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Soil Physics

Rate-Limited Boron Transport in Soils: The Effect of Soil Texture and Solution pH

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 THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION REFERENCES

 
Although boron (B) adsorption significantly depends on soil texture and pH, few attempts have been made to estimate their influence on B transport behavior. Adsorption and transport of B in three soils of different textures were investigated in batch and column experiments. The B adsorption on the soils in batch experiments was rapid and an apparent adsorption equilibrium was reached over the first several hours. The extent of adsorption on each of the soils was strongly dependent on pH, increasing sharply as the pH increased from 7.0 to 9.2–9.4. The Langmuir equation with the pH-dependent adsorption coefficient simulated well the B adsorption at equilibrium. Miscible-displacement experiments were conducted at two water fluxes of 2.9 and 0.19 cm h^–1 and at two pH values. The transport of B through the soil columns was retarded. The retardation increased with the increase of clay content and solution pH. The impact of the rate-limited adsorption on B transport was dependent on water flux and was controlled by mass-transfer processes. The B breakthrough curves (BTCs) for the loamy sand and sandy loam soils (where Br^– transport was ideal) were simulated using the ideal-transport-based (local equilibrium-nonequilibrium [LE-NE]) model. This model successfully described B transport at different water fluxes and pH values when using the adsorption parameters derived from batch equilibrium experiments. The adsorption rate coefficient values obtained from BTCs were smaller than those obtained from the batch kinetic data. The non-ideal transport behavior of B in the clay soil was associated with intra-aggregate and rate-limited adsorption in the mobile domain. A successful simulation of B BTCs for this soil for the two aggregate sizes (<2 and 4–4.75 mm) was obtained when used the two-domain, two-rate (TD-TR) model. The results indicate that the influence of rate-limited adsorption on NE B behavior was more pronounced at fast than at slow water flux. However, at slow water flux, the rate-limited adsorption had a secondary importance in comparison with the rate-limited mass-transfer between mobile and immobile water domains.

Abbreviations: BTC, breakthrough curve • CDE, convection-dispersion equation • LE, local equilibrium • LE-NE, local equilibrium-nonequilibrium • NE, nonequilibrium • TD, two-domain • TD-TR, two-domain, two-rate

	INTRODUCTION

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

 
BORON is an essential element for normal plant growth but the range between B concentrations in soil solution causing deficiency or toxicity symptoms in plants is relatively narrow (Keren and Bingham, 1985). Boron is readily adsorbed by soils and adsorbed B being unavailable to plants is considered not to be toxic (Keren and Bingham, 1985). The extent of boron adsorption depends on solution pH, mineral soil composition, and texture. Boron can be effectively leached from soil although the rate of removal is much slower for B than for non-reacting elements (Bingham et al., 1972). Batch and column displacement experiments are used to investigate the mechanisms responsible for B retention and transport in soils. Mathematical models accounting for the impact of different factors on B adsorption and transport in soils have been developed (Corwin et al., 1999, Shani et al., 1992; Communar et al., 2004). These models used adsorption isotherms obtained from batch experiments assuming that B interaction with the solid phase of the soil is rapid in comparison with the residence time (i.e., the condition of a local equilibrium [LE] is satisfied). It was found, however, that the LE models described B transport well for a homogeneous loamy sand soil only at low pore-water velocities but failed at fast velocities (Communar et al., 2004). Moreover, it was shown that the fast-velocity BTCs were significantly asymmetric and exhibited a faster spreading on B in comparison to those obtained at a slow velocity. Rate-limited B adsorption has been recognized as one of the reasons for a NE B behavior for this particular soil.

Two different approaches are commonly used to model adsorption NE for homogeneous soils. In the first approach, adsorption sites are arranged in series. Boron adsorption on these sites may include a rate-limited mass transfer and a rate-limited interaction between the adsorbed species and soil constituents. A two-step B retention mechanism where surface adsorption is followed by a slow diffusion of B into the crystal lattice of clay mineral was discussed by Couch and Grim (1968) and transport model accounting for such adsorption mechanism has been proposed by Streck et al. (1995). The lack of reversibility of B adsorption/desorption reactions may be due to B diffusion into or from the clay mineral (Griffin and Burau, 1974; Sharma et al., 1989). It was found, however, that the B intrusion into the soil clay mineral is negligible (Keren et al., 1994) in comparison with the B retention on soil-particle-surfaces and in micropores of individual particles. Therefore, B adsorption on soil constituents can be simulated assuming that these two types of sites are arranged in parallel (Selim et al., 1976; Cameron and Klute, 1977). Based on this assumption, a LE-NE model was used by Communar and Keren (2005) to simulate B transport for loamy sand soil. This model was based on the classical convection-dispersion equation (CDE) with source/sink terms accounting for the existence of equilibrium and NE adsorption sites on soil surface. Adsorption of B species on equilibrium sites was simulated using the Langmuir equation with the pH-dependent adsorption coefficient and the kinetic Langmuir type equation with the rate coefficient being mass-transfer coefficient was applied to NE sites. It was found that the LE-NE model successfully predicted B transport in loamy sand soil at various flow rates and pH values. No attempts have been made, however, for its application to other textures of homogeneous soils.

Numerous miscible displacement experiments (Nkedi-Kizza et al., 1982, 1984; Brusseau et al., 1989; Johnson et al., 2003) have shown that slow down of adsorption reactions in parked soil columns may be related to diffusion mass-transfer processes and that influence of these processes become more significant with the increase of physical heterogeneity of soils. It is clear that the typical homogeneous approach (like that used in the LE-NE model) is unable to account for the effect of porous-media structure on B transport behavior. A two-domain (TD) mobile-immobile approach was proposed by Coats and Smith (1964) to simulate solute transport in non-homogeneous soils. In this approach, soil water is partitioned into mobile and immobile phases and mass transfer between the phases is assumed to be proportional to concentration gradients. van Genuchten and Wierenga (1976) applied this approach to the transport of reacting solutes assuming that adsorption occurs instantaneously in the two soil regions. In this case, the NE behavior of solute is controlled by retarded intra-aggregate diffusion (i.e., by solute diffusion into the stagnant soil region with retardation caused by instantaneous adsorption on the soil surface). The adsorption model of van Genuchten–Wierenga has been successfully used to describe NE solute transport in aggregated soils (van Genuchten and Wierenga, 1977; Nkedi-Kizza et al., 1982, 1984; Johnson et al., 2003). It is questionable, however, whether this model is appropriate for simulating B transport in such soils when rate-limited B adsorption process occur in the sites associate with the mobile domain.

The objective of the present study was to evaluate the effect of soil texture and pH on B adsorption and transport in soils using the LE-NE and TD-TR models.

	THEORY

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

 
Sorption Models
Our basic assumption is that sites available for B adsorption are uniformly distributed through the soil matrix and that the matrix contains two types of adsorption sites: Type 1 on which B adsorption is a rate-limited process, and Type 2 on which B adsorption is always at equilibrium. In this case, the total amount of B adsorbed by a soil can be expressed as

[1]

where b₁ and b₂ are the B concentrations associated with the equilibrium and rate-limited sites, respectively, and f is the fraction of sites for which B adsorption is considered to be rate-limited. A rate-limited B adsorption (concentration b₁) is described by using the Langmuir rate equation (Communar and Keren, 2005)

[2]

Here, c and b are the total B concentrations in the liquid (mg L^–1) and in the solid (mg kg^–1) phases, respectively, b_m is the maximum B adsorption (mg kg^–1), k is the adsorption coefficient (L mg^–1), is the experimentally measured mass-transfer coefficient (h^–1) that reflects the B retention in micropores of individual particles, and t is time (h). The Langmuir isotherm corresponding to this reaction is used to describe B adsorption (concentration b₂) at equilibrium

[3]

In Eq. [2] and [3], c = c_BH + c_B^– and b = b_BH + b_B^–, where c_BH, c_B^– denote the concentrations of the B species, B(OH)₃⁰ and B(OH)₄^– in the liquid phases, b_BH, b_B^–, respectively, are the concentrations of the B species in the adsorbed phases and k is the pH-dependent adsorption coefficient (L mg^–1), defined as (Communar et al., 2004)

[4]

where k_BH, k_B^–, and k_OH are the affinity coefficients of the B species B(OH)₃⁰ and B(OH)₄^–, and of OH^–, respectively, A = K_h (10⁴ c_OH) is the pH-dependent coefficient since c_OH is the solution OH^– concentration and K_h = 5.9 x 10^–10 is the B hydrolysis constant at 298 K. Note that the Langmuir equation (Eq. [3]) with pH-dependent adsorption coefficient (Eq. [4]) represents the phenomenological equation of Keren et al. (1981) for equilibrium B adsorption.

Transport Models
For convenience, we define the dimensionless variables, = c/c₀ and = b/b₀, which represent the relative B concentrations in the liquid and the solid phases, respectively, where c₀ is the B concentration in the inlet solution, and b₀ = b_mkc₀ (1 + kc₀)^–1 is the B capacity at equilibrium with the concentration c₀. In terms of these variables, Eq. [2] is written as

[5]

and Eq. [3] becomes

[6]

where k₀ = kc₀. Based on the TD concept (Coats and Smith, 1964; van Genuchten and Wierenga, 1976), the transport of reacting solute, which is subjected to the rate-limited adsorption in the mobile domain, is defined by the following nondimensional equations

[7]

[8]

where the adsorption-desorption term (₁/T) for the dynamic soil region is described by Eq. [5] and an equivalent retardation factor R₂ for the stagnant soil region is defined as

[9]

where the term d₂/d₂ is obtained using Eq. [6]. The dimensionless variables in these equations are as follows

[10]

[11]

[12]

[13]

[14]

where q is the macroscopic Darcy water flux (cm h^–1), D (= |u|) is the longitudinal dispersion coefficient (cm² h^–1), is the pore-scale dispersivity of the porous media (cm), u (= q/₁) is the mean pore-water velocity (cm h^–1) defined for the mobile water domain, ₁₁ is the water content in the mobile domain, is the saturated water content, is the mass transfer coefficient (h^–1) between the mobile and immobile water domains, L is the column length (cm), p₀ (= b₀/c₀) is a constant, is the soil bulk density (g cm^–3), z is the distance measured from the column inlet (cm) and t is time (h). Here, Pe is the Peclet number, ₀ is the dimensionless rate coefficient for B adsorption in microporous particles (the Damkohler number, which represents a ratio of hydraulic residence time to reaction time), ₀ is the dimensionless mass transfer coefficient, and = ₁/ is the mobile water fraction.

In the proposed model, parameter f represents the fraction of sites (Eq. [1]) where the B adsorption is a rate-limited process and, therefore, we will refer to this model as the two-domain two-rate (TD-TR) model. This fraction parameter f is assumed to be mathematically equivalent to , where 0 1. Similar assumption has been widely used by others (Nkedi-Kizza et al., 1984; Selim et al., 1987; Selim and Ma, 1995).

For a specific case, when the rate coefficient ₀ is relatively large and exceeds the criterion for the Damkohler number, 10 for example (Jennings and Kirkner, 1984; Bahr and Rubin, 1987), the TD-TR model converges to the model proposed by van Genuchten and Wierenga (1976) in which an equilibrium adsorption in the mobile water domain is described by means of an equivalent retardation factor R₁

[15]

and the term ( ₁/T + fp_{0 1}/T) in Eq. [7] is expressed as R₁ /T.

When = 1 and the parameter f is in the range 0 f 1, the TD-TR model converges into the ideal-transport-based LE-NE model (Communar and Keren, 2005). In this case, an equivalent retardation factor R₂ (Eq. [9]) for the equilibrium sites is defined as

[16]

At an attainment of adsorption equilibrium at the rate-limited sites, an equivalent retardation factor R₁ becomes

[17]

and the LE-NE model results in the LE model, where the total retardation factor R (= R₁ + R₂) is defined as

[18]

The parameter f is absent in Eq. [18], indicating that when the LE condition is satisfied, the amount of B adsorbed by the soil depends solely on p₀ and k₀. Notice, that the LE-NE model also converges to the LE model, if f approaches 0, and when f approaches 1, the LE-NE is reduced to the NE model for one-site surface adsorption (Grove and Stollenwerk, 1985; Bahr and Rubin, 1987).

The governing equations associated with these model formulations were solved numerically using the Crank-Nicholson technique under the following initial and boundary conditions

[19]

[20]

where

[21]

[22]

where T_p is a pulse input duration.

	MATERIALS AND METHODS

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

 
Soil Description
The soils used in this study were: (i) Hamra, a loamy sand soil (Rhodoxeralf) from the coastal plain of Israel; (ii) a sandy loam soil (Haploxeralf) developed on wind-blown material, from the Sinai Desert; and (iii) a clay soil (Aquic Haploxerest) developed on basaltic alluvium. The loamy sand (Hamra) is the same soil as was used in our previous studies (Communar et al., 2004; Communar and Keren, 2005). Some characteristics of this soil along with the two other soils are presented in Table 1. These soils vary considerably with respect to texture but the predominant clay mineral in all of them is montmorillonite. The soil pH was determined at a water-soil ratio of 2:1. The oven-dried soils (40°C) were passed through a 2-mm sieve. In addition, aggregated with size 4.0 to 4.75 mm were selected from the clay soil and used in the column experiments.

View this table: [in this window] [in a new window]   Table 1. Characteristics of the soil used in the experiments.

Transport Experiments
Miscible-displacement experiments were conducted with Plexiglas columns, 12 cm in length and 5.2 cm in diameter. The loamy sand and sandy loam soils, both with particle size <2 mm were uniformly packed into Columns 1 through 4 and 5 through 8, respectively, and the clay soil with aggregates <2 mm and 4 to 4.75 mm was packed into Columns 9, 10 and 11, 12, respectively. To improve water saturation, uniformly packed soil columns were purged with CO₂. The soil columns were slowly saturated with the background solution that was used for the batch experiments. The solution was introduced from the bottom of the columns, and the saturation process continued for 2 wk. This procedure resulted in complete water saturation of all the soils. Prior to the displacement experiments, Columns 1, 2, 5, 6, and 9 through 12 were leached with the background solution at pH 7 whereas Columns 3, 4, 7, and 8 were leached with the solution at pH 9. The extractable B was leached from the sandy loam soil during the pH adjustment, and the leaching of the columns was continued until a steady state was reached with respect to solution composition, electrolyte concentration, and pH. The water flow velocity was controlled by a peristaltic pump, and effluent samples were collected with a fraction collector. The column experiments at each pH and each water flux were conducted in duplicate. Water saturation and steady-state flow conditions were satisfied during the displacement experiments. Bromide was used in this study as a tracer. The Br^– and B concentration in the input solutions were 10 and 5 mg L^–1, respectively, and the BTCs for Br^–, and B were generated from the columns at two water fluxes of 2.9 and 0.19 cm h^–1. Each B BTC from a soil column was obtained by introducing a B pulse followed by several pore volumes (PV) of boron-free solutions. The duration of B pulse was about 5 PV pore volumes for all displacement experiments. The fast-velocity experiments for the loamy sand and sandy loam soils adjusted to pH 7 (Columns 1 and 5) were conducted using the flow-interruption technique (Brusseau et al., 1989). In these experiments, the flow was stopped (for 120 h) when about 2.5 PV of B solution have been leached through the columns. The displacement experiments in Columns 9 through 12 (packed with clay soil) were conducted separately for Br and B. The duration of Br^– pulse was about 1.5 PV and the duration of B pulse was the same as in B displacement experiment for the previous two soils.

The solution volume was measured and effluent samples were analyzed for pH, Br^– and B. The bromide concentration in the effluents was determined by ion chromatography, and the B concentration by ICP-AES.

Model Parameter Estimation
The results of the batch kinetic adsorption experiments were analyzed using the Langmuir rate equation. The solution of this equation gives the following expression for the relative B concentration ( = c/c₀) in soil solution.

[23]

where c_1,2 = (± – B)/2k₀, F (t) = [(1 – c₁)/(1 – c₂)] exp (– t). The coefficients B, , and s are defined as B = [k₀ (s – 1) + 1], = , and s = (wc₀/mb_m), where w is the volume of solution at the initial B concentration c₀ in contact with m g of soil. Equation [23] was fitted to the plot of versus t to obtain b_m, k, and . The maximum B adsorption b_m and the pH-dependent adsorption coefficient k were also estimated from the B adsorption isotherms. For this case, values of b_m and k (Eq. [3]) were determined by plotting c/b data versus c at each pH and for known sets of values k-pH the magnitudes of the affinity coefficients k_BH, k_B^–, and k_OH for the species B(OH)₃⁰, B(OH)₄^–, and OH^–, respectively, were then calculated by using Eq. [4] written as (Communar et al., 2004)

[24]

where A_j, _j = [k (1 + A)]_j and ß_j = [ c_OH]_j labeled by the index j = 1,2,3 corresponds to the pH values at which the B isotherms were measured for each soil.

The input concentrations (c₀) for Br^– and B, the average water flow rate (q) and the total soil bulk density () were either measured or calculated for each soil column. Various techniques have been proposed to estimate the value of the fraction parameter in the TD-TR model. van Genuchten and Wierenga (1977) estimated by fitting BTCs, whereas Nkedi-Kizza et al. (1982) and Selim et al. (1987) measured ₁ experimentally by draining soil columns under water suction heads of 80 and 20 cm, respectively. Both of these techniques were used in our study. The mobile water content was first defined as ₁ = V₁/V, where V₁ is the volume of pore water drained out from the column under a tension of 60 cm of water and V is the column volume packed with soil; the immobile water content ₂ was calculated as the difference between the weight of the soil removed from the column and that measured initially during the packing of the column. The total water content (= ₁ + ₂), the fraction parameter (= ₁/) and the average pore-water velocity u were calculated for each soil column. The BTCs for Br^– were analyzed by using either the analytical solution for the classical CDE with a retardation factor R (= 1 + K_L/, where K_L [L mg^–1] is the distribution coefficient for linear adsorption) or the TD model (Coats and Smith, 1964), to obtain Pe, ₀, and . The values of obtained from physical measurement were used as initial estimates when the Br^– data were analyzed by means of the TD model. The retardation factor R₂ for B was determined using the results of the batch equilibrium experiments. The BTCs for B were analyzed by using either the LE-NE model or the TD-TR model.

The value for f and ₀ for the LE-NE model were obtained by fitting the measured BTCs for B. To simulate flow interruption in solute displacements, the governing equations were solved using q = 0 and D = D_B where D_B is the molecular diffusion coefficient for B. The D_B value of 0.036 cm² h^–1 for B(OH)₃⁰ was estimated using the model of Boudreau (1997). The mass transfer coefficient for B in the TD-TR model was calculated using the following relation (Brusseau, 1993; Maloszewski and Zuber, 1993)

[25]

where _Br is the mass transfer coefficient obtained from the Br^– data and D_Br is the molecular diffusion coefficients for Br^–. The D_Br value of 0.075 cm² h^–1 was taken from Cussler (1984). Thus, all input parameters for the TD-TR model, except ₀, were obtained from independent experiments.

	RESULTS AND DISCUSSION

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

 
Rate-limited and Equilibrium Boron Adsorption by Soils—Batch Experiments
The relative B concentration in soil solution as a function of time from the kinetic experiments for the loamy sand soil (pH = 7.0), sandy loam soil (pH = 7.1) and clay soil (pH = 7.2) are presented in Fig. 1 . The values b_m, k, and obtained from fitting Eq. [23] to the experimental data are given in Table 2. A sharp decrease of solution B concentration was observed during the first several hours. The reaction time to obtain equilibrium was approximately the same for all three soils despite the difference in clay content. As a result, the rate coefficient, , values were also approximately the same.

View larger version (16K): [in this window] [in a new window]   Fig. 1. Results of B adsorption kinetic experiments: a fraction of aqueous B initial concentration vs. time. Symbols represent the experimental points and solid lines represent concentrations calculated using Eq. [23] and data set of Table 2.

View this table: [in this window] [in a new window]   Table 2. Parameters of the Langmuir rate equation for the B adsorption on the loamy sand, sandy loam and clay soils obtained by fitting Eq. [23] to the batch kinetic data.

View larger version (25K): [in this window] [in a new window]   Fig. 2. (a)Boron adsorption isotherm for the sandy loam soil and (b) Langmuir plots of data at different pH values. Experimental points and the lines calculated using Eq. [3] and [4] and the adsorption coefficients bm, kBH, kB– and kOH of Table 3 are presented.

View this table: [in this window] [in a new window]   Table 3. Adsorption coefficients of the phenomenological Eq. [3] and [4] for the B adsorption on the loamy sand, sandy loam and clay soils. Values of bm and k (Eq. [3]) were determined by plotting c/b data versus c at each pH and for known sets of values k-pH the magnitudes of the affinity coefficients kBH, kB–, and kOH were then calculated by using Eq. [24].

View larger version (25K): [in this window] [in a new window]   Fig. 3. (a) Boron adsorption isotherm for the clay soil and (b) Langmuir plots of data at different pH values. Experimental points and the lines calculated using Eq. [3] and [4] and the adsorption coefficients bm, kBH, kB–, and kOH of Table 3 are presented.

View larger version (16K): [in this window] [in a new window]   Fig. 4. Apparent adsorption coefficient k as a function of pH. The lines are calculated using Eq. [4] and the adsorption coefficients bm, kBH, kB–, and kOH of Table 3. Open and solid symbols represent k values obtained from batch kinetic and equilibrium experiments, respectively.

Transport Experiments
Bromide Outflow
The conditions for the columns displacement experiments are given in Table 4. The Br^– BTCs for the loamy sand and sandy loam soils obtained at the fast (2.9 cm h^–1) and slow (0.19 cm h^–1) water fluxes are shown in Fig. 5 . All of the BTCs were close to each other and were essentially symmetrical indicating ideal transport behavior. The Br^– concentration did not drop during flow interruption (at PV = 2.5). This suggests that physical-heterogeneity-related processes were insignificant in these soil systems. The classical CDE was used to analyze the Br^– BTCs in Fig. 5. The retardation factors R for these BTCs were close to 1 and a linear relationship between the dispersion coefficient D and pore-water velocity was observed at the studied range of water fluxes. The dispersivity coefficient (= D/u) ranged from 0.26 to 0.34 cm (the average value of 0.3 cm) for the loamy sand soil and from 0.34 to 0.42 cm (the average value of 0.38 cm) for the sandy loam soil. Therefore, the average Peclet number values of 40 and 31.6 were used when simulating the B transport in the loamy sand and sandy loam soils, respectively (Table 5).

View this table: [in this window] [in a new window]   Table 4. Values of experimentally measured model parameters and conditions for displacement experiments.

View larger version (21K): [in this window] [in a new window]   Fig. 5. Measured and fitted breakthrough curves for Br– transport in the loamy sand and sandy loam soils at water fluxes, q of 2.9 and 0.19 cm h–1. Symbols represent the measured Br– concentrations. Solid lines were obtained by fitting the CDE to the fast and slow-velocity data (best-fit values for Pe are given in Table 5).

View this table: [in this window] [in a new window]   Table 5. Model parameters estimated from Br– transport.

View larger version (27K): [in this window] [in a new window]   Fig. 6. Measured and fitted breakthrough curves for Br– transport in the clay soil at water fluxes, q of 2.9 and 0.19 cm h–1. Solid lines were obtained by fitting the TD model to the fast and slow-velocity data (best-fit values for Pe, , and 0 are given in Table 5).

View larger version (31K): [in this window] [in a new window]   Fig. 7. Measured, fitted and predicted B breakthrough curves for the loamy sand soil at pH 7 and 9, and water fluxes, q of 2.9 and 0.19 cm h–1. Symbols represent the measured B concentrations (the average values from the two parallel experiments). Dashed line was calculated by the LE-NE model for the fast-velocity data at pH7 using the rate coefficient of Table 2 and solid lines were obtained by fitting the LE-NE model to the fast-velocity data at pH 7 and 9 (best-fit values f and 0 are given in Table 6) and by predicting the slow-velocity data at pH 7 and 9.

View this table: [in this window] [in a new window]   Table 6. Model parameters estimated from fast-velocity BTCs for B (q = 2.9 cm h–1).

The fast-velocity B BTC (pH 7) was predicted with the LE-NE model using the rate coefficient (1.61 h^–1) obtained from batch kinetic experiments (Table 2). The predicted BTC (dashed line) was shifted to the right of the fast-velocity BTC and has approached the slow-velocity BTC (Fig. 7). Such a right shift may indicate that the "true" value of in the soil column is smaller than the rate coefficient obtained from batch kinetic experiments. Therefore, the values for ₀ and f were estimated by curve-fitting the LE-NE model to the fast-velocity data.

The fast-velocity BTC (pH 7) was obtained from the flow interruption experiment in Column 1. The interruption of water flow (at c/c₀= 0.5) caused a drop in solution B concentration, but the pattern of concentration variation was rapidly restored when the water flow was resumed. In the absence of physical NE (the Br^– transport in this soil was ideal), such a drop/restoration of B concentrations can be related to a NE adsorption/desorption of B on the loamy sand soil. Such BTC shape (close to the flow interruption point) suggests that the axial B concentration redistribution along the column was negligible during the stagnation period. To validate this assumption, the simulation of flow interruption was conducted using D_B values of 0 and 0.036 cm² h^–1. In both cases, the model fitted well the measured data except for the concentration range between stagnation and BTC peak points. The simulation using the assumption of D_B = 0 showed a little overestimation of B concentration. This deviation may indicate that B diffusion took place during the interruption period. On the other hand, by using D_B = 0.036 cm² h^–1, the model underestimated the B concentration at this range. It is important to note, however, that the deviations in both cases were minor.

The fitted values for ₀ and f are given in Table 6. Notice that value of 0.35 h^–1 (calculated from dimensionless ₀ = 0.695) was 4.5 times less than value obtained from batch kinetic experiments (Table 2). This confirms the assumption (see above) that the diffusion mass-transfer is more pronounced in soil columns than under batch conditions. Best-fit values ₀ and f (Table 6) calculated from the fast-velocity BTC at pH 9 were very close to those obtained at pH 7. That is, the effect of pH on ₀ values was minor under these conditions. Similar observation was found for a loamy sand soil (Communar and Keren, 2005). The fraction parameter f was also found to be independent of pH (Table 6). The approaching of f value unity indicates that most of the adsorption sites are rate-limited type. When using the average values f (0.95) and (0.36 h^–1), the LE-NE model provided good predictions of the B BTCs obtained from the slow-velocity experiments at pH of 7 and 9. In these experiments with the column residence time t₀ of 30.3 h, the Damkohler number (the velocity-corrected ₀ value) was 10.947. It suggests that at slow water flux, the B transport in the loamy sand soil occurred under quasi-equilibrium conditions.

Sandy Loam Soil
The BTCs in Fig. 8 represent the displacement of B species in the sandy loam soil at pH values of 7 and 9 for the two water fluxes (2.9 and 0.19 cm h^–1). The B transport was more retarded in this soil than in the loamy sand soil (Fig. 7). This difference is due to the fact that the adsorption capacity of the sandy loam soil (b_m = 28.10 mg kg^–1) is greater than for the loamy sand soil (b_m = 17.24 mg kg^–1). As a result, the sandy loam soil adsorbed more B than the loamy sand soil at any given pH value. The pH and the water flux had a significant influence on B transport in the sandy loam soil. The B retardation increases as the water flux decreases and the pH increases.

View larger version (31K): [in this window] [in a new window]   Fig. 8. Measured, fitted and predicted B breakthrough curves for the sandy loam soil at pH 7 and 9, and water flow rates, q of 2.9 and 0.19 cm h–1. Dashed line was calculated by the LE-NE model for the fast-velocity data at pH7 using the rate coefficient of Table 2 and solid lines were obtained by fitting the LE-NE model to the fast-velocity data at pH 7 and 9 (best-fit values f and 0 are given in Table 6) and by predicting the slow-velocity data at pH 7 and 9.

The values of f and ₀ obtained by fitting the fast velocity BTCs at pH 7 and 9 with the LE-NE model are given in Table 6. The values of f = 0.97, ₀= 0.907 (pH 7) and ₀ = 0.823 (pH 9) indicate that most of adsorption sites in the sandy loam soil are rate-limited and that the B adsorption rate (as in the loamy sand soil) is independent of pH. Notice that the rate coefficient, = 0.41 h^–1 (calculated from the average ₀ value of 0.865) was smaller than (1.83 h^–1) obtained from the batch kinetic experiments (Table 2) with the sandy loam soil. Therefore, prediction executed with this rate coefficient ( = 1.83 h^–1) resulted in inappropriate description of the fast-velocity data at pH 7. As well as for the loamy sand soil, the predicted BTC (dashed line) was shifted to the right of fast-velocity BTC (pH 7) and approached the slow–velocity BTC (pH 7), showing a stronger B adsorption. In contrast, when using the rate coefficient = 0.41 h^–1 and f = 0.97, the LE-NE model (at ₀ value of 13.25) well predicted the B BTCs obtained from the slow-velocity (quasi-equilibrium) experiments at pH 7 and 9.

Clay Soil
The B displacement experiments in the clay soil were conducted only at pH 7, because this soil (with value b_m of 70.42 mg kg^–1) adsorbed much more B than the loamy sand soil (b_m = 17.24 mg kg^–1) and the sandy loam soil (b_m = 28.10 mg kg^–1). The BTCs for B in the clay soil with aggregate sizes <2 mm and 4.0 to 4.75 mm at two water fluxes of 2.9 and 0.19 cm h^–1 are shown in Fig. 9 . The B transport at slow water-velocity was more retarded than at the fast water-velocity for both aggregate sizes.

View larger version (37K): [in this window] [in a new window]   Fig. 9. Measured, fitted and predicted B breakthrough curves for the clay soil with aggregate sizes <2 mm and 4.0 through 4.75 mm and water flow rates, q of 2.9 and 0.19 cm h–1. Solid lines were obtained using the TD-TR model (best-fit values for 0 are given in Table 6). Dashed lines represent predictions made by the TD adsorption (ad) model of van Genuchten–Wierenga.

As illustrated in Fig. 9, the TD adsorption model of van Genuchten–Wierenga was unable to predict the fast-velocity BTCs for the clay soil. For both aggregate sizes <2 mm and 4 to 4.75 mm, the predicted BTCs (dashed lines) were shifted to the right of fast-velocity BTCs. Such a shift suggests that a rate-limited adsorption in the mobile water domain could affect B transport in this soil. To obtain ₀ for B adsorption, the TD-TR model was fitted to the fast-velocity B BTCs. This model provided very good simulations of the fast-velocity B BTCs, as illustrated in Fig. 9. The optimized values for are given in Table 6. As well as for the loamy sand and sandy loam soils, the rate coefficients obtained from the column experiments were smaller than those obtained from kinetic batch experiments. It was found that values for the rate coefficient, , were a function of aggregate size. The value of = 0.79 h^–1 was obtained for the soil with the small aggregates, whereas for the large aggregates, the value of was 0.34 h^–1.

When using the optimized values, the TD-TR model successfully predicted the slow-velocity B BTCs for the clay soil with aggregate sizes <2 mm and 4.0 to 4.75 mm. It is of interest to note that the rate coefficient values are two orders of magnitude larger than the mass-transfer coefficient _B values (Table 6). The smaller the _B values, the longer the time to reach an equilibrium in heterogeneous soils. On the other hand, the ₀ values at slow velocity were 22.64 and 19.62 for the clay soil with aggregate sizes <2 mm and 4.0 to 4.75 mm, respectively. Such a large ₀ values suggest that the contribution of the rate-limited adsorption in the mobile domain is relatively insignificant compared with the contribution of the rate-limited mass-transfer processes under slow water flux. To validate this assumption, the slow-velocity B BTCs were predicted using the van Genuchten–Wierenga adsorption model. Indeed, the resulted BTCs (dashed lines) were very close to those obtained from the TD-TR model.

	ACKNOWLEDGMENTS

 
This research was supported in part by a grant from the Ministry of Science, Culture and Sports, a grant from the Chief Scientist, Ministry of Agriculture and Rural Development, Israel and GIF (German-Israel Foundation). The authors thank Ms. Ludmila Tchansky for assistance with the analysis.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION 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. 618/05 Series.

Received for publication August 2, 2005.

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