or an initial condition f(r) and a zero flux at the surface

(7)

where _n, n = 1, 2, ... are the non-zero roots of . We introduce the dimensionless variables

(8)

where when studying leaching (i.e., the aggregate is initially saturated with solution at a concentration C_i > 0 and solutes are leached out by a succession of wet periods such that ) or when studying absorption (i.e., the aggregate is initially void of solutes so that and it exchanges solutes with the preferential flow pathways during wet periods such that C_s > 0),

(9)

(10)

(11)

We define the following coefficients:

(12)

(13)

(14)

(15)

(16)

(17)

where ^*_n, n = 1, 2, ... are the non-zero roots of (*)cot(*) = 1. For leaching, we obtain the solutions for the dimensionless concentration given in Table 1 . The results for absorption follow from a change in variables from C* to 1 - C*. In Table 1, r* is the dimensionless radius, r' is a dummy variable over which integration takes place, t* is the dimensionless time, C_j*(r*, t*) is the dimensionless concentration during cycle j, and F_L(t*) is the fraction leached at time t* (i.e., the total amount of solutes leached divided by the amount initially present). Given these analytical expressions, we can calculate the concentration over each cycle j, for any set of time parameters * and T*.

	Materials and methods

TOP ABSTRACT INTRODUCTION Theory NOTES Materials and methods Results Discussion Conclusions Appendix REFERENCES

Materials
For the first set of experiments, we used expanded clay pebbles of the type used in hydroponics (Professional Hydroponics, Adelaide, South Australia). They are made of moulded clay fired in a kiln to render them water stable. They are chemically and biologically inert. Though not quite spherical in shape, they were suitable for the purpose of testing the experimental technique. The average radius of the clay pebbles was 0.53 cm, the 0.05 percentile was 0.39 cm and the 0.95 percentile was 0.70 cm. The saturated water content was 0.29 ± 0.05 cm³ cm^-3. We packed the spheres in a polyvinyl chloride tube 300 mm long by 236 mm internal diameter in 1-cm increments (380 spheres per increment). We used KBr as the tracer and water as the background solution. The Br^- concentration in the leachate was determined using a Br^- specific electrode (Orion, Orion Research, Boston, MA).

For the second set of experiments, we used a large (300 mm long by 216 mm diameter) undisturbed soil core collected near Tully, North Queensland, Australia, according to the technique described by McKenzie and Jacquier (1995). The soil at this site is a Dermosolic Redoxic Hydrosol of the Coom series according to the new Australian classification (Isbell, 1996). It is similar to a Typic Tropaquept. The column consisted of subsurface material (0.1–0.4 m depth) described as medium heavy clay with strong 5- to 10-mm subangular blocky peds. The soil will be referred to according to its soil order (Hydrosol). For these experiments, we used CaBr₂ as the tracer and CaCl₂ as the background solution to ensure the soil's structure was preserved.

Experimental Procedure
To conduct leaching experiments on large columns (artificial aggregates or field soil), we used an apparatus that enabled solution to be applied at the top of the column and the outflowing solution at the base of the column to be collected at preprogrammed time intervals. The main elements of this leaching facility were a custom-made "table" to hold the soil columns, a disk infiltrometer to apply the inflow solution, a sand tension bed to control the suction at the base of the soil columns, a fraction collector (LKB Superrac, AMRAD Pharmacia, Brisbane, Australia) to collect outflow samples at known time intervals, and time domain reflectometry (TDR) probes and tensiometers, inserted at 80-mm and 220-mm depths, to monitor the variation in water content and suction. To obtain saturated flow conditions, we imposed a shallow ponded condition (5 mm) at the top of the column and zero suction at the base.

The experimental procedures for both sets of experiments were designed to reproduce as closely as possible the initial and boundary conditions used in our theory. We saturated the clay pebbles with tracer by applying the tracer solution from the base of the column to minimize entrapped air, and then replaced this solution several times to ensure the initial concentration within the spheres was equivalent to that of the tracer solution. We applied the background solution at the top of the column for a duration to simulate a wet period and then drained the column to reproduce a dry period of duration T. We repeated the last two steps until 90% of solutes had been leached from the spheres.

We saturated the field soil core with tracer by applying it from the base of the column and then replacing two pore volumes by applying more tracer solution from the top of the column. We stopped the flow (without draining) to allow solutes to redistribute within the column overnight and repeated the process the following day. The column was then drained at a suction of 25 to 30 cm, resaturated from the base with background solution (to minimize entrapped air and flow disturbances), with more background solution applied from the top of the column to reproduce a leaching event. We drained the column again at 25- to 30-cm suction to empty the main flow paths, left it drained for the duration of the dry periods (usually between 40 and 120 h), and repeated these steps until 90% of the solutes had been leached from the soil (i.e., until the cumulative amount of solutes in the leachate was equal to 90% of the amount of solutes initially present in the column).

Model Parameter Estimation
To determine the diffusion coefficient that described the movement of solutes into or out of the spheres, we saturated five spheres with KBr at a concentration C_i. We plunged each sphere in 20 cm³ of stirred water and monitored the Br^- concentration in the water every 20 s using a Br^- specific electrode. The concentration in the water could be measured but was too small at early times to invalidate the assumption in Eq. [6]. We thus derived the average concentration C(t) in a sphere from Eq. [6] with () = 0

(18)

We also have

(19)

where C_w(kt) is the concentration in the water measured at kt, V_w is the volume of water, _s is the saturated water content of the sphere, and V_s is the volume of the sphere. By fitting the theoretical expression, Eq. [18], to the experimental values given by Eq. [19], we obtained . D_a is related to the molecular diffusion coefficient in free water D_o by

(20)

where is the tortuosity factor, is the dispersivity of the medium, is the pore water velocity, and n is an empirical constant. We can neglect the pore water velocity in the sphere, so the tortuosity factor can be calculated as

(21)

Using our measured value of D_a (0.0320 ± 0.003 cm² h^-1) and (Weast, 1978), we obtained .

For the second set of experiments, we assumed that the molecular diffusion coefficient in free water of Br (D_o) in CaBr₂ was similar to that of Cl in for a solution at 0.1 mol L^-1 at 25°C (Weast, 1978) since the D_o value for CaBr₂ is not available in the literature. We calculated the tortuosity factor with the commonly used relationship of Millington and Quirk (1961) for a saturated system

(22)

where _s is the saturated water content of the aggregates. This water content represents the volume of water in the aggregates divided by the volume of the aggregates. We assumed that the volume occupied by the preferential flow paths V_p was equal to the volume of solution drained at 25- to 30-cm suction, and _s could be calculated with

(23)

where V_c is the volume of the soil core (10993 cm³), _c is the saturated water content of the core (determined using TDR measurement). We obtained and .

	Results

TOP ABSTRACT INTRODUCTION Theory NOTES Materials and methods Results Discussion Conclusions Appendix REFERENCES

 
Single Spherical Aggregate Model
Values of the fraction leached F_L using the analytical solution (Table 1) were obtained for various values of * and T*, during several consecutive time intervals. We first present numerical results in order to highlight the main conclusions drawn from the model.

If we consider the first wet period (leaching event in this case) and increase t*, we can determine ^*₉₀, the dimensionless time required to leach 90% of solutes out of the spherical aggregate. A plot of the fraction leached as a function of * gives (Fig. 2) . If we assume that the diffusion coefficient D_a does not depend on the radius a, the duration of the wet period that is required to leach 90% of solutes out of a spherical aggregate of radius a is given by . It varies in proportion to the square of the radius, which it must since it is a well-known result of diffusion theory (e.g., for as measured for the expanded clay pebbles, we get 1.425 h for a 0.5-cm radius, 5.7 h for a 1-cm radius, and 142.5 h for a 5-cm radius). If we consider the first wet–dry cycle (first wet period followed by first dry period), we can determine the time T^*₉₀ required to obtain an almost homogeneous distribution (concentration at the boundary equal to 90% of that at the center) of the solutes in the sphere after a wet period of duration *. For instance, by running the model with , we get .

View larger version (14K): [in this window] [in a new window]   Fig. 2 Single Spherical Aggregate (SSA) model output showing the fraction leached as a function of t* for continuous leaching

View larger version (23K): [in this window] [in a new window]   Fig. 3 Single Spherical Aggregate (SSA) model output showing the fraction leached as a function of t*L for various values of wet period duration (*). Note that * gives continuous leaching

View larger version (21K): [in this window] [in a new window]   Fig. 4 Single Spherical Aggregate (SSA) model output showing the fraction leached as a function of t*L for various wet period frequencies. Note that */T* gives continuous leaching

Comparison Between the Single Spherical Aggregate Model and Experimental Data
Column of Packed Porous Spheres
Figure 5 is typical of the results obtained when performing experiments on the column of packed porous spheres. It shows the fraction of solutes leached as a function of the total leaching time. The total duration of the wet periods was 14 min plus the time it took to drain the system (the contribution of the drained water to the cumulative fraction leached is indicated by the solid symbols). Draining took 1 min, so the value of was 15 min. The arrows indicate the dry periods (the duration of T is given by the numbers above arrows). We plotted the theoretical curves by calculating the fraction leached with the SSA model using the value of the diffusion coefficient of the spheres (0.032 cm² h^-1) and the value of the average radius of the spheres (0.53 cm). Curves for the 0.05 and 0.95 percentiles of the radius distribution (0.39 and 0.70 cm) are also included. Our measured data show a steeper increase in the fraction leached after resuming flow since the dry periods allowed solutes to redistribute within the spheres and increased the concentration gradient at the surface of the spheres. The increase in the fraction leached is less pronounced with consecutive leaching events, as it should be, since the concentration gradient at the surface of the spheres decreases as more and more solutes are leached out. We find that the magnitude of the increase obtained experimentally agrees very well with that predicted by the model when using the average radius. However, the measurements of the fraction leached do not coincide exactly with the theoretical curve calculated with the average radius. The range in actual sizes (0.35–0.73 cm radius) and the slightly nonspherical geometry of the aggregates may have contributed to this difference. However, these experimental results clearly demonstrate that changes in concentration gradients within spherical aggregates result in enhanced solute exchange, and that this process is well predicted by the SSA model. These results also show that our experimental technique is adequate to study the influence of variations in concentration gradients on solute exchange.

View larger version (34K): [in this window] [in a new window]   Fig. 5 Comparison between the Single Spherical Aggregate (SSA) model output and experimental data obtained with a column of packed spherical aggregates

View larger version (23K): [in this window] [in a new window]   Fig. 6 Experimentally determined breakthrough curve for the Hydrosol as compared with ideal miscible displacement. These experimental data show very early breakthrough and pronounced tailing, both indicators of preferential flow

View larger version (19K): [in this window] [in a new window]   Fig. 7 Comparison between the Single Spherical Aggregate (SSA) model output and experimental data for flow interrupted leaching experiments carried out on the Hydrosol core (Run 1)

View larger version (19K): [in this window] [in a new window]   Fig. 8 Comparison between the Single Spherical Aggregate (SSA) model output and experimental data for flow interrupted leaching experiments carried out on the Hydrosol core (Run 2)

View larger version (18K): [in this window] [in a new window]   Fig. 9 Comparison between experimental data for the flow interrupted leaching experiment (Run 1) and continuous leaching experiment (Run 3)

It is significant that for Runs 1 and 2, we get a steeper increase in the fraction leached after each dry period, and that this increase gets smaller with each subsequent leaching event, even though the field soil is much more complicated than the simple SSA model. Moreover, the cumulative fraction leached is greater for Run 1, which had flow interruptions imposed, than for Run 3, which experienced continuous leaching (Fig. 9). This shows that the imposition of dry periods in Run 1 has led to an increase in the fraction leached, as was suggested by our theoretical model (Fig. 3 and 4), with the leaching being increased by up to 20% toward the end of the experiments. These results highlight the role that diffusion, and especially the variation of concentration gradients within the undrained region, play in this field soil. Furthermore, application of the SSA model to our experimental data yields a value for the equivalent aggregate radius of 1.8 cm for this Hydrosol.

	Discussion

TOP ABSTRACT INTRODUCTION Theory NOTES Materials and methods Results Discussion Conclusions Appendix REFERENCES

 
Water and solute transport in preferential flow paths is dealt with in a very simple way in the SSA model, where preferential flow paths contain constant concentration of solutes and fill and drain instantaneously. This is clearly not the case when dealing with columns of porous material, and we evaluated the implications of these simplifications by comparing the SSA model to a numerical model that calculates the fraction leached out of a column of packed porous spheres with the same radius a and diffusion coefficient D_a (see Nkeddi-Kizza et al., 1982 for a detailed description of the column model). We compared the column model with the SSA model without dry periods (continuous leaching). We found that both models yielded almost identical results when preferential flow paths occupy a large fraction of the column volume (more precisely, when the water content in the preferential flow paths is 15% of the total water content), and when pore water velocities are high (10LD_a/a², where L is the length of the column). This suggests that for our columns, the processes controlling solute transport at the column scale would not influence greatly the exchange of solutes with the aggregates. To assess the influence of variations in concentration gradients, it is probably not necessary to use more complicated models involving many parameters, and the SSA model should predict the fraction leached reasonably well.

As mentioned above, drainage of the columns was not instantaneous. It took 1 min for the spheres and 40 min for the Hydrosol. Drainage of the Hydrosol was performed under 25- to 30-cm suction at the lower boundary. Using the SSA model and the values of a for the two systems, we can calculate the duration T₉₀ of the dry period required to obtain an almost homogeneous solute distribution. We get for the spheres and for the Hydrosol. Since the duration of drainage was much less than that of solute redistribution, the processes taking place during drainage should not have impacted greatly on the comparison between the SSA model and experimental data.

The value of the equivalent aggregate radius is an index that quantifies the importance of diffusion processes within a soil column rather than an accurate description of the size of the actual aggregates. The model was developed using a simplified representation that was later imposed on much more complex systems. First, we assumed a definite boundary between the aggregates and the preferential flow paths, which in reality would be diffuse and difficult to define. We also assumed that the aggregates were spherical and had the same radius, which is obviously not the case in a field soil. However, van Genuchten (1985) developed a method to extend the two-region modeling approach with spherical aggregates to more general conditions involving aggregates of arbitrary geometry. Since he showed that it was possible to transform an aggregate of given shape and size into an equivalent sphere with similar diffusion characteristics to the original aggregate, we chose the spherical geometry which had the advantage of introducing a single parameter, the radius a. This parameter provides an indication of the distance along which solutes have to diffuse before they are exchanged and flushed out of the soil column. It is a "lumped" parameter, which also accounts for other phenomena that can occur in soils and that are not dealt with explicitly in the simplified model (e.g., adsorption of solutes).

The value of the radius a was obtained by fitting the model to continuous and intermittent leaching experiments. Though continuous leaching experiments can give a value for the effective radius, they do not demonstrate the effects of variation in concentration gradients. Only intermittent leaching experiments give information about the mechanism taking place within the column. Therefore, there is a need to conduct more experiments on a wider range of soils to establish whether continuous leaching experiments would be sufficient to obtain a reliable value of a, which would enable accurate prediction of solute transport under alternating boundary conditions.

The SSA model gives the fraction leached as a function of one variable only, the dimensionless time . Therefore, when the effective radius a is known, the time scales controlling diffusion in a soil (e.g., ₉₀, T₉₀) can be calculated. If experiments conducted on a field soil compare well with the model (i.e., steeper increase in the fraction leached after a dry period), this suggests that diffusion is significant and that the value of the equivalent radius of the aggregates defines the duration of the wet and dry periods that would lead to efficient solute exchange. For instance, saturating the aggregates with fertilizers, so as to make them available for plant uptake, would be better achieved by applying the fertilizers in a succession of short irrigation events rather than in a single long event. From another point of view, chemicals such as salt already present in this field soil would be leached more efficiently by a succession of short leaching events than by one long event. Similarly, frequent short rain events would be more likely to produce pollution of the groundwater than one long rain event.

Our experimental results showed the fraction of solutes leached out of a field soil was not a linear function of the total time during which leaching occurred, since it also depended on the way leaching occurred (i.e., on the number and duration of the leaching events). This suggests the need for re-examination of solute transport models based on the assumption that there is a linear relationship between the solute input (e.g., solutes added to the surface of a soil column) and the solute output (e.g., solutes moving out of a soil column). For instance, Jury (1982) proposed to transform the input into an output by a stochastic function of time and net amount of water applied at the surface of the column. Our model shows that the output will not only depend on the net amount of water applied, but also on the duration of wet and dry periods. As early as 1965, Miller et al. (1965) found that intermittently ponding the soil led to most efficient leaching. The SSA model could perhaps provide some theoretical background to interpret these experimental results.

Experimental results obtained in this work expose limitations to solute transport modelling by those two-domain models that implicitly assume that concentration gradients are negligible. If in a field situation, the preferential flow paths drain and concentration gradients change within the undrained region, the steeper increase in the fraction leached after a dry period would not be predicted by such models. Under the dry boundary conditions of our experiments, the average concentration in the aggregates theoretically remained constant (since no exchange with the flow paths took place), so such models would not predict any change in the fraction leached upon resuming flow. Models that do not include intra-aggregate diffusion cannot predict the influence on solute transport of flow interruption with drainage of the main flow paths, when only the concentrations in the aggregates equilibrate, but they can predict an influence of flow interruption without drainage, when both the average concentrations in the aggregates and in the flow paths equilibrate as can occur during specific experimental conditions in the laboratory. However, in field situations it is likely that drainage of the main flow paths would take place and these models would fail to predict the more efficient leaching that our experiments have shown.

	Conclusions

TOP ABSTRACT INTRODUCTION Theory NOTES Materials and methods Results Discussion Conclusions Appendix REFERENCES

 
We developed a simple mathematical model to assess the impact of concentration gradients within aggregates, which are commonly ignored, on solute transport under alternating wet and dry periods. The model shows that when a single spherical aggregate is exposed to a series of wet and dry periods, concentration gradients even out during the dry periods so that upon reapplying a wet period, solute exchange is enhanced. Intermittent leaching experiments conducted on a field soil core showed that alternating wet and dry periods led to more efficient leaching than continuous leaching, with the leaching being increased by up to 20% for this soil. We used the SSA model to describe the influence of the variations in concentration gradients on the efficiency of leaching, and the model predictions were consistent with the experimental data, given an equivalent aggregate radius of 1.8 cm for the soil. This parameter, a diffusion distance, quantifies the time scales that characterize diffusion in soils. It is a "lumped" parameter, which also accounts for other phenomena that can occur in soils and that are not taken into account in the simplified SSA model (e.g., adsorption). Despite its simplicity, the SSA model gave a good description of the influence of concentration gradients in one field soil, which suggests that further testing on a wider range of soils to determine its applicability is warranted. We believe being able to determine and rank effective diffusion distances in field soils will enable development of better soil specific management strategies for soil applied chemicals. Benefits could include improved soil remediation techniques, plant nutrient availability, prediction of groundwater pollution, and improved soil salinity management through more efficient leaching.Gerke van Genuchten 1993

	ACKNOWLEDGMENTS

 
The authors would like to thank Randel Haverkamp for helpful discussion, and Eva Ford, Chris Goding, Ron Russo (CSIRO Land and Water) for their technical assistance. This work was supported by CSIRO Land and Water and the James Cook University Collaborative Grants program.

	NOTES

TOP ABSTRACT INTRODUCTION Theory NOTES Materials and methods Results Discussion Conclusions Appendix REFERENCES

 
¹ See the appendix for a complete list of variables and their definitions.

Received for publication February 18, 1998.

	Appendix

TOP ABSTRACT INTRODUCTION Theory NOTES Materials and methods Results Discussion Conclusions Appendix REFERENCES

 
aradius of spherical aggregate, cmb_n,mcoefficient in the SSA modelCsolute concentration, mol L^-1C*dimensionless solute concentrationC^*_jdimensionless solute concentration during cycle j in the SSA modelC_iinitial solute concentration, mol L^-1C_sconcentration at the surface of the aggregate during a wet period, mol L^-1[C(t)]average concentration in a sphere, mol L^-1C_wconcentration of the water when determining a diffusion coefficient, mol L^-1D_adiffusion coefficient, cm² h^-1D_oionic diffusion coefficient in free water, cm² h^-1f^Wet_jdistribution of the dimensionless concentration at the beginning of the wet period for cycle j in the SSA modelF_Lfraction leachedg^Dry_jdistribution of the dimensionless concentration at the beginning of the dry period for cycle j in the SSA modelqradial flux of solutes, mol cm^-2 h^-1q*dimensionless radial fluxq^*_jdimensionless radial flux during cycle j in the SSA modelrradius, cmr*dimensionless radiusr'variable of integrationttime, ht*dimensionless timet^*_Ltotal dimensionless leaching timeTduration of dry period, hT*dimensionless duration of dry periodT₉₀duration of the dry period required to obtain an almost homogeneous solute distribution in the aggregates (concentration at the boundary equal to 90% of that at the center), hT^*₉₀dimensionless duration of the dry period required to obtain an almost required to obtain an almost homogeneous solute distribution in the aggregates (concentration at the boundary equal to 90% of that at the center)V_svolume of a sphere, cm³V_wvolume of water in which a sphere is plunged to determine its diffusion coefficient, cm³V_cvolume of soil core, cm³V_pvolume occupied by the preferential flow paths, cm³variable of integrationduration of wet period, htortuosity factor_nnon-zero roots of (a)cot(a) = 1^*_nnon-zero roots of (*)cot(*) = 1ß_ncoefficient in the SSA model_j,ncoefficient in the SSA modeldispersivity of the medium, (cm² h^-1)/(cm h^-1)ⁿnempirical constantpore water velocity, cm h^-1_j,ncoefficient in the SSA model_ssaturated water content of the aggregates, cm³ cm^-3_csaturated water content of the soil core, cm³ cm^-3duration of wet period, h*dimensionless duration of wet period₉₀duration of the wet period required to leach 90% of solutes, h^*₉₀dimensionless duration of the wet period required to leach 90% of solutes

	REFERENCES

TOP ABSTRACT INTRODUCTION Theory NOTES Materials and methods Results Discussion Conclusions Appendix REFERENCES

 

• Beven K., Germann P. Macropores and water flow in soils. Water Resour. Res. 1982;18:1311-1325.
• Bouma J.B. Influence of soil macroporosity on environmental quality. Adv. Agron. 1991;46:1-37.
• Brusseau M.L., Hu Q., Srivastava R. Using flow interruption to identify factors causing nonideal contaminant transport. J. Contam. Hydrol. 1997;24:205-219.
• Carslaw H.S., Jaeger J.C. Conduction of heat in solids. Oxford: Oxford Clarendon Press, 1959.
• Coats K.H., Smith B.D. Dead-end pore volume and dispersion in porous media. Soc. Pet. Eng. J. 1964;4:73-84.
• Gerke H.H., van Genuchten M.Th. A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media. Water Resour. Res. 1993;29:305-319.
• Helferich F.G. Ion exchange. Hightstown, NJ: McGraw Hill, 1962.
• Isbell R.F. The Australian soil classification. Melbourne: CSIRO Publ, 1996.
• Jury W.A. Simulation of solute transport using a transfer function model. Water Resour. Res. 1982;18:363-368.
• Koch S., Fluhler H. Non-reactive solute transport with micropore diffusion in aggregated porous media determined by a flow-interruption method. J. Contam. Hydrol. 1993;14:39-54.
• McCoy, E.L., C.W. Boast, and R.C. Stehouver. 1994. Macropore hydraulics: taking a sledgehammer to classical theory. p. 303–348. In Adv. Soil. Sci.: Soil Processes and Water Quality. Lewis Publ., Boca Raton, FL.
• McKenzie N.J., Jacquier D.W. Procedures for field sampling and laboratory measurements of saturated and unsaturated hydraulic conductivity on large soil cores. CSIRO Division of Soils Divisional Report no. 125. Townsville, Australia: CSIRO, 1995.
• Miller R.J., Biggar J.W., Nielsen D.R. Chloride displacement in Panoche clay loam in relation to water movement and distribution. Water Resour. Res. 1965;1:63-73.
• Millington R.J., Quirk J.P. Permeability of porous solids. Trans. Faraday Soc. 1961;57:1200-1207.
• Nkeddi-Kizza P., Rao P.S.C., Jessup R.E., Davidson J.M. Ion exchange and diffusive mass transfer during miscible displacement through an aggregated Oxisol. Soil Sci. Soc. Am. J. 1982;46:471-476.[Abstract/Free Full Text]
• Rao P.S.C., Jessup R.E., Rolston D.E., Davidson J.M., Kilcrease D.P. Experimental and mathematical description of nonadsorbed solute transfer by diffusion in spherical aggregates. Soil Sci. Soc. Am. J. 1980;44:684-688 a.[Abstract/Free Full Text]
• Rao P.S.C., Rolston D.E., Jessup R.E., Davidson J.M. Solute transport in aggregated porous media: theoretical and experimental evaluation. Soil Sci. Soc. Am. J. 1980;44:1139-1146 b.[Abstract/Free Full Text]
• Rasmuson A., Neretnieks I. Exact solution of a model for diffusion in particles and longitudinal dispersion in packed beds. A.I.Ch.E. J. 1980;26:686-690.
• Reedy O.C., Jardine P.M., Wilson G.V., Selim H.M. Quantifying the diffusive mass transfer of non-reactive solutes in columns of fractured saprolite using flow interruption. Soil Sci. Soc. Am. J. 1996;60:1376-1384.[Abstract/Free Full Text]
• van Genuchten M.Th. A general approach for modelling solute transport in structured soils. Int. Assoc. Hydrogeologists Memoires 1985;17:513-526.
• van Genuchten M.Th., Wierenga P.J. Mass transfer studies in sorbing porous media. I. Analytical solutions. Soil Sci. Soc. Am. J. 1976;40:473-480.[Abstract/Free Full Text]
• Weast, R.C. (ed.) 1978. Handbook of chemistry and physics. 58th ed. CRC Press, Boca Raton, FL.
• White R.E. The influence of macropores on the transport of dissolved and suspended matter through soil. Adv. Soil Sci. 1985;3:95-120.

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