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Published in Soil Sci. Soc. Am. J. 67:1635-1646 (2003).
© 2003 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

DIVISION S-1—SOIL PHYSICS

Evaluation of the Fluoride Retardation Factor in Unsaturated and Undisturbed Soil Columns

Louis Bégin, Josée Fortin* and Jean Caron

Département des Sols et de Génie Agroalimentaire, FSAA, Université Laval, Québec, QC, Canada, G1K 7P4

* Corresponding author (josee.fortin{at}sga.ulaval.ca).


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 THEORY
 RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 
Fluorides deposited on the soil surface near aluminum smelters represent a risk for ground water contamination. This study was conducted to evaluate F retention in soils sampled near an aluminum smelter. The F retardation factor (R) was evaluated at different depths in four coarse-textured soils by percolating a Br and F solution under steady-state conditions through 26 unsaturated and undisturbed soil columns. The convective-dispersive equation (CDE) and convective-lognormal transfer function (CLT) models were used to evaluate R, using Br and F breakthrough curves (BTCs) and F accumulation profiles evaluated with oxalate-extractable F (Fox). Following percolation of 4.0 to 13.7 pore volumes of F solution through the soil columns, F BTCs were obtained in 5 out of 26 columns. In the other columns, all F remained in the soil profiles, indicating higher F retention. When R was evaluated using F accumulation profiles, the CDE-evaluated retardation factor (RCDE) was consistently higher than the one evaluated with the CLT (RCLT), by as much as 111%. This was explained by a difference in the models' behavior near the soil surface. The retardation factor varied among soils and depths by a 20-fold factor, from 4.4 to 91. The highest retardation factors were obtained in slightly acid and neutral soils. The retardation factor was lower in strongly acid and alkaline soils. The large range of R values obtained and its influence on the velocity of F movement in the soil show that R is one of the critical factors controlling the risk of ground water contamination by F.

Abbreviations: Alox, oxalate-extractable Al • BTC, breakthrough curve • CDE, convective-dispersive equation • CDTA, trans-1,2-diaminocyclohexanetetraacetic acid • CLT, convective lognormal transfer function model • CV, coefficient of variation • Feox, oxalate-extractable Fe • Fox, oxalate-extractable F • Ftot, total F • pdf, probability density function • R, retardation factor • RCDE, CDE-evaluated retardation factor • RCLT, CLT-evaluated retardation factor • TISAB, total ionic strength adjustment buffer • Vfeff, effective mean flux concentration velocity • Vreff, effective mean resident velocity • {theta}, volumetric water content • [{theta}], effective water content • {phi}, mobile water fraction


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 THEORY
 RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 
FLUORIDES emitted by industrial sources are brought to the soil surface by fallout of particulate fluorides and through absorption of gaseous fluorides in rain and snow (Hluchan et al., 1964 [as cited by Groth, 1975]). Applications of phosphate fertilizers, sewage sludges, and some pesticides also bring fluorides to the soil (Kabata-Pendias and Pendias, 1992, p. 245). These fluorides may represent a risk for ground water contamination (Wenzel and Blum, 1992). In drinking water, the F concentration should not exceed 1.5 mg L-1 (Health Canada, 1996), to avoid risks of fluorosis.

It is known that fluorides are strongly retained in a variety of soils, as was demonstrated by several authors using sorption isotherms (Flühler et al., 1982; Omueti and Jones, 1977; Peek and Volk, 1985). Some authors have studied F retention in soil columns in the laboratory or in soil profiles in the field and also concluded that F was strongly retained (MacIntire et al., 1955; Murray, 1983; Tracy et al., 1984). In these studies, however, F retention was quantified as the proportion of added F retained in a volume of soil after F and water application at the soil surface. These proportions of retained F are indicative of the intensity of F retention but are specific to the conditions used, that is, the pattern of F application in time and the amount of water applied.

A more convenient approach to evaluate solute retention in soil columns is to measure the retardation factor (Baetslé, 1967), which compares the velocity of a solute to that of water. Retardation factors can then be used in models of solute transport through soil. Kau et al. (1999) measured F retardation factors in kaolin and bentonite clay plugs. However, it was done in the absence of a convective water flow (i.e., the solute flux was due to diffusion only) and under saturated conditions. To our knowledge, F retardation factors have never been measured in soil columns.

Different transport models are available to describe solute transport in soils. The CDE (Nielsen and Biggar, 1962) and the CLT (Jury, 1982) are the most commonly used. The validity of one of these models is often postulated in solute transport experiments, without further examination of the impact of this choice on the results obtained. The quality of fit of these models to observed flux concentrations at a given depth in the soil is equivalent, as they can be closely fitted to each other. However, at depths different from that of calibration, the two models predict different flux concentrations, the difference residing in the evolution with depth of the predicted travel time variance (Jury and Roth, 1990, p. 42). The resident concentrations predicted by the two models also differ. The validity of a specific model cannot be assumed a priori, since the choice of the model may possibly affect the retardation factor obtained.

In this study, F retardation factors were evaluated in undisturbed soil columns sampled near an aluminum smelter, under steady-state unsaturated conditions. Both the CDE and CLT transport models were used to determine the retardation factors.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
THEORY
 RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 
Soil Location and Sampling
Soil columns from four sites located near an aluminum smelter in operation for 5 yr were used. Site A is located 0.8 km south of the smelter and is made of a calcareous sand used as filling material. Sites B and C are 60 m away from each other, 0.6 km northeast of the smelter. Site B is a Cryaquod covered with grass vegetation whereas Site C is a Humicryod under forest. Site D is a Cryaquod covered with grass vegetation, located 1.6 km southwest of the smelter. The reference point for distances corresponds to the point of maximum F deposition on the site of the smelter. This point was determined from the measurements made at 17 sampling points on the site of the smelter (L. Bégin, unpublished data, 2001).

Three soil columns were sampled at each site by driving 15-cm i.d. plastic tubes with a beveled extremity into the soil with a sledgehammer to depths of 50, 40, and 60 cm respectively for Sites B, C, and D. At Sites B and D, there was no apparent sign of compaction after the column had been driven into the soil. At Site C, about 1-cm compaction was observed in the first 20 cm. The tubes were carefully manually dug out and brought back to the laboratory, where they were cut into 20-cm long sections. For the columns sampled at Site B, the two top sections were 20 cm deep and the bottom section was 10 cm deep. For Site A, repacked soil columns were used, because direct column sampling was impossible due to the large quantity of rocks present in the soil. The soil was repacked to a bulk density similar to the one encountered in situ (1.76 Mg m-3). To repack the columns, successive amounts of 622 g of soil material (2 cm soil) were added on top of the columns. Following each soil addition, the soil surface was tapped with a 15-cm o.d. piston to bring the soil to the appropriate volume. A total of 26 columns were sampled and prepared for the soil column experiments (nine soil layers, three replicates except for Site B (40–50 cm) where two replicates were used) (Table 1).


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  		Table 1. Physical and chemical properties of the soils used in the determination of the F retardation factor.

 
At each site, adjacent to the sampled columns location, two 2-cm i.d. soil cores were sampled to a depth of 90 cm. The first core was cut in 5-cm long sections in which the F concentration was measured to evaluate the initial F concentration profile. The second core was cut in 20-cm long sections and was used to determine the physical and chemical properties of the soils and to verify the nonreactivity of the Br tracer. Texture was determined by the hydrometer method (Day, 1965) and soil organic C following Walkley and Black (1934). The pH was measured using a 1:1 soil/water ratio and an Orion Model 8165 combination pH electrode (Orion Research, Boston, MA). Oxalate-extractable Al (Alox) and Fe (Feox) were determined following McKeague and Day (1966) and carbonates using an approximate gravimetric method (Goh et al., 1993, p. 179–180). Soil bulk density was measured on the soil columns at the end of the experiment. Porosity was estimated using the soil bulk density and the particle density estimated with the formula given in De Kreij and De Bes (1989). Soil properties are presented in Table 1.

Bromide Retention
Bromide is commonly used as a tracer and has become widely regarded as virtually nonreactive (Brooks et al., 1998). However, Br anion exclusion and retardation have already been observed in different soils and minerals (Brooks et al., 1998; Ishiguro et al., 1992; Melamed et al., 1994). Consequently, the nonreactivity of Br must be verified for the soils used in this experiment. To do so, 5-g samples of air-dried soil from each soil layer, obtained from the second soil core sampled at each site, were transferred into 50-mL polypropylene tubes and 10 mL of a KBr solution containing 30 mg Br L-1 and 0.01 M CaCl2 was added. Two replications were done in separate tubes for each soil layer. In a third tube, 5 g of soil was mixed with 10 mL of a 0.01 M CaCl2 solution. The tubes were agitated at 200 rpm for 16 h on a rotative shaker and then centrifuged for 10 min at 1500 x g. The Br concentration was determined in the supernatant as described below. For each soil layer, the concentration measured in the tube without added Br was subtracted from the mean Br concentration measured in the supernatant of the two soils that were in contact with the Br solution. After this correction, the amount of Br sorbed or repulsed by the soil was determined by difference between initial and final concentrations in solution. Separate subsamples of air-dried soil were dried at 105°C for 24 h to evaluate the initial soil water content. The initial mass of soil and total volume of liquid was corrected accordingly. The distribution coefficient (Kd) (Hamaker and Thompson, 1972) was calculated and used, together with the volumetric water content ({theta}) and soil bulk density ({rho}b), to evaluate the Br retardation factor in each soil layer (Jury and Roth, 1990):

[1]

Soil Column Experiments
Column Setup
The soil column system used in the present experiment is shown in Fig. 1 . It consisted of a glass bead tension table (Topp and Zebchuk, 1979), onto which the soil column was placed. An acrylic tension infiltrometer (Reynolds and Elrick, 1991) was placed on top of the column to supply water and solution at a constant rate. The infiltrometer was held by a support to avoid soil compaction during the experiment. Paraffin films were disposed at the infiltrometer-column and column-table junctions to avoid evaporation.



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  		Fig. 1. Column experiment setup.

 
Flow Regime
The water potential of the infiltrometers and tension tables was adjusted to obtain the desired water flux, which was set to 0.9 cm d-1 in the present study. At the beginning of the experiment, water was supplied to the columns until steady state was reached. Due to the high organic matter content of the 0- to 20-cm layer of Site C, which is responsible for a low density and a high porosity, it was necessary in this case to apply a pressure on top of the soil, using the infiltrometer, to initiate water flow. As soon as a sufficient flow was reached, the pressure was released by attaching the infiltrometer to the support. This operation resulted in a soil compaction of about 2 cm. Once steady-state flow was reached in the columns, water in the infiltrometers was replaced with a solution containing 100 mg L-1 of F as KF and 30 mg L-1 of Br as KBr. Then, the percolation experiment started at the same steady-state flux of 0.9 cm d-1. The water potential of the infiltrometers and tension tables was adjusted when necessary to maintain the flux and was always kept negative to avoid saturated conditions. The water potential varied between -0.2 and -3 kPa and its mean value was -1 kPa. The volumetric water content of each column was measured every 5 d with two time domain reflectometry (TDR) probes inserted horizontally at 5 and 15 cm from the top of the column. One probe inserted at the center of the column was used in the 10-cm columns. The experiment was conducted at room temperature (23 ± 2°C).

Bromide and Fluoride Breakthrough Curves
Over a period of about 50 d, a total of 7.0 to 7.8 L of solution was applied to each column. Depending on column length and water content, this volume corresponded to between 4.0 and 13.7 pore volumes of water. The column effluent was collected at the bottom of the tension table. It was sampled twice a day for the first 2 wk and then once a day for the remaining of the experiment. The volume of effluent was determined by gravimetry, assuming a density of 1 Mg m-3. A selection of samples was analyzed for F- and Br- concentrations to determine their BTCs.

The F concentration in the effluent samples was determined using a Fisher Accumet Selective Ion Analyzer Model 750 (Fisher Scientific Ltd., Nepean, ON) equipped with an Orion Model 96-09 combination F electrode. Samples were mixed with total ionic strength adjustment buffer (TISAB) in a 1:1 proportion before determination. Total ionic strength adjustment buffer solution contained 1 M glacial acetic acid, 1 M NaCl, and 4 g L-1 trans-1,2-diaminocyclohexanetetraacetic acid (CDTA) and was prepared according to Menzies et al. (1993). Bromide was determined using a Dionex 4000i ion chromatograph (Dionex Co., Sunnyvale, CA) with a CDM-2 conductivity detector. Samples and eluents were lead via a Dionex AG4A-SC anion guard column through a Dionex AS4A-SC separator column (Dionex Co., Sunnyvale, CA) and an AMMS-1 anion micromembrane suppressor using a GPM-2 pump module. Sample introduction was automated with a Dionex ASM-3 sampler (Dionex Co., Sunnyvale, CA). A 50-µL injection loop was used. The eluent was a 1.8 mM Na2CO3/1.7 mM NaHCO3 solution, pumped at a constant flow of 2.0 mL min-1. The regenerant was 13.5 mM H2SO4, pumped at a constant flow of 3 mL min-1. Total run time was 7 min.

Fluoride Accumulation Profiles
At the end of the experiment, the columns were cut in 2-cm deep sections to determine the F concentration profile. A few columns were sampled in 1-cm increments to achieve a better resolution of the profile. Soil samples were air-dried and sieved to 2 mm. They were weighed before and after drying to determine the volumetric water content in the column at the end of the experiment. After thorough mixing, a subsample was taken from each sieved sample and ground to pass a 0.25-mm sieve. Oxalate-extractable F (Bégin and Fortin, 2003) was determined on each sample and combined with soil density (particles <2 mm) to obtain the final F resident concentration profile in the columns (solute mass per soil bulk volume). Oxalate-extractable F concentrations were also determined on the samples obtained from the core samples taken in the field beside the soil columns, to evaluate the initial F resident concentration profile. Fluoride accumulation was calculated as the difference between the final and initial concentration profiles. In this study, Fox was preferred to total F (Ftot) to evaluate the F resident concentration, because the high and variable initial Ftot concentrations induced an important background noise in the data (Bégin and Fortin, 2003).

Tension Table Breakthrough Curves
To be able to take into account the effect of the tension table on Br and F transport in the column-table system, a solution-filled tension infiltrometer was placed directly at the surface of a tension table and the breakthrough curve of each solute was measured at the bottom of the table. This was replicated on two different tension tables. The water flux was maintained equal to that used in the column experiment (0.9 cm d-1).


   THEORY
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 THEORY
RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 
CDE and CLT Models
The one-dimensional convective-dispersive solute transport through a homogenous medium, with linear and reversible equilibrium sorption and without degradation of the solute, under steady-state flow can be described by the CDE:

[2]
where Cr*1 is the solute normalized resident concentration in the liquid phase , Cr1 is the resident concentration in the liquid phase at distance x and time t, C0 is the input concentration, D is the effective diffusion-dispersion coefficient, v is the average pore-water velocity, and R is the retardation factor. The retardation factor for Br was fixed for each soil layer to the value calculated with the batch experiment. With the high F and Br concentrations used in this experiment, the initial resident concentration can be considered negligible for both solutes, so the system was considered initially free of solute:

[3]

If the assumption is made that molecular diffusion and dispersion in the fore section (x < 0) can be ignored, that is, if the tension infiltrometer is considered as a perfectly mixed reservoir, the following flux-type inlet boundary condition can be defined (van Genuchten and Parker, 1984):

[4]
where C*0 = 1 is the normalized input concentration. Strictly, this inlet boundary condition would apply only for a system in which the entrance reservoir is not physically connected to the column. However, Schwartz et al. (1999) compared the effect of dispensing a solution using dispensing tips or a platen-type inlet apparatus and observed no significant alteration of the observed effluent concentrations and fitted parameters. Consequently, the use of that boundary condition is an acceptable approximation for the system used. If we assume that solute distribution inside the finite column is unaffected by the presence of the tension table, thus considering the column to be part of an effectively semi-infinite system, we may complete the system of equation with:

[5]

The adequate analytical solution of Eq. [2] to [5], expressed in terms of flux concentrations and cumulative drainage (I) is (van Genuchten and Parker, 1984; Lapidus and Amundson, 1952):

[6]
where Cf*(x,I) = Cf (C,I)/Co is the normalized flux concentration in the column at depth x and cumulative drainage I (cm water), Cf (x,I) is the flux concentration, and v' (cm soil cm-1 water) and D' (cm2 soil cm-1 water) are the solute velocity and diffusion-dispersion coefficient expressed in terms of cumulative drainage. Equation [6] can be used to calculate flux concentrations inside and at the exit boundary of the column. However, in this experiment, flux concentrations were measured at the exit of the tension table. The travel of solute molecules through the tension table induces a delay in their appearance at the exit of the column-table system and results in increased dispersion. Thus, transport parameters estimated using the concentrations measured at the bottom of the tension table and Eq. [6], neglecting the effect of the tension table, would be in error (James and Rubin, 1972). For example, in this study the dispersion in the tension table was responsible, in some cases, for 20% of the total travel time variance observed. The effect of the tension table can be accounted for by considering the column-table system as a two-layered soil system. In this case, concentrations at the exit of the tension table can be evaluated with a transfer function (Jury et al., 1986), using the tension table input concentrations and the probability density function (pdf) of the travel times through the table. To represent solute transport through the tension table, the travel time pdf [ff (L2, I)] of the CDE model was used (Jury and Sposito, 1985):

[7]
where L2 is the depth of the tension table and D'2 and v'2 are its transport parameters. The choice of a convective-dispersive pdf for the table is arbitrary. However, this choice has no impact on predicted concentrations, as predictions are always made at calibration depth, which was arbitrarily set to unit length (L2 = 1 cm). Mass conservation implies that flux concentrations at the inlet of the tension table be equal to flux concentrations at the outlet of the soil column. So, the concentrations at the exit of the table were evaluated by convoluting the outflow concentrations of the soil column with the pdf of the tension table:

[8]
where L1 is the depth of the soil column. When the CDE model is used in both the column and table, Eq. [8] is strictly equivalent to the solution proposed by James and Rubin (1972). Nevertheless, Eq. [8] does not require, to be valid, that the CDE model be used in the column or tension table. The only assumption needed for Eq. [8] to be valid is that the respective travel times in the soil column and tension table are uncorrelated. This assumption is verified by seeing that the travel time in the column depends on the particular flow path used by a solute molecule to travel through the soil column, whereas the travel time in the table is influenced primarily by the distance between the center of the table, where the solute drains, and the solute point of entry at its surface. This is analogous to the case presented in Utermann et al. (1990) for the flow of solute from the soil surface to a tile drain.

The CDE parameters of the tension table were obtained by fitting Eq. [6] to the breakthrough curves obtained with tension infiltrometers placed directly on tension tables. The transport parameters v' and D' in the soil column were adjusted so as to minimize the sum of squares of differences between Br concentrations calculated with Eq. [8] and concentrations measured at the exit of the tension table.

The effective water content in the soil column, [{theta}], was calculated from the CDE velocity parameter: [{theta}] = v'-1. The [{theta}] represents the soil water that is involved in transport in the soil column. The mobile water fraction, {phi}, was calculated by relating the volumetric water content to the effective water content, as follows: {phi} = [{theta}] {theta}-1.

The CLT model analytical solution corresponding to Eq. [6] is (Ellsworth et al., 1996):

[9]
where I was divided by R to account for linear and reversible equilibrium sorption, Iu is a unit cumulative drainage (to provide that the logarithmic argument is unitless), µ and {sigma} are the CLT model parameters and {lambda} is the calibration depth. µ and {sigma} were determined for Br by substituting Eq. [9] in Eq. [8] and using the same procedure as for the determination of the CDE parameters.

Fluoride Retardation Factor
When the F retention in the soil is low, the F reaches the bottom of the column during the experiment. In this case, the F BTC can be measured to evaluate the retardation factor. Assuming that Br and F move through the same transport volume when in the dissolved phase, the CDE and CLT parameters, except R, were considered the same for both solutes. Fluorides v' and D' (µ and {sigma} for the CLT) were set to the values obtained for Br in the same column. The retardation factor was adjusted so as to minimize the sum of squares of differences between measured and predicted F flux concentrations at the bottom of the tension table (Eq. [8]).

When the retention is higher, all F remains in the soil column. In this case, the F resident concentration profile was used to determine the retardation factor. The analytical solution of Eq. [2] to [5], expressed in terms of liquid resident concentrations and cumulative drainage I is (Lindstrom et al., 1967; van Genuchten and Parker, 1984):

[10]
where Cr1(x, I) is the liquid phase resident concentration at depth x and cumulative drainage I. The total resident concentration Cr1 in the liquid and sorbed phases is given by:

[11]

As the measured concentrations represent the mean concentration of a 1- or 2-cm layer and because the resident concentration is not a linear function of depth, measured concentrations (final F - initial F) were compared with the mean predicted concentration of a soil layer :

[12]
where ai and bi are the depths corresponding to the top and bottom limits of layer i. Also, because the F recovery with Fox is incomplete (Bégin and Fortin, 2003), the measured concentrations need to be corrected. To do so, F recovery ({alpha}) was calculated in each column:

[13]
where Vi and Crti are the volume and total resident concentration (final F - initial F) in layer i, V0 and C0 are the volume and concentration of the solution applied to the column, and n is the number of layers in the column. Assuming that F recovery was the same for every sample in a soil column, the measured resident concentrations were corrected by dividing them by {alpha}. Here again, v' and D' for F were equal to those of Br. The retardation factor was adjusted so as to minimize the sum of squares of differences between measured and predicted resident concentrations (Eq. [12]). These retardation factors, calculated using the CDE model, are referred in the text as RCDE.

The CLT model analytical solution corresponding to Eq. [10] is (Vanderborght et al., 1997):

[14]

RCLT was determined by substituting Eq. [14] in Eq. [11] and using the same procedure as for the determination of RCDE. Calculations were done using Mathcad (version 4.0) (Mathsoft, Inc., Cambridge, MA). Maple V Release 4 (version 4.00c) (Waterloo Maple Inc., Waterloo, ON) was used in some cases to verify the results obtained with Mathcad, because the complementary error function (erfc) is miscalculated by Mathcad when its argument is too large.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 THEORY
 RESULTS AND DISCUSSION
CONCLUSION
 REFERENCES
 
Bromide Retention
The Br retardation factors obtained in the nine soil layers are presented in Table 2. There was little or no Br sorption or repulsion in Soils A, C, and D. However, Br was significantly retained in the three layers of Soil B, with retardation factors varying from 1.15 to 1.28. These results show that Br does not always behave as an ideal tracer in Spodosols. However, in this study, Br retardation was taken into account in the calculation of v' and D' (see the Theory section above), and thus in the calculation of the F retardation factors. Consequently, the evaluated F retardation factors were not biased because of Br retention.


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  		Table 2. Bromide retardation factor.

 
Tension Table Breakthrough Curves
The Br and F BTCs of one of the tension tables are presented in Fig. 2 , along with the adjusted CDE model. The CDE model adequately described the transfer of both solutes through the table. The two BTCs were almost identical, so the Br transport parameters were used in the travel time pdf for both solutes.



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  		Fig. 2. Bromide and F breakthrough curves obtained with a tension table. The solid and dashed lines represent the CDE model adjusted to the Br and F breakthrough curves, respectively.

 
Flow Regime
The mean water flux in each column ranged from 0.79 to 0.98 cm d-1, which is near the desired water flux (0.9 cm d-1). In most columns, the water content increased slightly during the experiment. The mean water content increase, as evaluated with the TDR probes, was of 0.01 cm3 water cm-3 soil. This represents a small increase compared with the relatively high water content observed in the columns (Table 3).


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  		Table 3. Water content ({theta}), effective water content ([{theta}]) and mobile water fraction ({phi}) in the soil columns. All values represent the mean value obtained with three columns, except for the Soil B (40–50 cm), where two columns were used.

 
Bromide Breakthrough Curves
Measured Br BTCs typical of each of the nine soil layers used in this experiment are presented in Fig. 3 , along with the CDE model adjusted to the data. Only the CDE model is presented because the CDE and CLT models were almost indistinguishable. A good agreement was obtained between the CDE and CLT models and the observed Br BTCs. The mobile water fraction, {phi}, varied from 0.72 to 0.92 in the nine soil layers studied (Table 3). Values below one indicate that part of the water in the soil columns was immobile. These values are of the same order of those reported in a steady-state experiment conducted with Br in unsaturated soil columns by Meyer-Windel et al. (1999).



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  		Fig. 3. Examples of Br (diamonds) and F (circles) breakthrough curves obtained in each soil layer. Three columns were used for each soil layer, except for Site B (40–50 cm), where two columns were used. The solid lines represent the CDE model adjusted to the Br and F breakthrough curves. The CLT model is not represented but is nearly indistinguishable from the CDE model. Two F breakthrough curves are presented for Site C (20–40 cm) to show the strong variation of F retention observed in different columns of that soil layer. No F was detected in the effluent of the columns of Sites A, B, and D.

 
The Péclet number (Pe = v'L/D', where L is the column depth) was calculated for each soil column (data not shown). A small Péclet number indicates a large dispersivity relative to the distance from the inlet to the sampling point. Opinions diverge about the adequacy of the semi-infinite boundary condition (Eq. [5]) for finite soil columns with small Péclet numbers. Van Genuchten and Parker (1984) recommend the use of the semi-infinite boundary condition for all Péclet numbers, while Parlange et al. (1985) recommend using it only for Péclet numbers greater than about four. In all the soil columns used in this experiment, the Péclet number ranged from 3.6 to 105, with only two values smaller than four. The use of the semi-infinite boundary condition was thus adequate for the columns used.

Fluoride Breakthrough Curves
In five out of six soil columns from Site C, the relatively low F retention resulted in the appearance of F at the outlet of the tension table during the experiment. In the other soil layers, all F remained in the soil and was thus not detected in the effluent solution. Some F BTCs and the CDE model adjusted to them are presented along with the Br BTCs in Fig. 3. The CLT model is again omitted from this figure, because of the similarity with the CDE model curves. A good fit of the CDE and CLT models to the F BTCs was obtained, even if v', D', µ, and {sigma} were calculated from the Br BTCs. This supports the assumption that F and Br moved through the same transport volume when in the dissolved phase.

Fluoride Accumulation Profiles
The initial Fox concentration profiles are presented in Table 4. The initial Fox concentration was <30 mg L-1 soil in all 5-cm soil layers, except in the 0- to 5-cm layer of Site B, where it reached 83.8 mg L-1 soil. The initial Fox concentrations varied with depth, especially in Sites B and C, but were small compared with the F accumulations obtained in the soil columns.


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  		Table 4. Initial oxalate-extractable F (Fox) concentration profiles in the soils.

 
Typical F accumulation profiles in each soil layer are presented in Fig. 4 , except for Site C (0–20 cm), for which all the F retardation factors were measured from the F BTCs. The accumulation profiles show varying degrees of F retention. In most cases, the major part of F remained in the first 5 cm of the soil profile, showing that F is strongly retained in these soils. However, in the soil columns from Site A, F migration reached about 15 cm. Fluoride migration was even more important in five out of six columns from Site C, where F was measured in the outflow (Fig.3).



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  		Fig. 4. Examples of F accumulation profiles in each soil layer. Three columns were used for each soil layer, except for Site B (40–50 cm), where two columns were used. Data points represent the increase in F total resident concentration. The vertical dotted line is at 0 mg F L-1 soil. The solid and dotted curves represent the CDE and CLT models adjusted to the accumulation profile, respectively.

 
The use of Fox to determine the F accumulation profiles resulted in a very low background noise. The concentration in the lower part of the profiles was very stable and near zero (Fig. 4). The mean F recovery obtained with the oxalate extraction for each soil layer is presented in Table 5. Except for the soil from Site A, F recovery was within the same range of values in all layers, ranging from 58 to 74%. Within a site, F recovery was little influenced by depth, which suggests that site-specific correction factors could be determined to evaluate F accumulation without bias using Fox. The lower recovery in the calcareous material of Site A has already been observed by Bégin and Fortin (2003).


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  		Table 5. Mean F recovery in the soil columns obtained with the oxalate-extractable F (Fox) method.

 
Fluoride Retardation Factors
CDE and CLT Models
The CDE and CLT models adjusted to the accumulation profiles are presented in Fig. 4. In these models, v', D', µ, and {sigma} were obtained from the Br BTCs and the only adjustable parameter was the retardation factor. In general, both models adequately fitted the observed F accumulation profiles. In some cases, however, the CDE model fitted the profiles more closely than the CLT.

The calculated retardation factors are presented in Table 6 for each soil column and model, along with the mean, standard error, and coefficient of variation (CV) for each layer and site. The retardation factors evaluated using the CDE model (RCDE) were generally higher than those obtained with the CLT (RCLT). The means of RCDE and RCLT were equal or nearly equal in only two layers, Site A (0–20 cm) and Site C (0–20 cm). In the seven other layers, RCDE was greater than RCLT by 23 to 111%. This is explained by the low depth reached by F in these columns and by a difference in the behavior of the models near the soil surface. The effective mean resident velocity of a solute obeying the CDE is greater near the surface than at greater depths. This is due to the surface boundary condition of the CDE, which does not allow the solute to diffuse upward. This breaks the symmetry of the diffusion process, so the solute moves downward faster than it would in an infinite medium (Jury and Roth, 1990, p. 55). The influence of the upper boundary condition is reduced progressively as the depth reached by the solute increases. On the contrary, Vreff is constant with depth for a solute obeying the CLT. So when the models are calibrated at a common depth of 10 or 20 cm, the CDE model predicts, above the depth of calibration, a faster migration of the solute, as evaluated by its first depth moment, than the CLT does. The consequence is that the CDE returns a greater retardation factor than the CLT when both models are fitted to an accumulation profile limited to a depth inferior to the depth of calibration. This explains why RCDE was greater than RCLT in most cases. In Site C (0–20 cm), there was no important difference between RCDE and RCLT because they were evaluated using flux concentrations instead of resident concentrations, and the effective mean flux concentration velocity is constant with depth and equal for the two models when they are fitted to observed flux concentrations at a given depth. In Site A (0–20 cm), the difference was also small, this time because of the greater depth reached by the solute in these columns and because of the smaller dispersivity of this soil (D'/v' = 0.30 cm, compared with 0.62 to 3.15 cm for the other soils), which reduces the effect of the surface boundary condition.


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  		Table 6. Fluoride retardation factors measured in soil columns, using the CDE and CLT models.

 
Variability of the Retardation Factor
It is not possible, from the data available, to determine which of the CDE, the CLT, or an intermediate model is appropriate in the soils used in this experiment. Consequently, it is not possible to determine which of the retardation factors obtained, RCDE or RCLT, are the most representative of the true retardation factor. The differences between RCDE and RCLT, although numerically important, are nevertheless relatively low compared with the high variability of the retardation factor among the studied soils. RCDE values varied from 4.4 in the 0- to 20-cm layer of Site C to 91 in the 40- to 60-cm layer of Site D, while RCLT values ranged from 4.4 to 61 in the same soil layers (Table 6).

The retardation factor was also variable among the columns of the same soil layer. In six out of nine layers, the retardation factor coefficient of variation (CV) was <=20% for both models (Table 6). In these cases, the precision in the evaluation of the retardation factor can be considered good. In the three other soil layers, the CV of the retardation factor was >30% for the CDE, indicating a greater variability of the retardation factor among the columns of the same layer or a reduced precision in its evaluation. With the CLT, the CV was higher than 30% in only one soil layer.

In the 20- to 40-cm layer of Site C, RCDE varied from 1.31 to 80 and RCLT from 1.31 to 32. In this soil layer, the important variability of R is explained by the important soil heterogeneity at this site. Although the model used assumes soil homogeneity, this assumption is obviously violated at this site. The soil at Site C is a Spodosol located in a forested zone, where the depth of soil horizons varies greatly in space. Because the columns were sampled regardless of the soil horizons' depth, the specific horizons present, and their respective proportions, varied from one column to another at this site. Observation of the soil profiles in the columns at the end of the experiment allowed to get a better insight into these variations. The 0- to 20-cm layer was made of organic material (75–100% of the columns depth). Columns I and II also included a part of the eluvial horizon, in contrast with Column III, which only contained organic material. However, the observed heterogeneity had little or no effect on the retardation factor in this layer, since the three values obtained are similar (Table 6). In the 20- to 40-cm layer, the impact of soil heterogeneity is obvious. In Columns I and II, 5 and 8 cm of the eluvial horizon were respectively present, followed by a horizon of high organic C accumulation. In Column III, a spodic horizon with a low level of organic C was present at the top of the column, which explains the higher retention observed, as F is known to accumulate in such horizons (Murray, 1983). Consequently, in the 20- to 40-cm layer of Site C, the high variability of R may be explained by the presence of different soil horizons.

The retardation factors evaluated with the CDE in the 0- to 20- and 20- to 40-cm layers of Site D also present important coefficients of variation, even if the soil at this site was visually much more homogenous than at Site C (Table 6). The CDE-evaluated retardation factors in the three layers of this site are the highest of the nine soil layers. Fluoride accumulation in these columns was almost limited to the top 4 cm and consequently to the two top samples. In this case, the calculated retardation factor depends mainly on the ratio of concentrations in the two top samples. Analytical errors in the measurement of Fox or inaccuracy in the sampling depths can result in increased errors in the evaluation of the retardation factor in these columns. Consequently, in the 0- to 20- and 20- to 40-cm layers of Site D, R variability is probably more attributable to the low resolution of the sampling scheme and to the low depth reached by F than to variations in soil properties.

Within a site, R varied with depth. At Site B, RCDE and RCLT reached their maximum value in the 20- to 40-cm layer. At Site D, both RCDE and RCLT increased from the 0- to 20- to the 20- to 40-cm layer. RCLT still increased from the 20- to 40-cm to the 40- to 60-cm layer, while RCDE was almost unchanged. Within each of these sites, R values seem to increase with the Alox content (see Tables 1 and 6).

Factors Affecting the Determination of the Retardation Factor
Other factors may have affected the determination of R, regardless of the model used. First, in most columns F moved through only the top portion of the entire soil profile, so the evaluated retardation factors are only representative of that part of the soil column. As soils are made of a succession of horizons whose chemical properties vary, R cannot be considered fully representative of the entire soil layer when F does not reach the bottom of the column, which is the case when retention is high.

Also, the chosen F concentration may have affected the retardation factor. The experiment was originally designed to evaluate F accumulation using Ftot. Because the high and variable natural background of Ftot concentrations in soils can mask even substantial F accumulations (Polomski et al., 1982), a high F concentration (100 mg L-1) was used to obtain enough precision in the evaluation of F accumulation. This concentration is relatively high compared with those measured in rainwater and snow near the smelter studied here, which were lower than 10 mg L-1 (L. Bégin, unpublished data, 2001). The models used assume a linear sorption isotherm. However, Flühler et al. (1982) observed, in a column percolation experiment with F, that an increase of the percolating solution F concentration from 10 to 200 mg L-1 resulted in an earlier F appearance at the bottom of the soil column, which suggested a nonlinear sorption isotherm in that concentration range. Fluoride sorption isotherms were done for the soils used in the present study and are presented elsewhere (Bégin, 2002). For Soil A (0-20 cm), the isotherm was linear up to an equilibrium liquid phase F concentration of 180 mg L-1, so the use of a linear transport model was justified in this soil layer. In the other soil layers, the isotherms were linear up to F concentrations varying between 10 and 80 mg L-1. If in some soils the liquid phase resident concentration in the column reached a value above the isotherm linear range, the use of a nonlinear transport model would have been more appropriate. However, in all the soil layers, except Soil A (0–20 cm) for which the isotherm is anyway linear, sorption was so high that CrL never reached the input F concentration of the front (100 mg L-1), not even near the soil surface. This can be seen by observing the F accumulation profiles of these soils (Fig. 4). If the maximum CrL concentration had been reached in the soils, a constant F accumulation would have been observed up to a certain depth, which is not the case. It is in fact possible that the concentrations were within or near the limit of sorption linearity for most of the soils used. However, because the liquid phase resident concentration in the soils at the end of the experiment is not known, it is difficult to judge to which extent this hypothesis is valid. As the available data was not sufficient to adjust a nonlinear model, the choice of using a linear model was maintained, but it is still possible that the retardation factors were underestimated because of F sorption nonlinearity.

Finally, the possibility of rate-limited sorption must be taken into account. The models used are based on the assumption that equilibrium between the solid and liquid phases is reached. When high water fluxes are used, it may not be the case, which can result in underestimated retardation factors. However, Flühler et al. (1982) observed in an acid soil that F equilibrium between the solid and liquid phases was reached in <3 h during a batch sorption experiment. In soils with high carbonate contents, however, equilibrium was reached, in some cases, in more than 1 wk. Barrow and Shaw (1977) observed that F sorption increased during soil incubations up to 75 d after the beginning of the incubations. However, observation of their results indicate that more than 99% of added F was removed from solution during the first day of incubation, so subsequent sorption was relatively unimportant. These results tend to indicate that, with the low water flux used (0.9 cm d-1), risks of rate-limited F sorption were slight in most of the soils used. However, the presence of carbonates in the soil of Site A could make it more susceptible to rate-limited sorption. The water flux used in this experiment was higher than the mean water flux in the field. With about 1100 mm yr-1 of rain and snow (L. Bégin, unpublished data, 2001), the mean water flux is about 0.3 cm water d-1. The net downward flux is even lower when runoff and evapotranspiration are taken into account. Assuming that the sorption was not rate-limited in the columns, the lower water flux observed in the field should not affect the value of the retardation factor. However, the presence of carbonates in the soil at Site A may be responsible for a higher retardation factor in the field due to the lower water flux. Also, during storms, the net downward flux in the field may be considerably higher than the flux used in this experiment over a short period. At that time, the sorption could be rate-limited and the F may move faster than predicted.

Comparison with Earlier Studies of Fluoride Retention
The retardation factors evaluated from soil columns sampled at the different sites (Table 6) are in agreement with studies of F retention published earlier. Murray (1983) observed a strong F retention in Spodosols, which is confirmed here by the high retardation factors obtained at Sites B (RCDE = 40–79, RCLT = 33–53) and D (RCDE = 67–91, RCLT = 39–61). The low retardation factors obtained at Site C (except in Column III of the 20- to 40-cm layer) are explained by the very low soil pH (3.9–4.1), which favors the formation of soluble metal-F and HF complexes. As was observed by Wenzel and Blum (1992), F retention, evaluated here by the retardation factor, is lower in very acid (Site C, pH 3.9–4.1) and alkaline soils (Site A, pH 8.0). The retardation factors measured by Kau et al. (1999) by diffusion of F solutions through kaolin and bentonite clay plugs (R = 59–159) compare with the values obtained in this experiment in the more retentive soil layers, using the CDE model. The reported R values are also similar to those obtained for phosphate by Shimojima and Sharma (1995) (R = 1.4–1.6) and Robertson et al. (1998) (R = 20–100).

Practical Implications and Further Studies
As was seen earlier, the F retardation factors obtained in the nine soil layers ranged from 4.4 to 91 when both models are considered, which corresponds to a 20-fold difference in their capacity to slow down F migration toward ground water. The value of the retardation factor can have a considerable influence on the time required before ground water contamination is observed in a given soil. Consider two soils similar in water content ({theta} = 0.25 cm3 water cm-3 soil) that differ only by their retardation factor, respectively 4.4 and 91. In these soils, considering that all the water is mobile, climatic conditions that produce a net downward water flux of 500 mm yr-1 would result in a water velocity of 2 m soil yr-1. Under the same conditions and with the given retardation factors, F would have a mean velocity of about 45 cm yr-1 in the first soil, compared with only 2 cm yr-1 in the second one. In the first case, F would reach a 1-m deep water table in a mean of about 2 yr, while in the second case it would need about 50 yr.

Of course, these calculated velocities suppose that the retardation factors obtained in soil columns would be similar under field conditions. However, several factors could influence the applicability of the calculated retardation factors in the field. The nonlinearity of F sorption was already mentioned. In addition, the following may affect the effective retention observed in the field: (i) rapid water fluxes during storms and snowmelt; (ii) soil temperature; (iii) compounds depositing with F near industrial sources that can interact with F, for example Al, which may form soluble AlFx complexes near aluminum smelters, or other substances that can form sparingly soluble compounds in association with F; (iv) the transient water flux regime present in the field; (v) preferential infiltration of water and solute; and (vi) uptake by plants of gaseous F in the air or soluble F in the soil solution and subsequent return of this F to the soil. The influence of these factors on F retention should be studied in more details in the future. The calculated velocities are also only representative of the soil layers where they were measured. In the field, R values at greater depths could be different from the values obtained here, which could influence the velocity of F migration toward ground water. For example, at Site C, the presence of a spodic horizon under the 0- to 20- and 20- to 40-cm layers should result in an important slowdown of F migration.


   CONCLUSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 THEORY
 RESULTS AND DISCUSSION
 CONCLUSION
REFERENCES
 
The retardation factor varied among soils and depths by a 20-fold factor, from 4.4 to 91. The highest retardation factors were observed in slightly acid and neutral soils. The retardation factor was lower in strongly acid and alkaline soils. In general, the results were in agreement with earlier studies of F retention. The choice of the transport model used to determine the retardation factor affected its value, with the CDE giving higher values than the CLT. The evaluation of F retardation factors opens the way to the modeling of F transport in soils near industrial F sources, by giving a direct measurement of the relative velocities of water and F in unsaturated soils. The conditions under which the retardation factors have been evaluated (unsaturated conditions, slightly perturbed soils) were more representative than batch sorption isotherms of the conditions observed in the field. However, due to the high amount of work and time necessary to determine R values in soil columns, a comparison of the two techniques would be useful to determine if batch sorption isotherms could accurately approximate R values measured in soil columns.


   ACKNOWLEDGMENTS
 
We thank Jocelyn Boudreau, Frédéric Fournier, Daniel Marcotte, Georges Thériault, Denys Tremblay, and Luc Trépanier for their invaluable help in the laboratory and in the field. We also want to thank the Natural Sciences and Engineering Research Council of Canada and the Fonds pour la formation de Chercheurs et l'Aide à la Recherche for their financial support.

Received for publication August 30, 2002.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 THEORY
 RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 





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