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Soil Science Society of America Journal 67:765-777 (2003)
© 2003 Soil Science Society of America

DIVISION S-2—SOIL CHEMISTRY

Comparison of Naphthalene Diffusion and Nonequilibrium Adsorption-Desorption Experiments

Jesper Gamst*,a, Per Moldrupb, Dennis E. Rolstonc, Torben Olesenb, Kate Scowc and Toshiko Komatsud

a Environment and Resources, Technical University of Denmark DK-2800 Kgs. Lyngby, Denmark
b Dep. of Environmental Engineering, Aalborg University, DK-9000 Aalborg, Denmark
c Soils and Biogeochemistry, Dep. of Land, Air and Water Resources, Univ. of California, Davis, CA 95616
d Graduate School of Science and Engineering, Saitama University, 255 Shimo-okubo, Saitama, 338-8570 Japan

* Corresponding author (jeg{at}er.dtu.dk)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 THEORY
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Diffusion of hydrophobic organic compounds (HOC) is a key process controlling transport of contaminants in soils. However, the separate effects of sorption and diffusion on net (effective) HOC diffusion are not fully understood. In this study, effective diffusion of naphthalene in five unsaturated soils was evaluated by: (i) naphthalene adsorption-desorption experiments (batch method), (ii) naphthalene effective diffusion experiments (half-cell method), and (iii) trace-gas diffusivity experiments (chamber method). There was no soil type effect on gas diffusivity in repacked unsaturated soil, but a pronounced soil type effect on naphthalene sorption behavior. Varying degree of adsorption nonlinearity (Freundlich n'a) and apparent adsorption-desorption nonsingularity ({omega}) and {omega} increased with decreasing n'a were observed. In the half-cell experiments, gas diffusion was the governing naphthalene transport mechanism. Three effective diffusion coefficients were calculated from the half-cell experiments, based on concentration profile from either the whole (Deff) cell, the source (desorption) half-cell (Deff,D), or the recipient (adsorption) half-cell (Deff,A). Generally, the observed Deff decreased with naphthalene-soil contact time, because of aging effects. The Deff, Deff,A, and Deff,D values (half-cell method) could only to some extend be estimated from Freundlich isotherm parameters (batch method). A suggested index of effective diffusion nonsingularity, H = Deff,D/Deff,A, showed that H was correlated with {omega} and inversely correlated with n'a. Thus, the sorption nonlinearity (n'a) was found to provide good indications of degree of nonsingularity in both HOC adsorption-desorption and effective diffusion. The combination of batch and half-cell experiments generally gave useful insight towards understanding and predicting the influence of sorption nonlinearity and nonequilibrium on HOC diffusion.

Abbreviations: HOC, hydrophobic organic chemicals • SOM, soil organic matter


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 THEORY
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
DIFFUSION OF HOC in soils affects and in some cases controls the spreading of the chemicals. Diffusion of HOCs in the vadose zone consists of several interacting processes of which three appear to be the dominating and controlling mechanisms; gaseous diffusion, liquid diffusion, and intraparticle and intraorganic matter diffusion (controlling adsorption-desorption reactions). Gas-phase diffusion coefficients are generally considered 103 to 104 larger than solute diffusion coefficients (Petersen et al., 1994), and the intraparticle and intraorganic matter diffusion is considered to be orders of magnitude lower (Grathwohl, 1998). Hence, it is important to recognize that the effective diffusion of HOCs in soil is not alone controlled by the soil-water content, but also by soil and chemical properties because these strongly affect the partitioning of HOCs between the soil phases and therefore controls the velocity at which HOCs move.

Gaseous diffusion has been shown to be dominant for many volatile HOCs in unsaturated soil because of a significant partitioning into the gaseous phase (McArthy and Johnson, 1993; Petersen et al., 1994; Batterman et al., 1996). Solute diffusion has been shown to be dominant for HOCs of lower volatility (Ritter et al., 1973; Scott and Paetzold, 1978; Gerstl et al., 1979) and obviously also in saturated or high water content soils (Lindstrom et al., 1968; Myrand et al., 1992; Sawatsky et al., 1997; Beigel et al., 1997). Studies of HOC diffusion in unsaturated soils at different water contents have shown that the solute-gas partitioning defines whether gas or solute diffusion is the controlling transport mechanism (Graham-Bryce, 1969; Ehlers et al., 1969; Scott and Phillips, 1972; Gerstl et al., 1979; Lindhardt and Christensen, 1994; Beigel et al., 1997; Olesen et al., 2001). The retardation of a HOC compared with a conservative tracer is mainly controlled by intraparticle or intraorganic matter diffusion (Grathwohl, 1998; Pignatello, 2000). Costanza and Brusseau (2000) proposed that gas-water interface adsorption could also contribute significantly to the overall observed retention, especially in low organic soils, but for HOCs with high affinity for soil organic matter (SOM) the gas-water interface adsorption is likely insignificant.

When modeling and predicting effective HOC diffusion in soil, the adsorption-desorption reactions have often been described as linear, instantaneous and reversible (Jury et al., 1983; Myrand et al., 1992). However, several studies have shown that adsorption of HOCs to soil tends to be nonlinear and the nonlinearity tends to increase with increasing contact time (Weber et al., 1992; Xing and Pignatello, 1996). Also adsorption of HOCs to soil often requires weeks to months to reach apparent adsorption equilibrium (Ball and Roberts, 1991; Pignatello and Xing, 1996). Furthermore, nonsingularity between adsorption and desorption has been observed for several chemicals, soils, and sediments (Kan et al., 1994; Huang and Weber, 1997; Altfelder et al., 1999; Selim et al., 1999; de Jonge et al., 2000; Gamst et al., 2001).

The influence of adsorption-desorption reactions on the transport of HOCs in soils has been investigated in several studies (Macintyre et al., 1992; Beigel et al., 1997; Bouchard, 1999; Altfelder et al., 2001; Olesen et al., 2001). Some studies have used the linear adsorption coefficient (KD) obtained from batch experiments to predict the breakthrough curves in column experiments, resulting in both under and overestimation as well as reasonable predictions (Macintyre et al., 1992; Bouchard, 1999; Yamaguchi et al., 2000). Increasing retardation with increasing incubation time has been observed in studies of effective diffusion of HOCs in soils (Scott and Phillips, 1972; Beigel et al., 1997; Olesen et al., 2001). In sand without SOM, Beigel et al. (1997) observed no increase in retardation with increasing incubation time and claimed, in agreement with Olesen et al. (2001), that increased retardation with increased incubation time was caused by slow adsorption kinetics and apparent desorption nonsingularity because of interactions between the chemical and the SOM. Walker and Crawford (1970) showed for two pesticides in six soils, with a fraction of organic C (foc) of 0.51 to 19.98%, that the effective diffusion coefficient (Deff) decreased with increasing value of the linear adsorption coefficient KD, measured in batch experiments, the correlations between Deff and either KD or foc were, however, not useful for predictive purposes.

These observations on the connection between batch and column experiments imply that further understanding of how slow adsorption kinetics and apparent desorption nonsingularity affects transport of HOCs in soils is needed. Also, new insight on how (and if) adsorption and desorption results obtained from batch experiments can be used in transport modeling is needed. The purpose of this study was therefore to evaluate the influence of nonlinear adsorption, adsorption kinetics and apparent adsorption-desorption nonsingularity on diffusive transport of naphthalene in five soils to evaluate if knowledge obtained from batch adsorption experiments is useful for predicting HOC diffusive transport.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
THEORY
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Soils
Five soils were used in this study. The soils differed with respect to origin, texture, and SOM. Hiroshima soil was collected from the 5- to 20-cm layer at an agricultural field just west of Higashi-Hiroshima city, Hachihomatsu-cho town, Hiroshima prefecture, Japan. Yolo soil was collected from the 5- to 20-cm layer at an agricultural field in Yolo County, CA (Typic Xerorthent). Lerbjerg 5 soil is from a Danish arable agricultural site and was retrieved from the 0- to 20-cm depth in a field near Lerbjerg, Denmark. Lundgaard soil was retrieved from the 0- to 20-cm depth at an experimental farm near Lundgaard, Denmark (Orthic Haplohumod). Forbes soil was collected from the 5- to 20-cm layer in the Sierra Nevada foothills outside Auburn in Placer County, California. All soils were air-dried and sieved to <2 mm. Some properties of the soils are shown in Table 1.


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  		Table 1. Soil properties.

 
Gas Diffusivity
Gas diffusivity experiments were conducted for Hiroshima, Yolo, and Forbes soils in this study, while gas diffusivity (O2 diffusion) data for Lerbjerg 5 and Lundgaard soils are from Moldrup et al. (2000). The three soils were packed in 325-cm3 cores (0.06-m length and 0.083-m i.d.). The soils were thoroughly mixed with water to obtain the desired water content of: Hiroshima: 0.06, 0.12, 0.20, and 0.24 cm3 H2O cm-3 soil; Yolo: 0.13, 0.17, 0.22, 0.25, and 0.33 cm3 cm-3; and Forbes: 0.20, 0.25, 0.30, 0.40 cm3 cm-3. For each soil-water content, two replicates were packed in the cores in 1-cm layers at a bulk density of: Hiroshima sandy loam, 1.30 g cm-3; Yolo silt loam, 1.35 g cm-3; and Forbes loam, 1.00 g cm-3. Between each layer the surface was scraped with a spatula to secure good contact between the layers. The soil cores were then allowed to equilibrate for 3 to 4 wk. Soil cores were analyzed for gas diffusivity by the one-chamber diffusion method and with the equipment described by Rolston (1986). Soil gas-diffusion coefficients (DP,g) were measured with Freon 12 (dichlorodifluoromethane, Matheson Gases, Newark, CA) as the experimental gas at 24°C. Petersen et al. (1994) analyzed Freon 12 adsorption from the gas phase to the Yolo soil and did not find any measurable adsorption to this soil, thus it was assumed that Freon 12 could be used as a conservative nondegradable tracer gas. The Freon 12 concentration in the chamber diffusion experiments was determined by measurement on gas chromatograph (Sri 8610 GC with FID, SRI Instruments, Torrance, CA) at several successive times in the chamber during the experiment. The value of DP,g was determined by fitting the analytical solution given by Taylor (1949) to the measured concentration versus time profile in the chamber by minimizing the sum of least squares. To minimize drying of the soil cores, the diffusion experiments were conducted at a relative humidity of 100%, and the observed water loss in the experiments was <0.002 g g-1 soil.

Naphthalene Adsorption and Desorption
Adsorption and desorption experiments were conducted for Forbes and Hiroshima soils in this study, while data for Yolo, Lerbjerg 5, and Lundgaard soils are from Gamst et al. (2001). Sorption experiments were performed with 14C-labeled 1-naphthalene with a purity >99.9% (C10H8) (Sigma Chemical, St. Louis, MO) with a specific activity of {approx}3.00 x 108 Bq mmol-1. A stock solution containing 14C-labeled naphthalene with an activity of {approx}4.51 x 108 Bq L-1 was prepared in methanol (128 mg L-1), and a stock solution containing 10 mg L-1 unlabeled naphthalene (Fisher Scientific, Fair Lawn, NJ) in 0.01 M CaCl2 was prepared. Before each experiment, solutions of nonlabeled naphthalene were prepared in 0.01 M CaCl2 at initial concentrations of 0.10, 0.50, 1.0, 2.5, 5.0, and 10.0 mg L-1 from the stock solution. Subsequently, 14C-labeled naphthalene with an activity of {approx}6.66 x 103 Bq L-1 ({approx}4.0 x 106 cpm L-1) was added to the solutions. The concentration of methanol in the solutions was {approx}0.15 g L-1. The influence of methanol in solution on the sorption results was tested by conducting sorption experiments at two different concentrations of nonlabeled naphthalene on the five soils, with determination of the naphthalene concentration on a gas chromatograph (Chrompack 438S with FID, Wcot fused Silica 32 mm ID CP-sil 8CB Chrompack capillary column; Varian, Lexington, MA). In accordance with results of others (Curtis et al., 1986; McGinley et al., 1993), no effect of the presence of methanol on adsorption could be determined. Soil and the 0.01 M CaCl2 solution were autoclaved for 2 h before each experiment to prevent bacterial degradation of naphthalene.

Sorption experiments were conducted at 10°C using a batch technique. Solids to solution ratios were chosen to ensure that 20 to 80% of the naphthalene mass was adsorbed. Air-dried soil (Hiroshima: 7.8 g, Forbes: 2.66 g) was weighed into 48-mL glass centrifuge tubes. Altfelder et al. (1999) and Farcasanu et al. (1998) observed that chemical uptake from air-dried soils initially was faster compared with field moist soils, especially at short time scales (hours to days), and recommended rehydration of the air-dry soils before conducting sorption experiments. Therefore, 3 mL (Hiroshima) and 2 mL (Forbes) 0.01 M CaCl2 was added to the tubes containing air-dried soil and sealed with Teflon coated screw caps and allowed to rehydrate at 10°C for 7 d. Following rehydration, 40 mL of naphthalene solution was added and again the tubes were sealed with Teflon coated screw caps. The headspace of the tube was typically very small (<2 mL). Three replicates were made for each naphthalene concentration. The tubes were rotated vertically (50 rpm). Adsorption isotherms were measured on a short-term (48 h) and on a longer-term (504 h) time scale. Soil and solution were separated by centrifuging at 1225 x g for 15 min. From each tube, two replicates were used to determine concentration of 14C-naphthalene by liquid scintillation counting (Beckman LS 6000 IC, Beckman Instruments, Fullerton, CA) using 0.25 mL of the supernatant mixed with 4 mL of scintillation cocktail (Universol, Costa Mesa, CA). For each initial concentration of naphthalene, two blanks without soil material, but otherwise treated similarly, were included. Analysis of naphthalene concentration before and after transferring solution from the stock solutions to the blanks showed small initial losses presumably because of evaporation (<2%). This was taken into account by assuming that the initial amount lost during solution transfer was similar in both the blanks and in the tubes containing soil. Further analysis on blanks showed no sorption to glass tubes or Teflon caps with time.

Desorption were conducted as successive dilution desorption steps measured at two different initial concentrations after both the short-term and longer-term adsorption experiments. Seven to nine successive dilution desorption steps were measured; all conducted on a short-term basis (48 h). Before each desorption step, the samples were centrifuged at 1225 x g for 15 min, and 35 mL of the supernatant was replaced by 0.01 M CaCl2. At the end of the desorption experiments, naphthalene was extracted from the soils using up to five successive methanol extraction steps to determine the mass balance. These analyses showed that 93 to 99% of the initial amount of naphthalene was recovered. Some of these analyses were conducted on a gas chromatograph (Chrompack 438S with FID, Wcot fused Silica 32 mm ID CP-sil 8CB Chrompack capillary column) to make sure that the extracted material was naphthalene and not degradation products. In all samples, the concentration of naphthalene measured using liquid scintillation counting was similar to the concentration of naphthalene measured on a gas chromatograph.

Naphthalene Effective Diffusion
Diffusion of naphthalene was measured for the five soils analyzed in this study using the half-cell method described in detail by Shackelford (1991). Eight-centimeter aluminum half-cells (91 cm3) and lids of aluminum were used. Viton O-rings (DuPont Dow Elastomers, Wilmington, DE) were used in all fittings to seal the cells and the experimental setup was air tight in the range of -0.09 MPa to 1.3 MPa. Some physical and chemical properties for naphthalene are presented in Table 2. Air-dry soil was mixed with water to obtain the desired water content and the experiments were performed in unsaturated soil at varying water contents (Table 3). A stock solution containing 14C-labeled naphthalene with a activity of 4.51 x 108 Bq L-1 was prepared in methanol (128 mg L-1) (Stock 1) and a stock solution of unlabeled naphthalene (Fisher Scientific, Fair Lawn, NJ) was prepared in hexane (10000 mg L-1) (Stock 2). For each experiment a solution was prepared, containing 3 mL hexane, 14C labeled naphthalene from Stock 1 corresponding to 185 Bq g-1dry soil (0.1 µg naphthalene g-1 soil), and unlabeled naphthalene from Stock 2 corresponding to the concentrations listed in Table 3. The prepared solution was then added to the wet soils and mixed until the hexane was evaporated. During this mixing procedure 2 to 6% of the added naphthalene was lost because of evaporation. The actual concentration of naphthalene in the experiment was measured subsequent to the mixing procedure and used as C0. The soils were then packed at the bulk densities listed in Table 3, with one half-cell containing soil with naphthalene (source cell) and one half-cell containing soil without naphthalene (recipient cell). The soils were packed in 2-cm layer and between each layer the surface was scratched with a spatula to obtain good contact between the layers. The half-cells were then sealed with aluminum lids, and allowed to equilibrate for a specified period (Table 3).


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  		Table 2. Physical and chemical properties of naphthalene at 10°C.

 

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  		Table 3. Overview of naphthalene effective diffusion experiments, showing water contents, initial naphthalene concentration, bulk density, equilibration time, incubation time at varying water contents and incubation times at constant water contents (see Materials and Methods above).

 
After the equilibration period, the source and recipient half-cells were connected and incubated horizontally at 10°C. The incubation times both for the experiments with varying water contents and the experiment with varying incubation time and constant water contents are listed in Table 3.

After incubation, the soil in each half-cell was sliced in 0.33-cm slices (within 0–1 cm on each side of the interface), 0.5-cm slices (within 1–2 cm distance from the interface), and 1.0-cm slices (within 2–8 cm distance from the interface). The concentration of 14C-labeled naphthalene was determined by a scintillation fluid extraction method described by Gamst et al. (2002), and initial experiments to determine extraction efficiency, necessary extraction time, concentration dependency, and time dependency of the method were conducted. We found that the scintillation fluid extraction-method could be applied to the soil-chemical combination used in this study at all time scales and concentrations. From each slice, one to three replicates of 0.3-g soil samples were weighed into a glass scintillation vial and mixed thoroughly with 15 mL of Packard Insta-Gel Plus (Packard Bioscience, Groningen, NL) scintillation liquid. The soil particles settled to the bottom of the scintillation vial and were subsequently analyzed by liquid scintillation counting for 5 min (Beckman LS 6000 IC, Beckman Instruments, Fullerton, CA) every week until the determined 14C concentration did not increase, as described by Gamst et al. (2002). The samples were stored dark at room temperature (24°C). As observed by Gamst et al. (2002) the extraction efficiency of the scintillation fluid extraction method was high and recovery of added naphthalene, C0, was >96% for the soils used. Mass balance calculations showed that the average concentration at end of the experiment agreed with the concentration calculated from the amount of naphthalene added.


   THEORY
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 THEORY
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
The gas and solute diffusion coefficients are governed by the length, geometry, and connectivity of the diffusive pathways in the gaseous and liquid phases and are often predicted from empirical equations for nonreactive chemicals (e.g., Freon 12 and Cl-). Olesen et al. (2001) showed that diffusion in the liquid phase only influences the effective diffusion of naphthalene in soil at water contents very close to saturation. Since all naphthalene diffusion experiments in this study were conducted at water contents below field capacity, the contribution from diffusion in the liquid phase to the effective diffusion of naphthalene was considered negligible.

If the air-filled porosity of the soil, {epsilon} (cm3 soil air cm-3 soil), and the soil water content, {theta} (cm3 soil water cm-3 soil), are assumed constant and solute diffusion is negligible, effective diffusion of a sorbing chemical such as naphthalene in the soil can be described by,

[1]

[2]
where F is the chemical flux (µg cm-2 soil d-1), Ctotal is the total chemical concentration (µg cm-3 soil), z is soil depth (cm soil), Deff is the effective diffusion coefficient (cm2 soil d-1), Rg is the ratio of total/gas-phase concentration at equilibrium (Ctotal,equilibrium/Cgas,equilibrium) hereafter referred to as the retardation factor for the gas phase (cm3 air cm-3 soil), and DP,g is the gas-diffusion coefficient in soil (cm3 soil air cm-1 soil d-1), defined by,

[3]
where D0,g is the gas diffusion coefficient in free air (cm2 d-1) and fg is a tortuousity term (-). The dependency of fg on air-filled porosity, {epsilon} (cm3 air cm-3 soil), was determined for each soil from gas diffusion experiments with a trace gas (see Materials and Methods above). The gas diffusion coeffient, D0,g, for naphthalene (Table 2) and fg({epsilon}) can be used to calculate DP,g for naphthalene at a given {epsilon} and used in Eq. [2]. If instantaneous and reversible equilibrium between the soil phases is assumed, where Henry's constant, KH (cm3 soil water cm-3 soil air), describes the distribution between the liquid and gas phase, and KD (cm3 soil water g-1 soil) is the linear adsorption coefficient, the retardation factor for the gas-phase becomes,

[4]
where {rho}b is the soil bulk density (g soil cm-3 soil). Following Olesen et al. (2001), Eq. [4] and [2] were used to estimate the apparent linear sorption coefficient (KD,app) observed in the effective naphthalene diffusion experiment. Equation [4] is only an approximation of Rg since sorption typically will be nonlinear and time-dependent (Gamst et al., 2001).

Assuming constant {epsilon} and {theta}, the flux equation, Eq. [1], combined with the continuity equation yields the governing differential equation for one-dimensional diffusion of a sorbing chemical,

[5]
where t is time (d) and the soil chemical concentration (g cm-3 soil) Ctotal = Cg{epsilon} + Cl{theta} + S{rho}b, where Cg is the gas phase concentration (g cm-3 soil air), Cl is the solute concentration (g cm-3 soil water), S is the adsorbed concentration (g g-1 soil), and Deff is given by Eq. [2]. A numerical solution to Eq. [5] (Moldrup et al., 1996) was used to estimate the effective naphthalene diffusion coefficients (Deff) from the measured concentration versus distance profiles.

Adsorption isotherm data for HOCs are typically well described by the Freundlich isotherm model,

[6]
where K'F is the Freundlich coefficient (mg(1 - n) Ln kg-1) related to sorption capacity and n' is the Freundlich exponent related to sorption nonlinearity. We use ' to indicate that both parameters will vary with time until a true equilibrium is reached (Gamst et al., 2001) and to indicate that isothermal phase distribution measurements are not at equilibrium. If the variation of the Freundlich parameters with contact time is known, the retardation factor can be estimated from,

[7]

We note that the retardation factor calculated in Eq. [7] is concentration and time dependent and can be used in Eq. [2] to estimate the effective diffusion coefficient only at a given concentration (Grathwohl, 1998) and at a given time. Thus, Eq. [7] is a linear approximation of nonlinear concentration dependency where (S/C1 = KD) is replaced by in the retardation factor. Huang and Weber (1998a) showed that K'F was very time-dependent, but that n' could be assumed constant at sorption times >4 d. Also with Rg being a function of Cl and thus Ctotal, Rg should be solved separately at each point location within the half-cell. In the present study, however, we only use Eq. [7] to calculate an approximate value of Deff ( = DP,g/Rg) at a given concentration and at a given time.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 THEORY
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Gas Diffusivity
Figure 1 shows the relative gas diffusivity (DP,g/D0,g) for the five soils as a function of soil-air content. Changes in soil texture do only minimally influence the gas diffusivity in repacked soils, in accordance with observations made by Moldrup et al. (2000). Moldrup et al. (2000) developed a gas diffusivity model for sieved repacked soils that predicted the measured data well (results not shown). However, small prediction errors were observed and to avoid unnecessary inaccuracies, an empirical fg({epsilon}) function (polynomial) was fitted to the measured trace gas diffusivity data for each soil and used to calculate DP,g({epsilon}).



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  		Fig. 1. Relative gas diffusivity data for repacked Hiroshima, Yolo, Lerbjerg 5, Lundgaard, and Forbes soils. § data from present study (Freon 12), §§ data from Moldrup et al. (2000) (O2).

 
Naphthalene Adsorption and Desorption
Adsorption and desorption isotherms for the five soils were measured on a short-term (48 h adsorption and 48 h consecutive desorption step) and a longer-term (504 h adsorption and 48 h consecutive desorption step) time scale (Fig. 2) . It is noted that all successive desorption steps used in desorption isotherms were measured on a short-term time-scale (48 h). Adsorption and desorption isotherms were nonlinear (Fig. 2 and Table 4) and the Freundlich isotherm model (Eq. [6]) fitted the adsorption and desorption isotherms well. Freundlich isotherm parameters are listed in Table 4, illustrating a major difference between the adsorption-desorption behavior of the five soils.



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  		Fig. 2. Measured adsorption-desorption isotherms on either a short-term (closed symbols, 48-h adsorption and 48-h desorption step) or a longer-term (open symbols, 504-h adsorption and 48-h desorption step) basis. Best-fit Freundlich isotherms (Eq. [6]) for adsorption-desorption isotherms are shown as solid lines. § data from present study, §§ data from Gamst et al. (2001) measured under similar conditions and time scales.

 

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  		Table 4. Freundlich isotherm parameters for the adsorption and desorption isotherms, where Chigh and Clow indicates desorption isotherm parameters for the desorption isotherm measured at the high and low initial solute concentration respectively. Also listed are the best-fit linear adsorption coefficients, KD.

 
Hiroshima (Fig. 2a), Yolo (Fig. 2b), and Forbes (Fig. 2e) soils exhibited pronounced apparent adsorption-desorption nonsingularity that was higher in the longer-term experiment. Lerbjerg 5 soil (Fig. 2c) changed from exhibiting minor apparent nonsingularity at short-term experiments to pronounced apparent nonsingularity at longer-term experiments while Lundgaard soil (Fig. 2d) showed minor apparent adsorption-desorption nonsingularity. The differences in the apparent sorption nonsingularity of the soils are likely because of differences in the nonequilibrium conditions of the experiments. The Lundgaard soil (Fig. 2d) exhibited only small changes in adsorbed amount from short-term to longer-term experiment and minor apparent desorption nonsingularity, thus most of the adsorption sites are likely more accessible and equilibrium more likely to have been achieved (Pignatello, 2000). For Hiroshima (Fig. 2a) and Forbes (Fig. 2e) soils, the adsorbed amount increased considerably from the short-term to longer-term adsorption and differences in observed adsorption and desorption were more pronounced. Thus, these soils are clearly in a nonequilibrium condition likely caused by a large fraction of difficult accessible sorption sites. Yolo (Fig. 2b) and Lerbjerg 5 (Fig. 2c) soils exhibited only a small change in adsorbed amount from short-term to longer-term experiment but the apparent nonsingularity increased in the longer-term experiment, likely because of intraparticle diffusion into the narrow pores of the clay minerals and the SOM. Overall, nonequilibrium conditions likely explain much if not all of the apparent isotherm nonsingularity, with results further complicated by the fact that adsorption will continue to occur during desorption phases of experimentation if adsorption times are insufficient.

Apparent adsorption-desorption nonsingularity has been observed frequently and several suggestions to parameterize this from experimental observations have been made (Ma et al., 1993; Huang and Weber, 1998b; Yuan and Xing, 2001). In this study, the apparent nonsingularity was characterized by the expression of nonsingularity suggested by Ma et al. (1993) for desorption isotherms measured by the successive dilution technique,

[8]
where {omega} is a measure (in %) of nonsingularity and n'A and n'D are the Freundlich exponents for the measured adsorption and desorption isotherms (Table 4), respectively. This index is strictly only applicable for comparison purposes if the ratio of the replaced supernatant and the time scale are similar in all experiments. The soils used in this study have fairly similar ratios (0.73–0.80) and time scales are similar. Gamst et al. (2001) suggested to classify the soils into two groups from {omega}, using their classification Lundgaard soil is a Type I soil showing minor apparent desorption nonsingularity ({omega} < 100%) and Hiroshima, Yolo, and Forbes soils are Type II soils, soils showing pronounced apparent desorption nonsingularity ({omega} > 100%), while Lerbjerg 5 is a Type I/II because of the change between short-term and longer-term data. The adsorption and desorption behavior of the Lundgaard, Yolo, and Lerbjerg 5 soils are discussed more thoroughly by Gamst et al, (2001).

Yuan and Xing (2001) found a good correlation between the Freundlich adsorption nonlinearity parameter, n'A, and a nonsingularity index (n'D/n'A) for adsorption-desorption isotherms of three different HOCs on three different humic acids. Figure 3 shows {omega} for the adsorption and desorption isotherms measured in this study (Forbes and Hiroshima soils) as a function of n'A. Data for the naphthalene adsorption-desorption experiments on five soils (Lundgaard, Lerbjerg 5, Yolo, and two additional soils) from Gamst et al. (2001) and three humic acids from Yuan and Xing (2001) are also shown. The data from Yuan and Xing (2001) is strictly not comparable with our data because their time scale were slightly different (72 h adsorption and 72 h successive desorption step), but with a similar ratio of replaced supernatant (0.75). Generally, the nonsingularity index, {omega}, increases with increasing adsorption isotherm nonlinearity (decreasing n'A) (Fig. 3). It is noteworthy that n'A appears to be a reasonable indicator for the degree of desorption nonsingularity and, also, that the observations on the seven soils with a heterogeneous SOM composition from this study and Gamst et al. (2001) are in quite good agreement with the observations made by Yuan and Xing (2001) on a pure organic material (humic acid) (Fig. 3).



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  		Fig. 3. Degree of nonsingularity, {omega} (Eq. [8]), of the measured naphthalene adsorption-desorption isotherms as a function of the adsorption isotherm nonlinearity, n'A. Open symbols represent short-term (48-h adsorption and 48-h desorption step) and closed symbols longer-term (504-h adsorption and 48-h desorption step) experiments. The broken line at {omega} = 100% defines whether the soil is a Type I or II soils (Gamst et al., 2001). § data from present study, §§ data from Gamst et al. (2001), §§§ data from Yuan and Xing (2001).

 
The observed trend in Fig. 3 should, however, not at present be used to develop a predictive empirical relation between {omega} and n'A, because {omega} is dependent on both the length of desorption step and the ratio of replaced supernatant. The differences in apparent nonsingular behavior for the soils are probably controlled by differences in the type and quality of the SOM. This is probably also the case for adsorption nonlinearity. Thus, there might be a connection between the portion of SOM that causes nonlinear sorption and the part causing adsorption-desorption nonsingularity.

Nonlinearity and Nonsingularity Effects on Effective Diffusion of Naphthalene
Naphthalene effective diffusion was measured at varying soil water content for all five soils, varying incubation times for four of the soils and varying concentration for two of the soils (see Materials and Methods above). Examples of measured concentration versus distance profiles at selected contact times (equilibrium time + incubation time) for the five soils are shown in Fig. 4 . Also shown is the calculated diffusion profiles (Eq. [5]) based on the best-fit effective diffusion coefficient, Deff. Concentration versus distance profiles for diffusion experiments performed with lower concentration of naphthalene, but otherwise similar experimental conditions, are also shown for Yolo (Fig. 4b) and Lerbjerg 5 (Fig. 4c) soils (closed symbols). Generally, the concentration versus distance profiles in Fig. 4 exhibit effect of the sorption nonlinearity and nonequilibrium; a slight discontinuity compared with the calculated profiles is observed around the interface between the half-cells and furthermore the measured concentration profiles are asymmetrical if compared with Cl- diffusion (Olesen et al., 1999) because movement in the source cell appears slower than in the recipient cell. Gamst et al. (2002) showed that the discontinuity and asymmetrical concentration profiles were because of how sorption nonlinearity and nonequilibrium affected the diffusion process rather than extraction problems with the scintillation fluid extraction method. The discontinuity around the interface is likely caused by nonequilibrium conditions in the source cell where insufficient equilibration time may cause continuing uptake in the source cell.



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  		Fig. 4. Examples of measured concentration versus distance profiles for naphthalene diffusion at either high initial concentration (Ch, open symbols) or low initial concentration (Cl, closed symbols) at selected contact times (equilibrium time + incubation time) in (a) Hiroshima ({theta} {approx} 0.13 m3 m-3, t = 722 h), (b) Yolo ({theta} {approx} 0.18 m3 m-3, t = 504 h) (c) Lerbjerg 5 ({theta} {approx} 0.24 m3 m-3, t = 386 h), (d) Lundgaard ({theta} {approx} 0.07 m3 m-3, t = 143 h) and (e) Forbes ({theta} {approx} 0.21 m3 m-3, t = 2448 h). The lines are model fit (Eq. [5]) to measured data to obtain the Deff value.

 
Yolo and Lerbjerg 5 soils exhibited nonlinear sorption (Fig. 2 and Table 4) and consequently higher retardation at lower concentration is expected (Eq. [6] and [7]). In Fig. 4b and 4c, diffusion experiments at two concentrations are shown, illustrating the effect of nonlinear sorption. Both the minor spreading of naphthalene and the considerable difference between Deff,h (high concentration) and Deff,l (low concentration) show that retardation is higher at lower concentrations. Yolo soil exhibited the highest degree of sorption nonlinearity of the two soils (Table 4) and consequently the largest relative difference between Deff,h and Deff,l were observed for this soil (Fig. 4b). Hu and Brusseau (1998) similarly observed increasing retardation with decreasing concentration in a transport experiment for a HOC that also exhibited nonlinear adsorption in batch experiments.

In the Forbes soil experiment (Fig. 4e) only minor diffusive movement of naphthalene was observed. Although the Forbes soil exhibits high adsorption capacity in batch experiments (Table 4) and high degree of apparent adsorption-desorption nonsingularity (Fig. 2e), the almost negligible diffusive movement was unexpected. The observed Deff corresponds to an apparent KD value of 1.5 x 105 L kg-1, which are orders of magnitude higher than KD measured in batch experiments (Table 3). The diffusion experiments conducted on the Forbes soil (three water contents and three incubation times) all showed similar results. The explanation might be that naphthalene is irreversibly adsorbed in the Forbes soil, but desorption results showed that >30% of the initially adsorbed naphthalene was released (Fig. 2e). Since the scintillation fluid extraction method showed high recoveries after 116 d of contact time in the source cell (>90%), low extraction efficiency is not the explanation. Schwartz and Scow (1999) observed degradation of phenanthrene in the Forbes soil indicating that this eventual irreversible adsorption does not cause HOCs to be nondegradable in this soil.

The naphthalene diffusion experiments consist of two half-cells, one where soil and naphthalene have been in contact for a given equilibration time (source cell) and one with clean soil (recipient cell). Therefore, the retardation mechanisms are expected to be different in the two cells. In the source cell retardation is likely dominated by desorption because adsorption of naphthalene to the soils have occurred within the equilibration time. Opposite, adsorption is likely the controlling retardation mechanism in the recipient cell where naphthalene diffuses into clean soil, where decreasing concentration will cause relatively stronger adsorption because of nonlinear sorption. Thus, the analysis of the measured concentration versus distance profiles were divided into three parts, an estimation of an effective diffusion coefficient for the whole cell, Deff, the desorption cell (source cell), Deff,D, and the adsorption cell (recipient cell), Deff,A. Figure 5 shows an example of this interpretation of the half-cell diffusion experiments for Hiroshima soil. The apparent difference between Deff,D and Deff,A (Fig. 5) illustrates the trend in the difference between adsorption and desorption controlled retardation in the diffusion experiment. The apparent higher diffusion rates in the recipient cell are caused by nonequilibrium conditions in both the source and the recipient cells. Nonequilibrium will in the source cell cause continuing uptake and consequently a lower apparent Deff,D, while in the recipient cell a larger relative fraction of naphthalene is in the gas-phase causing a higher Deff,A.



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  		Fig. 5. Concentration versus distance profile for naphthalene diffusion in Hiroshima soil ({theta} {approx} 0.13 m3 m-3, contact time = 722 h). The solid line represents best fit to data in the desorption half-cell and the broken line represents best fit to data in the adsorption half-cell.

 
Aging Effects on Sorption and Diffusion of Naphthalene
Following Olesen et al. (2001), the effective diffusion coefficients, Deff, Deff,A, and Deff,D were used to estimate an apparent linear sorption coefficient (Eq. [2] and [4]) in the whole cell (KD,app), the adsorption cell (KD,app,A) and in the desorption cell (KD,app,D). Figure 6 illustrates how contact time (aging) affects the apparent KD in the whole cell as well as in the adsorption and desorption half-cells for Hiroshima, Yolo, and Lerbjerg 5 soils (additional data for Lerbjerg 5 from Olesen et al. (2001) are included). The KD,app increase with increasing contact time for Lerbjerg 5 and Hiroshima soils, while KD,app is almost stable for the Yolo soil at all contact times (Fig. 6). Data for the Forbes soil are not shown in Fig. 6 because the little naphthalene movement in the experiment could not justify a separate analysis of movement in the source and recipient cell. However, it must be noted that KD,app for the whole cell increases from 3 x 103 to 1.5 x 105 L Kg-1 in the contact time experiment, indicating increasing sorption with time.



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  		Fig. 6. Apparent KD–values obtained in either the whole cell (closed symbols), the desorption half-cell (open symbols) or in the adsorption half-cell (dotted open symbols) for Hiroshima, Yolo, and Lerbjerg 5 as a function of contact time in the diffusion experiments. Part of the data for Lerbjerg 5 are from Olesen et al. (2001).

 
Comparison of the variation in KD,app in the Hiroshima soil with the batch adsorption-desorption experiments (Fig. 2a) gives some insights in the connection between batch and column experiments. The {approx}35 d and the {approx}50 d contact time experiments represents 5 and 20 d equilibration time before connection of the two half-cells, followed by 30 d incubation time, see Materials and Methods above, thus the major difference in experimental conditions is the equilibration time. If compared with short-term (2 d) and longer-term (21 d) batch experiments it was shown that longer-term adsorption resulted in increased amount adsorbed and pronounced apparent adsorption-desorption nonsingularity (Fig. 2a and Table 4). In the effective diffusion experiments, longer equilibration time (20 d compared with 5 d) resulted in higher KD,app and higher relative difference between KD,app,A and KD,app,D (Fig. 6). Therefore, the increase in the relative difference between KD,app,A and KD,app,D with increasing contact time indicates increasing nonsingularity with increasing contact time in effective diffusion experiments.

Values of KD,app for the Yolo soil slightly increases with increasing contact time (Fig. 6), which is comparable with the batch results that showed a small increase in the amount adsorbed between short and longer term experiments (Fig. 2b).

For Lerbjerg 5 soil, the KD,app in the effective diffusion experiments is strongly affected by aging (Fig. 6), which to some extent is comparable with the batch experiments where a change from minor apparent desorption nonsingularity at short-term experiments to pronounced apparent desorption nonsingularity at longer-term experiments was observed (Fig. 2c). The pronounced effect of aging in the diffusion experiment compared with batch experiment is likely caused by different intraparticle conditions because of the high clay content in the Lerbjerg 5 soil (Table 1).

The physical effects of the soil in the batch experiment will to some extent damage the soil aggregates and an additional soil particle and SOM surface will become easily available for naphthalene sorption. Opposite, more of the aggregates formed by the primary clay particles and SOM will stay intact during the column (half-cell) diffusion experiments, potentially causing very different intraparticle pathways in the two types of experiments. Thus the strong aging effect in the Lerbjerg 5 diffusion experiment compared with batch experiments are likely a combined effect of adsorption and desorption on SOM and intraparticle diffusion through soil aggregates.

Increasing retardation with longer contact time has been observed previously in effective HOC diffusion experiments (Scott and Phillips, 1972; Beigel et al., 1997; Olesen et al., 2001). Scott and Phillips (1972) explained the time dependency with degradation and slower movement of degradation products. This can be excluded from our work, because no degradation was observed in any of the experiments. Beigel et al. (1997) explained the increased retardation by aging effects on both adsorption and desorption reaction with the SOM and proved this by using a sand without SOM that showed no effect of aging. Beigel et al. (1997) and Olesen et al. (2001) compared the time dependent increase in KD,app in effective HOC diffusion experiment with the increase in KD,app (S/C) observed in a batch desorption experiment and did find some connection. However, both their and our results show that batch adsorption-desorption experiments cannot directly be compared with effective diffusion experiments. Thus, it must be recognized that batch adsorption-desorption is not directly comparable with the adsorption-desorption reactions in the diffusion experiment but can be used as an indicator of how effective diffusion of HOC in soils will be affected. The stronger effect of aging in column compared with batch experiments for high clay content soils as observed here and by both Beigel et al. (1997) and Olesen et al. (2001) are likely in part caused by the different intraparticle diffusive pathways through soil aggregates in column compared with batch experiments.

Estimating Deff from Batch Experiments
It was tested if batch adsorption-desorption isotherm parameters can be used to predict the effective-diffusion coefficients obtained in half-cell experiments. The simplest estimation of Deff can be obtained by combining Eq. [2] and [4] (assuming a linear, equilibrium adsorption isotherm). However, the use of the linear sorption coefficient (KD) in the retardation factor for the gas-phase (Eq. [2] and [4]) is a very simplified interpretation of data because of sorption nonequilibrium, nonlinearity, and apparent desorption nonsingularity. As an alternative, Eq. [7] based on the nonlinear Freundlich isotherm and allowing K'F and n' to vary between adsorption and desorption was used to estimate the apparent naphthalene retardation factor for the gas-phase in Eq. [2]. Longer-term Freundlich adsorption (recipient cell) and desorption (source cell) isotherm parameters (Table 4) were used together with the average, total concentration of naphthalene in each of the source and recipient cell to estimate Cl in each cell from Ctotal = {epsilon}ClKH + {theta}Cl + {rho}bCln'K'F. Thereby, a concentration dependent retardation factor for the gas-phase could be estimated from Eq. [7] and used in Eq. [2]. These were used to predict an effective naphthalene diffusion coefficient (Eq. [2]) in both the source (desorption) and recipient (adsorption) cells. It must be noted that Eq. [7] is only an approximation of a concentration and adsorption-desorption dependent retardation factor for the gas-phase since adsorption-desorption nonsingularity and nonequilibrium are not fully taken into account. Thus, using Eq. [2] together with Eq. [7] should only be considered an improved method to get a rough estimate of Deff, as compared with using KD (Eq. [4]). The predicted effective diffusion coefficients were compared with measured effective diffusion coefficients as a function of water content and at constant soil chemical contact times in Hiroshima, Yolo, Lundgaard, and Lerbjerg 5 soils (Fig. 7) . The Forbes soil was excluded from this analysis because the huge difference between effective diffusion KD,app and batch KD clearly indicates that a successful prediction of Deff from batch results is impossible.



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  		Fig. 7. Obtained Deff–values in either the whole cell, the source (desorption) half-cell or in the recipient (adsorption) half-cell for (a) Hiroshima (t = 1200 h, except for tshort equilibrium = 840 h, (b) Yolo (t = 816 h), (c) Lerbjerg 5 (t = 672 h) and (d) Lundgaard (t = 456 h, except for tshort incubation = 384 h), shown as a function of water content. Also shown is the Deff values estimated from the batch adsorption (broken line) or desorption (solid line) using Freundlich isotherm parameters (Table 4) and the best-fit longer-term linear isotherm (KD) (dotted line).

 
For Hiroshima soil at {theta} < 0.2 m3 m-3, Deff,A and Deff,D were underestimated when using Eq. [2] and [7] together with the measured Freundlich isotherm parameters (Fig. 7a). Deff was only for this soil well estimated by Eq. [2] and [4] using the best-fit linear adsorption isotherm (KD value) from the batch experiment. This was unexpected since batch experiments showed that adsorption was very nonlinear and adsorption-desorption was very nonsingular (Fig. 2 and Table 4).

For both Yolo soil (Fig. 7b) and Lerbjerg 5 soil (Fig.7c), predictions of Deff,A and Deff,D from Eq. [2] and [7] were in reasonably good agreement with the observed Deff,A and Deff,D values from the half-cell experiments, although slightly overestimated in the adsorption cell and slightly underestimated in the desorption cell. Predictions of Deff based on the linear adsorption isotherm (KD) yielded a pronounced overestimation.

For the Lundgaard soil, both Deff,A and Deff,D predicted from Eq.[2] and [7] were overestimated while Deff was largely overestimated using Eq. [2] and [4]. It is noted that Deff,A in this case is predicted to be smaller than Deff,D, illustrating the sensitivity to the isotherm parameters, that is, changes in the used concentration (Cl) caused dramatic changes in the predicted retardation factor for the gas-phase. Interestingly, the minor apparent desorption nonsingularity in the batch experiments (Fig. 2d) is comparable with the half-cell experiment, where the relative difference between measured Deff,A and Deff,D is small (Fig. 7d).

Overall, the Deff,A and Deff,D values calculated from the Freundlich adsorption and desorption isotherm parameters using Eq. [2] and [7] yielded more realistic predictions of the Deff,A and Deff,D values from the diffusion (half-cell) experiments, as compared with using the linear adsorption coefficient (KD). However, since the solute concentration (Cl) is difficult to estimate correctly from the measured total concentration in the soil, there is a high degree of uncertainty associated with the predicted Deff,A and Deff,D values in Fig. 7. Further, the nonequilibrium effects are not well represented by this method (Eq. [7]). In summary, estimating the effective diffusion coefficients from the Freundlich adsorption and desorption isotherm parameters will mostly give improved predictions compared with using the linear isotherm, but Deff values are still not predicted with a high degree of accuracy because of solute concentration and nonequilibrium sorption effects, hereunder the basic differences between intraparticle pathways at the particle and aggregate scale in batch and half-cell experiments.

Relating Half-Cell Deff Nonsingularity to Adsorption-Desorption Nonsingularity
Comparing batch adsorption-desorption experiments with half-cell effective diffusion experiments for the soils in this study has shown both good and poor connections between these two types of experiments. Especially, there seem to be a good connection between the adsorption-desorption behavior observed in the batch experiments with observations in the half-cell experiments, but parameter values do not appear directly comparable. In Fig. 3, a good correlation between the batch desorption nonsingularity index, {omega}, and the adsorption nonlinearity parameter, n'A, was shown. To compare these parameters with the half-cell experiments, we defined a half-cell Deff nonsingularity index H from the effective diffusion coefficients obtained in the half-cells,

[9]

In Fig. 8 , the half-cell Deff nonsingularity index H is correlated with {omega} (Fig. 8a) and with n'A (Fig. 8b). Reasonable correlations were observed between both the half-cell Deff nonsingularity index H and the batch nonsingularity index ({omega}) and between H and the batch adsorption nonlinearity parameter n'A. There is a huge standard deviation on H, likely because each H value represents experiments with different conditions; water content, incubation time, and equilibration time. The best-fit linear correlations between H and either {omega} or n'A (fine dotted line), forced through the point where adsorption-desorption theoretically is linear and completely reversible (1.0, 1.0) is shown as a solid line in Fig. 8. Also shown in Fig. 8 is the nonrestricted best fit linear correlation between H and either {omega} or n'A for the four soils (coarse broken line). These two types of fit illustrate the good correlation of the parameters, but are not supposed to indicate predictive possibilities, since measurement for only one chemical in four soils is not enough to develop a predictive relation. It is highly interesting, based on the results of Fig. 8b and 3, that the adsorption nonlinearity parameter n'A appears to be a strong indicator of both apparent batch adsorption-desorption nonsingularity, {omega}, and half-cell Deff nonsingularity, H.



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  		Fig. 8. (a) Half-cells nonsingularity, H (Eq. [9]), as a function of batch nonsingularity, {omega} (Eq. [8]), the broken line is the linear correlation and the dotted line is the linear correlation forced through (1.0, 1.0) and (b) Half-cells nonsingularity, H, as a function of adsorption isotherm nonlinearity, n'A, the broken line is the linear correlation and the dotted line is the linear correlation forced through (1.0, 1.0). Error bars represent standard deviation.

 

   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 THEORY
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
The influence of sorption nonlinearity and nonequilibrium on diffusive transport of naphthalene and the possibility of linking naphthalene sorption parameters obtained in batch experiments to naphthalene effective diffusion in half-cell experiments were evaluated. Generally, if nonlinear adsorption, slow adsorption and apparent adsorption-desorption nonsingularity were observed in batch sorption experiments, this was also observed in the half-cell effective diffusion experiments. However, the adsorption and desorption isotherm parameters obtained in batch experiments were not in all cases useful to estimate the effective naphthalene diffusion coefficient from the half-cell experiments, in part because of the very different experimental conditions occurring in batch desorption experiments compared with half-cell effective diffusion experiments.

Good correlation was observed between the Freundlich adsorption nonlinearity parameter n'A and the adsorption-desorption nonsingularity parameter {omega}. Furthermore, good correlation between n'A and half-cell Deff nonsingularity was observed. This indicates that an estimate of the possible degree of batch desorption nonsingularity as well as half-cell desorption nonsingularity can be obtained merely from the nonlinearity of the measured adsorption isotherm.


   ACKNOWLEDGMENTS
 
This study was supported by the European Doctorate School of Technology and Science at Aalborg University and the Danish Technical Research Council, Research Talent Project entitled: "New methods for measuring and predicting liquid and gaseous phase transport properties in undisturbed soils"; Grant 5P42ESO4699 from the National Institute of Environmental Health Sciences, NIH, at U.C. Davis, The Danish-American Fulbright Commision, Copenhagen, Denmark and the Japanese Ministry of Education, Science, Sports and Culture (Monbushu International Scientific Research Programme: Joint Research no. 12555156). The contents of this publication are solely the responsibility of the authors and do not necessarily represent the official view of the NIEHS, NIH, or EPA. We thank Dianne Louie, Mathew Quork, Atac Tuli and Michael Whiting, Dep. of Land, Air and Water Resources, U.C. Davis, for their assistance in experimental phases of this work.

Received for publication December 31, 2001.


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




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