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Published in Soil Sci. Soc. Am. J. 69:311-317 (2005).
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

Division S-1—Soil Physics

Equilibrium and Nonequilibrium Transport of Boron in Soil

G. Communar and R. Keren*

Institute of Soil, Water and Environmental Sciences, the Volcani Center, Agricultural Research Organization (ARO), P.O. Box 6, Bet Dagan 50250, Israel

* Corresponding author (rkeren{at}agri.gov.il)


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Though B adsorption on soil is considered to be reversible and rapid, the use of models based on the assumption of local equilibrium often provide poor descriptions of B transport in soil columns. This study was conducted to reconcile inconsistencies between the findings of transport and batch-adsorption experiments. The B displacement experiments in the loamy sand soil were conducted at various pH values (6.9, 8.3, and 9.3) and pore-water velocities (3.6 and 0.16 cm h–1). The B transport in soil was strongly controlled by the pH-dependent and rate-limited adsorption (the soil heterogeneity was insignificant). The impact of rate-limited adsorption was dependent on pore-water velocity. The two-site (local equilibrium–nonequilibrium [LE–NE]) model accounting for the existence of equilibrium and nonequilibrium adsorption sites was used to describe nonideal transport of B in loamy sand soil. The Keren's phenomenological equation was used to simulate B adsorption on equilibrium sites and the Langmuir rate equation was applied for the rate-limited sites. The B adsorption parameters in the model were obtained from batch experiments. The fraction parameter f (representing the fraction of soil in which B adsorption is assumed to be rate-limited) and the dimensionless rate coefficients {gamma}0 (the Damkohler number) for B adsorption–desorption reactions were calculated by fitting the LE–NE model to the breakthrough curves (BTCs) for B measured from the fast-velocity experiments. The fraction parameter was >0.9, indicating that most of B adsorption sites on the loamy sand soil are rate-limited. The {gamma}0 values calculated from B adsorption BTCs were greater than that for desorption, indicating that hysteresis in B adsorption–desorption processes can be observed during nonequilibrium B transport in soil. The LE–NE model well reproduced the general B transport behavior in the soil over the observed pH and velocity ranges.

Abbreviations: BTC, breakthrough curve • LE, local equilibrium • LE–NE, local equilibrium-nonequilibrium • NE, nonequilibrium • SAR, sodium adsorption ratio


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
IN PART 1 of this study (Communar et al., 2004), the B transport in loamy sand soil was simulated combining the Keren's phenomenological equation (Keren et al., 1981) with a one-dimensional convection-dispersion equation. This model was successful in prediction of B transport behavior when the displacement experiments were conducted with relatively small water flow rates. With higher water flow rates, the B transport occurred under nonequilibrium conditions, and predictions based on the local equilibrium approach overestimated the B adsorption. The present study continued a previous investigation of B transport in the loamy sand soil at various pH values and water flow rates.

There is considerable evidence that B retention by soil is a rate-limited process (Couch and Grim, 1968; Griffin and Burau, 1974; Sharma et al., 1989; Keren et al., 1994). Couch and Grim (1968) proposed a two-step mechanism for B retention where a rapid chemical adsorption was followed by a slow diffusion of B into the clay mineral. Griffin and Burau (1974) and Sharma et al. (1989) observed a slow B desorption from soil and assumed that it could be due to a slow B diffusion from the interior surfaces of clay mineral to the solution phase. Keren et al. (1994) showed, however, that B adsorption coefficient calculated from kinetic experiments well agreed with those obtained from static batch experiments. Such an agreement may indicate that B adsorption on clay surfaces is reversible process. In batch experiments, 2 h was enough to reach B apparent equilibrium (Mezuman and Keren, 1981). A longer residence time, however, can be required to achieve B equilibrium in soil system characterized by physical (van Genuchten and Wierenga, 1976) or chemical (Selim et al., 1976; Cameron and Klute, 1977) heterogeneity.

The effect of pH on B adsorption is well known (Keren and Bingham, 1985) and its impact on B transport in loamy sand soil under equilibrium condition was illustrated by Communar et al. (2004). No information is available, however, on pH dependent nonequilibrium B in soils. The two-site approach (Selim et al., 1976; Cameron and Klute, 1977) accounting for the existence of equilibrium and nonequilibrium adsorption sites was used in this study to describe B transport in loamy sand soil at various water flow velocities and pH values. In this model, B adsorption on equilibrium sites was simulated using the Keren's phenomenological equation whereas the Langmuir rate equation was applied to describe B adsorption on nonequilibrium sites.

The objective of this study was, therefore, to evaluate the effects of water flow velocity and pH on nonequilibrium B transport in soil.


   MATERIALS AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Soil Description
Hamra, a loamy sand soil (Rhodoxeralf) from the coastal plain of Israel was used in this study. The soil material consisted predominately of sand with discrete inclusion of clay minerals. The average sand, silt, and clay fractions were 85.4, 9.1, and 5.4%, respectively and the organic C content was 0.06%. The pH (for a 1:1 soil/water ratio) was 6.9. Analysis did not detect B in the soil. The soil was dried in an oven at 40°C and passed through a 2-mm sieve before use.

Batch Experiments
Boron adsorption on the loamy sand soil was determined previously by Communar et al. (2004). Boron adsorption experiments were performed in batch systems using 50-mL polypropylene centrifuge tubes containing 15-g soil samples and 35 mL of background solution at total CaCl2 + NaCl concentration of 20 mmolc L–1 and sodium adsorption ratio (SAR) of 6, pH values of 7, 8.5, and 10, and at a temperature of 25 ± 2°C. Before B addition, the soil suspensions were adjusted to the various target pH values by successive washings with a background solution at each pH level. After centrifugation and removal of the supernatant, the background solutions at appropriate pHs were added to the soil samples at initial B concentrations ranging from 0.5 to 25 mg L–1 and were shaken for 5 d. Following equilibration, the samples were centrifuged and filtered, and separate aliquots of the supernatant were analyzed for B using ICP emission spectrometry.

Transport Experiments
To accomplish the objective mentioned above, miscible displacement experiments were conducted to investigate a rate-limited adsorption and transport of B in soil columns.

The transport experiments were conducted in plastic columns with an inside diameter of 5.2 cm and length of 10 cm at room temperature (25 ± 2°C). The columns were uniformly packed with the soil in 1-cm increments. Each increment was tapped firmly to achieve homogeneous packing and uniform bulk density of 1.37 g cm–3 (porosity of soil was 0.48). The surface of the packed soil was slightly disturbed before each new addition to ensure continuity. The columns were connected to a peristaltic pump and slowly saturated from the bottom with the background solution that was used for the batch experiments. Before the B adsorption–desorption studies, the soil columns of Series G, H, and K were adjusted to pH 6.9, 8.3, and 9.3, respectively. The soil pH adjustment was continued until a steady state was reached, with respect to pH. The pH in the columns was monitored with a pH meter during their adjustment. Bromide was used in this study as a tracer and the BTCs for Br– and B were generated from the soil columns at pore-water velocities of 3.6 or 0.16 cm h–1. Water saturation and steady-state flow conditions were satisfied during the displacement experiments and each column experiment was conducted in duplicate. The experiments on columns G1 (pH 6.9), H (pH 8.3), and K1 (pH 9.3) were conducted at pore-water velocity 3.6 cm h–1. The background solution (at pH 6.9, 8.3, and 9.3) containing 5 mg L–1 of B was introduced into the columns (G1, H, and K1, respectively) till the B concentration in the effluent equaled the initial B concentration. At this time, the leaching solution was replaced with the B-free background solution (at the same pH) to observe B desorption. A pulse injection experiment on Columns G2 (pH 6.9) and K2 (pH 9.3) were conducted at two pore-water velocities (3.6 and 0.16 cm h–1). A pulse of B-containing background solution (at pH 6.9 and 9.3 and B concentration of 20 mg L–1) was injected into Columns G2 and K2, respectively. Once the pulse was injected the columns were flushed with the B-free background solution (at the same pH).

Effluent samples were collected by a fraction collector, the solution volume was measured and solution samples were analyzed for B by ICP–AES and the Br concentration was determined by ion chromatography.

Models and Computations
Equilibrium and Rate-limited Boron Adsorption Model
The B species formation in the solutions and competitive adsorption of B(OH)3, B–4, and OH– ions on the soil surface were simulated by the use of the following reactions

[1]

[2]
where ci (mg L–1) and bi (mg kg–1) with index i = 1, 2, 3 denote the concentrations of B(OH)3, B–4 species and OH–, in the dissolved and adsorbed phases, respectively, k+i and k–i are the forward and backward rate coefficients for the corresponding surface reactions and SOH is the amount of vacant sites on the soil surface, defined as

[3]
where bm (mg kg–1) is the apparent maximum B adsorption. The concentrations of the B species in the solution can be specified as (Keren et al., 1994)

[4]
where c is the total B concentration in the solution (mg L–1) and A {cong} Kh x 1014c3, Kh is the B hydrolysis constant (Kh = 5.9 x 10–10 at 298 K) and c3 (= cOH) is the concentration of OH– ions in the solution that is calculated from the solution pH.

On the basis of the mass action Eq. [2], the temporal change of the concentrations ci and bi, ignoring activity corrections, can be described by the following rate equations (Keren et al., 1994)

[5]
where t is time, k+i is the forward rate coefficients of the reaction (L mg–1 h–1) and k–i is the corresponding backward reaction rate coefficient (h–1). At t -> {infty}, that is, when the local equilibrium is achieved, Eq. [5] leads to

[6]
where ki = k+i/k–i with index i = 1, 2, and 3 is the adsorption coefficient kBH, kB–, and kOH for B(OH)3, B–4, and OH–, respectively. Combination of Eq. [3] and [6] for i = 1, 2 yields the competitive isotherm for B adsorption (Keren et al., 1981), which after elimination of concentrations c1 and c2 (with the use of Eq. [4]) may be written in a compact form (Communar et al., 2004)

[7]
where b(= b1 + b2) is the total amount of adsorbed B and k (L mg–1) is the pH-dependent apparent adsorption coefficient defined as

[8]

Note that Eq. [7] with the pH-dependent adsorption coefficient k (Eq. [8]) presents a compact form of the Keren's phenomenological equation. To describe the B adsorption dynamics, let us combine Eq. [5] for i = 1 and 2. Then, the resulting rate equation, after elimination of concentrations c1 and c2 and replacement of term SOH by its expression

[9]
can be written as

[10]
where k is the adsorption coefficient defined by Eq. [8]. Equation [10] can be further simplified by assuming that the difference between the backward rate coefficients k–1 and k–2 for the species B(OH)3 and B–4, respectively, is small (i.e., k–1 {cong} k–2). In this case, Eq. [10] can be written as

[11]
where {gamma} is the experimentally measured rate constant (h–1) for B adsorption–desorption reactions. The coefficients k and bm in Eq. [11] are the same as defined by the Keren's equation. Rate equations similar to Eq. [11] have been used by a number of investigators (Heister and Vermuelen, 1952; Grove and Stollenwerk, 1985; Bahr and Rubin, 1987; Bahr, 1990).

Several different formulations were used to simulate the interactions between B and the solid phase. The amount of B adsorbed by soil was expressed as (Selim et al., 1976)

[12]
where bE and bK are the concentrations of the B species at equilibrium and rate-limited adsorption sites, respectively, and f is the fraction of soil for which B sorption is assumed to be rate-limited. The concentrations bE and bK in Eq. [12] are described by the use of Eq. [7] and [11], respectively. It is assumed that coefficients bm and k have identical values for both adsorption sites. In this case, Eq. [12] obeys the Langmuir isotherm (Eq. [7]), if the B adsorption equilibrium is reached. A similar assumption was used by Selim et al. (1976) for linear adsorption and Selim and Amacher (1988) and Barnett et al. (2000) for Langmuir and Freundlich type reactions.

Transport Model
The transport of the B species in homogeneous soil columns was described using the one-dimensional convection–dispersion equation (CDE), written in the following dimensionless form

[13]
where Z = z/L is the dimensionless distance measured from the column entrance (z is the distance and L is the column length), T = t/t0 is the dimensionless time or the number of pore volumes leached through a column (t0 = L/u is the residence time in the column and u is the pore-water velocity), Pe = uL/D is the Peclet number (D {cong} {lambda}|u| is the dispersion coefficient [cm2 h–1] and {lambda} (cm) is the pore-scale dispersivity of the porous media), p0 = {rho}b0/{theta}c0 is constant ({theta} is the volumetric water content and {rho} [g cm–3] is the dry soil bulk density). In this equation, = c/c0 and = b/b0 are the dimensionless concentrations, where c0 is the input B concentration of solute and b0 = f(c0) is the B capacity of the soil that is reached at saturation with the concentration c0

[14]
where k0 = kc0, and RE is the equivalent retardation factor for equilibrium adsorption sites

[15]

The dimensionless concentration E and K are now defined by the following equations

[16]
and

[17]
where {gamma}0 = {gamma}t0 is the dimensionless rate coefficient (the Damkohler number representing a ratio of hydraulic residence time to reaction time).

Equations [13] and [17] represent the two-site model (LE-NE) for equilibrium-nonequilibrium surface adsorption. When the fraction parameter, f -> 1, the LE-NE model converges to the one-site nonequilibrium (NE) model (Grove and Stollenwerk, 1985; Bahr and Rubin, 1987). When f -> 0 or if the dimensionless rate coefficient, {gamma}0, is large enough, the model converges to the local equilibrium (LE) model.

For the purpose of simulation and model evaluation, the appropriate initial and boundary conditions were stated as follows. The conditions postulating uniform initial distribution of the concentrations and in a finite soil column were used

[18]
when simulating the B adsorption or B desorption process separately. For a continuous solution input, the boundary condition at z = 0 was written as

[19]

To simulate B transport in soil column under pulse injection, the boundary condition [19] was replaced by

[20]
where Tp is the pulse size measured in pore volumes. For all cases, the boundary condition at z = L was

[21]

The governing Eq. [13], [16] and [17] subject to the above initial and boundary conditions were solved numerically using the Crank–Nicholson technique.

Model Parameters Estimation
The LE–NE model contains the following independent parameters p0, k0, f, {gamma}0, and Pe. The B adsorption coefficients were calculated from the adsorption isotherms (batch experiment). The procedure used to calculate the coefficients bm, kBH, kB–kOH of the Keren's phenomenological equation is given by Communar et al. (2004). The values of bm and k for Eq. [7] were evaluated by plotting c/b data versus c at each pH and Eq. [8] was then used to calculate the magnitudes of the coefficients kBH, kB–, and kOH from a set of k–pH values. The values for p0(= {rho}b0/{theta}c0) and k0(= kc0) were calculated from these data for the given solution pH and B concentration. All the BTCs for Br– (figures not shown) obtained from the homogeneously packed columns were essentially symmetrical, indicating ideal transport behavior. Accordingly, these BTCs could be interpreted using the analytical solution of the classical CDE with a retardation factor R(= 1 + {rho}KL/{theta}, where KL(L mg–1) is the distribution coefficient for linear adsorption). Best-fit model parameters for R and D were obtained by use of the nonlinear least squares optimization method. The agreement between the calculated and the experimental concentrations was estimated from minimization of the function {Phi}

[22]
where and are the measured and calculated values of the relative concentration at time Tl, and N is the number of data points. The retardation factors for the soil columns were ranged from 0.96 to 1.04. This indicates that the impact of physical heterogeneity of the soil (mobile–immobile domains) on Br– transport was insignificant. Best-fit values for D were dependent on pore-water velocity u but the ratio D/u {approx} {lambda} remained practically invariable (an average {lambda} value was equal 0.256 cm) in the range of the flow rates used in these experiments. Thus the Peclet number (Pe {cong} L/{lambda}) of 39 was fixed and only two parameters f and {gamma}0 were optimized from the nonlinear curve-fitting procedure when simulating the BTCs for B.


   RESULTS AND DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
The B adsorption isotherms determined at pH values of 7, 8.5, and 10 are shown in Fig. 1 (solid circles) and the best-fit values for the adsorption coefficients bm, kBH, kB–, and kOH are given in Table 1. Note that the B adsorption capacity and the affinity coefficients for B–4, B(OH)3 species, and OH– are independent on pH in the studied range. The order of the affinity coefficients values is B3 < B–4 < OH–. This sequence is in accordance with that reported by Keren and Bingham (1985) for various soils and clays. It was found (Communar et al., 2004) that B adsorption on this soil increases as the pH increases from 7 to 9.3 and then decreases at higher pH values. Similar behavior was observed for clay (Keren et al., 1981; Keren and Mezuman, 1981; Goldberg and Glaubig, 1985, 1986) and soils (Mezuman and Keren, 1981; Goldberg et al., 2000). The solid lines in Fig. 1 were calculated using Eq. [7] and [8] and the B adsorption coefficients bm, kBH, kB–, and kOH (Table 1). The good agreement between the experimental results and the calculated values indicates that these equations provide an accurate description of pH-dependent B adsorption on the given soil.



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  		Fig. 1. Boron adsorption isotherms for the soil, adjusted to three pH values of the background solution, at a total (CaCl2 + NaCl) concentration of 20 mmolc L–1 and sodium adsorption ratio (SAR) of 6. Experimental points and calculated lines are presented.

 

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  		Table 1. Sorption coefficients of the isotherm equation.{dagger}

 
The maximum B adsorption by the soil was obtained at pH 9.3 (Communar et al., 2004). Therefore, the column experiments in the present study were conducted at the pH range of 6.9 to 9.3. The dynamics of the adjustment of the soil columns to the various pHs are presented in Fig. 2. In general, the buffer capacity of the soil was relatively high, so that the effluent pH did not change until after 190 and 130 pore volumes of the solution at pH 8.3 and 9.3, respectively, had been leached from the columns of Series H and K. Thereafter, the pH values increased rapidly to the steady-state values of 8.3 and 9.3. Under these conditions, the soil-solution pH can be considered as a constant rather than as an independent variable.



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  		Fig. 2. Dynamics of the adjustment of the soil columns to the various pHs.

 
The conditions for B displacement experiments are given in Table 2. The BTCs for B obtained from the Columns G1 (pH 6.9), H (pH 8.3), and K1 (pH 9.3) at pore-water velocity of 3.6 cm h–1 are shown in Fig. 3a, 3b, and 3c, respectively. The adsorption and desorption BTCs indicated that B retardation was affected by pH: the higher the pH, the greater the retardation. Predictions of the experimental BTCs (dashed curves in Fig. 3) based on the LE model and the batch isotherms parameters overestimated the B adsorption. Boron concentration appeared in the effluent much earlier than the predicted and the experimental BTCs showed tailing at high and low B concentrations during adsorption and desorption, respectively. A possible reason for the discrepancy between the predicted and measured BTCs is the occurrence of nonequilibrium (i.e., rate-limited) adsorption and/or desorption, which could be caused by the relatively short residence time (t0 = 2.77 h) of the solution in the columns in these fast-velocity experiments. A reasonable agreement between the simulated and experimental BTCs was obtained when using the LE-NE model. Best-fit values for f and {gamma}0 are listed in Table 2. The calculated f values are larger than 0.9, indicating that most of the adsorption sites on the soil surface are rate-limited.


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  		Table 2. Experimental conditions of column experiments and best-fit values for B adsorption–desorption rate coefficients.{dagger}

 


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  		Fig. 3. Measured, predicted and fitted breakthrough curves for B adsorption and desorption on Columns (a) G1, (b) H, and (c) K1 at water flow rates u of 3.6 cm h–1. Dashed lines represent predictions made by using the LE model and the batch-measured isotherm parameters (Table 1) and solid lines were obtained by fitting the LE–NE model to the experimental breakthrough curves (best fit values for f and {gamma}0 are given in Tables 2).

 
The dominant B species in the solution over the pH range 6.9 to 8.3 was B(OH)3 whereas at pH 9.3 the solution contained both species, B–4 and B(OH)3, in approximately equal concentrations. However, the coefficients {gamma}0 (Table 1) calculated from B adsorption and desorption BTCs were independent of pH. For example, the dimensionless rate coefficients {gamma}0 obtained from the B adsorption BTCs for the Columns G1, H and K1 with the initial pH of 6.9, 8.3 and 9.3, were ranged from 3.8 to 4.2 (average value of 4) and those obtained from the B desorption BTCs were ranged from 1.6 to 1.9 (average value of 1.7). Such pH-independence of {gamma}0 indicates that kinetic equation (Eq. [11]) with the apparent pH-dependent adsorption coefficient k (Eq. [8]) well simulates the pH effect on B adsorption process. The dimensionless coefficient {gamma}0 reflects the adsorption–desorption rate. The average value for the B adsorption rate coefficient was about 2.3 times greater than the average value for desorption. In accordance with Keren et al. (1994), this indicates that the B adsorption reaction is faster than the B desorption reaction. The B BTCs shown in Fig. 4a, 4b, and 4c were obtained by combining the data given in Fig. 3a, 3b, and 3c, respectively, and specifying a pulse of duration Tp. The solid lines in Fig. 4 represent the predictions made by the use of the LE–NE model for an average value of adsorption–desorption rate coefficient, {gamma}0 = 2.85 and the pulse duration Tp of 5.85, 6.95, and 8.1, for Columns G1 (pH 6.9), H (pH 8.3), and K1 (pH 9.3), respectively. Figure 4 illustrates that the resulted BTCs are essentially asymmetrical for all pH values; the asymmetry of the BTCs increases as the pH increases (since the nonlinearity of the B adsorption isotherms becomes greater at higher values pH). One can see that the adsorption slope of the experimental BTCs was well predicted but a small deviation was observed for the desorption part. This deviation is due to the slower rate of B desorption than adsorption.



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  		Fig. 4. Measured and predicted breakthrough curves for the transport of B in columns a) G1, b) H, and c) K1 under pulse injection conditions. Observed data points were taken from Fig. 3. Predictions were made by using the LE-NE model and an average rate coefficient {gamma}0 = 2.85. A pulse durations Tp = 5.85, 6.95, and 8.1 were used to simulate the experimental breakthrough curves from columns G1 (pH 6.9), H (pH 8.3), and K1 (pH 9.3), respectively.

 
Jennings and Kirkner (1984) and Bahr and Rubin (1987) noted that the use of the LE model might be justified when {gamma}0 value exceeds 10. The greater the {gamma}0 value the smaller is the deviation from equilibrium; a complete coincidence between the LE and NE models is reached only in {gamma}0 of 100 and more. The calculated {gamma}0 value of 2.85 was smaller than that satisfying the local equilibrium assumption. This explains why the LE model was unable to accurately predict the experimental data shown in Fig. 3. Water flow velocity is an important variable affecting the time-scale of column experiments (James and Rubin, 1979) and the resulted value of {gamma}0. The effect of water flow velocity on B transport in the soil is illustrated in Fig. 5. The BTCs shown in Fig. 5 were obtained from the soil Columns G2, K2, and G3, K3 at a short pulse-injection duration (Tp = 0.8) for two pore-water velocities 3.6 and 0.16 cm h–1, respectively. When the LE–NE model was used to simulate the fast-velocity experiments (Columns G2 and K2), the best-fit value of {gamma}0 was 3.5. This value is not significantly different from the average {gamma}0 value of 2.85 estimated for the continuously B transport experiments (Fig. 3), which were conducted under the same conditions except the input B concentration (5 versus 20 mg L–1). This indicates that the coefficient {gamma}0 is independent of B concentration in the soil solution. The pore-water velocity u = 0.16 cm h–1 for the slow-velocity experiments (Columns G3 and K3) was chosen so that the calculated coefficient {gamma}0 exceeds the lower criterion value for the Damkohler number of 10. At {gamma}0 = 1.7 for B desorption obtained from the continuous injection experiments conducted at u = 3.6 cm h–1 (t0 = 2.78 h), the rate coefficient {gamma} (Eq. [11]) is 0.62 h–1. At u = 0.16 cm h–1 (t0 = 62.5 h), the calculated velocity-corrected {gamma}0 value was 39. The predictions (solid lines in Fig. 5) made by using the LE–NE model and this {gamma}0 value agreed well with the experimental BTCs (open circles) determined at pH values of 6.9 and 9.3.



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  		Fig. 5. Measured, fitted and predicted breakthrough curves for the transport of B in columns G2, 3 (pH 6.9) and K2, 3 (pH 9.3) at pore water velocity u of 3.6 and 0.16 cm h–1, respectively, under pulse injection conditions (Tp = 0.8). Solid lines represent BTCs obtained by the fitting the LE-NE model to the experimental data (at u = 3.6 cm h–1) ({gamma}0 = 3.5 was obtained) and dashed lines represent predictions of the experimental data (at u = 0.16 cm h–1) by using the LE-NE model and {gamma}0 value of 39.

 
Note that at f values reported in this study, the LE–NE model give results very similar to those of the NE model. Besides, the LE model could be used to predict the BTCs at slow-velocity (Fig. 5) since the rate-limited B adsorption at {gamma}0 value of 39 approached equilibrium.


   CONCLUSIONS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
The results indicate that physical heterogeneity of the loamy sand soil was insignificant (the Br– transport was an ideal approach) and that the nonequilibrium transport of the B species was controlled by rate-limited adsorption. Using the B adsorption parameters obtained from the batch experiment, the LE–NE model accounting for the existence of equilibrium and nonequilibrium adsorption sites accurately described the general behavior of the B species in the soil at the pH range from 6.9 to 9.3 at two pore-water velocities, 3.6 and 0.16 cm h–1. The impact of the rate-limited adsorption on B transport in the soil was dependent on pore-water velocity. The fraction parameter f and the dimensionless rate coefficient {gamma}0 were calculated by fitting the LE–NE model to the BTCs for B measured from the fast-velocity experiments. It was found that most of adsorption sites on the soil surface are rate-limited since the f values were >0.9. The {gamma}0 values were independent on pH, indicating that the Langmuir rate equation incorporating the pH-dependent adsorption coefficient well reproduces the pH effect on the B transport in the soil. The rate of B adsorption was higher than that of B desorption. Under these conditions, hysteresis in B adsorption–desorption processes can be observed during nonequilibrium B transport. Since the rate coefficients for the B adsorption–desorption reactions reported in this study were substantially large, it was possible to select the hydrodynamic conditions (the pore-water velocity and the residence time for solution in the columns) at which B transport in the soil approaches equilibrium.


   ACKNOWLEDGMENTS
 
This research was supported in part by a grant from the Ministry of Science, Culture and Sport, and a grant from the Chief Scientist, Ministry of Agriculture and Rural Development, Israel.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Contribution from the Institute of Soil, Water and Environmental Sciences, the Volcani Center, Agricultural Research Organization (ARO), P.O. Box 6, Bet Dagan 50250, Israel. No. 613/04 Series.

Received for publication May 18, 2004.


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




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The SCI Journals Agronomy Journal Crop Science
Vadose Zone Journal Journal of Plant Registrations
Journal of Natural Resources
and Life Sciences Education		 Journal of
Environmental Quality