Published online 12 March 2007
Published in Soil Sci Soc Am J 71:306-313 (2007)
DOI: 10.2136/sssaj2005.0370
© 2007 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SOIL PHYSICS
Effect of Transient Irrigation on Boron Transport in Soils
G. Communar and
R. Keren*
Institute of Soil, Water and Environmental, Sciences, The Volcani Center, Agricultural Research Organization, P.O. Box 6, Bet Dagan 50250, Israel
* Corresponding author (rkeren{at}agri.gov.il).
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ABSTRACT
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Water redistribution and solute concentration changes caused by water evaporation can affect B transport in unsaturated soils under a subsurface transient water flow regime. Our objective was to assess the effect of nonequilibrium adsorption on B transport in unsaturated, homogeneous soil under periodic infiltration cycles using adsorption and transport parameters obtained from independent batch and column experiments. Column experiments using flow interruption were conducted at two pore-water velocities: 0.25 and 2.5 cm h–1. Transport of B at low velocity was unaffected by flow interruption, whereas interruption of fast flow resulted in appreciable perturbation of the B concentration in outflows. The convection–dispersion equation (CDE) with a rate-limited reaction term was fitted to the fast-flow B breakthrough curves (BTCs) to determine the mass-transfer rate coefficients controlling nonequilibrium B transport behavior in soils. This CDE, coupled with the Richards equation, was used to simulate B transport in unsaturated soils under irrigation cycles consisting of water infiltration, internal drainage (redistribution), and evaporation. The B transport under transient nonmonotonic flow depended strongly on the rate-limited step of B adsorption. At a small value of the mass-transfer coefficient, the B BTCs had a characteristically jagged shape, showing increase–decrease cycles in solution B concentrations. The B adsorption tended to balance the solution B concentration increase caused by water evaporation. The final B concentrations, however, exceeded unity in the upper part of the BTCs that were obtained at different soil depths. The results revealed that deviation from adsorption equilibrium may lead to appreciable changes in solution B concentration, especially in the topsoil where the water flow is explicitly transient and nonmonotonic.
Abbreviations: BTC, breakthrough curve • CDE, convection–dispersion equation • LE, local equilibrium • NE, nonequilibrium • RE, Richards' equation
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INTRODUCTION
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The interaction of B with the soil matrix plays an important role in controlling the B concentration in the soil solution and its availability to plants. This interaction is usually studied by using batch or column techniques, and combining these two techniques enables the impacts of various factors on B adsorption and transport in soils to be estimated. Boron is readily adsorbed by soil, although its adsorption is affected by various factors such as soil mineral composition, soil texture, and soil-solution pH (Keren and Bingham, 1985; Goldberg et al., 2000). Under batch conditions, the adsorption of B by soil constituents (Keren and Mezuman, 1981) and by soils (Mezuman and Keren, 1981; Communar and Keren, 2006) is a relatively rapid process. Nevertheless, B transport, even in homogeneous soils, was found to be nonequilibrium (Communar et al., 2004; Communar and Keren, 2005). Miscible displacement experiments based on the flow interruption technique (Brusseau et al., 1989; Reedy et al., 1996; Johnson et al., 2003) were implemented by Communar and Keren (2006) to analyze the influence of physicochemical factors on B transport in homogeneous soils. Although the BTCs for B were unaffected by flow interruption under low-velocity flow, in fast-flow experiments a significant concentration perturbation was observed after flow interruption. The B adsorption-rate coefficients obtained from batch kinetic experiments were larger than those obtained from the fast-flow BTC data (Communar and Keren, 2006). These findings suggested that the diffusion mass-transfer limitation was more pronounced in soil columns than under batch conditions. Nonequilibrium B transport in homogeneous, water-saturated soil columns was successfully described by the CDE, with a source–sink term accounting for a rate-limited mass-transfer process.
Although considerable work has been done on B mobility in water-saturated soils, there are no data on the influence of transient water flow on B transport in unsaturated soils. A number of additional factors such as water redistribution and solute concentration augmentation by water evaporation can affect B transport in unsaturated soils under a transient water flow regime in the subsurface. The impact of these factors on the transport of nonreactive solutes was analyzed by several investigators (Bresler, 1973; Wierenga, 1977; Russo et al., 1989), who used the classical CDE combined with the Richards equation (RE) for water flow. Russo et al. (1989) showed that under transient, nonmonotonic water flow (when evaporation occurs between infiltration events), the water content and the solute concentration may undergo significant cyclic changes. As found in column displacement experiments with flow interruption (Communar and Keren, 2006), the solution B concentration may drop when a drainage stage follows infiltration. On the other hand, however, water evaporation between successive irrigations may increase the solution B concentration. These additional factors should be taken into consideration when analyzing field data, because the range between B concentrations in soil solution causing deficiency and toxicity symptoms in plants is relatively narrow (Keren and Bingham, 1985).
Shani et al. (1992) simulated the transport of B and of a nonreactive solute under field situations using the RE coupled with the CDE for equilibrium adsorption. They took into account infiltration, drainage, evaporation, and extraction of water by plant roots. The prediction of nonreactive solute transport in the soil was satisfactory, but some deviations were observed between the calculated B concentrations and those measured in a field study. These deviations were attributed to physical or chemical phenomena that took place in unsaturated soil systems. Zurmühl (1998) also noted that transport models based on the local equilibrium (LE) assumption might not always be suitable to predict the solute concentration under a transient-flow regime. As was found for water-saturated soil columns (Communar and Keren, 2005, 2006), the use of the LE models may lead to overestimation of B mobility in unsaturated soils.
In this study, we show for the first time how transient, nonmonotonic flow can affect the transport of B in homogeneous, unsaturated soils. For that purpose, the simulations of B transport were performed using the RE coupled with the nonequilibrium (NE) model and transport parameters obtained from independent experiments. The objective was to assess the effect of nonequilibrium adsorption on B transport in unsaturated soils under periodic infiltration cycles.
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THEORY
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Transport Equations
Transient water flow and solute transport in homogeneous soils may be described by Eq. [1] and [2], respectively (Shani et al., 1992; Zurmühl, 1998; Flury et al., 1999):
 | [1] |
 | [2] |
where t is time (h); z is the vertical, positively downward distance (cm); c is the solute concentration in the liquid phase (mg L–1); b is the solute concentration in the adsorbed phase (mg kg–1); 
is the soil bulk density (g cm–3); 
is the volumetric water content (m3 m–3); q is the macroscopic Darcy water flux (cm h–1); h() is the soil water pressure potential (cm); K() is the unsaturated hydraulic conductivity (cm h–1); J is the convection–dispersion flux; and D is the diffusion–dispersion coefficient (cm2 h–1), defined as
 | [3] |
[3]
where 
denotes the pore-scale dispersivity of the porous media (cm) and De is the effective molecular diffusion coefficient (cm2 h–1).
Equation [1] requires an expression relating the adsorbed concentration b to the liquid concentration c. For B adsorption by soils, this relation can be described by the following equation (Communar and Keren, 2005):
 | [4] |
where bm is the maximum B adsorption (mg kg–1), k is the adsorption coefficient (L mg–1), and 
is the mass-transfer coefficient (h–1) that reflects the B retention in micropores of individual particles. The NE model, based on the CDE (Eq. [1]) and Eq. [4], was successfully used (Communar and Keren, 2005, 2006) to describe B transport in the water-saturated soil columns ( = s, where s is the soil porosity or the saturated water content). For a long residence time or when is large, the B adsorption can be described by the Langmuir equation:
 | [5] |
Under these conditions, the NE model converges to the LE model.
The water retention characteristic (h) and the unsaturated hydraulic conductivity function K() required to complete the RE (Eq. [2]) are described using the Mualem–van Genuchten model (van Genuchten, 1980):
 | [6] |
 | [7] |
where S = ( – d)/(s – d) is the water saturation, d is the air-dry water content, Ks is the saturated hydraulic conductivity, and 
(cm–1), n and m = 1 – 1/n are fitting parameters.
The governing partial differential equations are supplemented with the initial and boundary conditions appropriate to infiltration. For the RE, these conditions are stated as
 | [8] |
 | [9] |
 | [10] |
where i(hi) is the initial water content, corresponding to the initial water pressure potential hi, L is the length of the soil column or the soil depth (cm), and q* is the input water flux (cm h–1), which is assumed to be a function of time. For the solute transport, the appropriate initial and boundary conditions are
 | [11] |
 | [12] |
 | [13] |
where c0 is the input solute concentration (mg L–1).
Note that serious mass balance and convergence problems can develop when the pressure-head-based form of the RE is used to describe the transient flow of water (Celia et al., 1990). The prescribed flux at the boundary surface is also a factor that can cause convergence problems when the flux is larger than the soil permeability and the soil below the wetting front is dry (Zhang et al., 2002). To produce accurate solutions, the temporal derivatives in the RE and the NE model were evaluated by using a fully implicit time approximation combined with the modified Picard iteration scheme (Celia et al., 1990; Huang et al., 1998) and the spatial derivatives were approximated by cell-centered finite differences with uniform grid spacing. A procedure proposed by Zhang et al. (2002) was used to reduce the numerical fluctuations that would arise because of lack of feedback between the boundary flux (Eq. [9]) and the calculated flux. The set of algebraic equations representing the RE and the NE model was solved consistently at each iteration level by applying the standard Tomas algorithm (Anderson et al., 1984, p. 128). The values of and q in the grid points obtained from the RE at each time level were used in the NE model to obtain the B concentrations, c and b. All of the nonlinear coefficients in these equations were updated at each iteration stage by using their values from the previous iteration stage as argument, and the iterative procedure at each time level was continued until the prescribed errors were achieved (for water content, 
= 10–6 cm3 cm–3 and for concentration, c = 10–4 mg L–1). To simulate B transport in soil under saturated conditions (column displacement experiment), the set of equations representing the NE model was solved independently.
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MATERIALS AND METHODS
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Laboratory Studies
The soils used in this study were: (i) a loamy sand soil (Rhodoxeralf) from the coastal plain of Israel and (ii) a sandy loam soil (Haploxeralf) from the Sinai Desert developed on wind-blown material. These soils are similar to those used in our previous studies (Communar et al., 2004; Communar and Keren, 2006). Some characteristics of the soils, all obtained by routine procedures, are presented in Table 1. The soil pH was determined at a water/soil ratio of 2:1. The predominant clay mineral in all of the soils is montmorillonite. The oven-dried soils (40°C) were passed through a 2-mm sieve before use.
Batch Experiments
Boric acid adsorption by the soils was studied at pH 7.0 ± 0.1 in 50-mL polypropylene centrifuge tubes containing 15-g soil samples and 35 mL of background solution of CaCl2 + NaCl at a total concentration of 20 mmolc L–1, with a Na adsorption ratio of 6. The details of all preparatory procedures used to adjust the soil pH and to determine the B adsorption isotherms at a given pH were described by Communar et al. (2004). Preliminary adsorption kinetics experiments with these soils showed a fast reduction of the solution B concentration during the first few hours. Relatively fast B adsorption by similar soils was also observed by Mezuman and Keren (1981) and Communar and Keren (2006) under batch conditions. Therefore, after centrifugation and removal of the supernatant, the background solutions (pH 7) at initial concentrations ranging from 0.5 to 5 mg L–1 were added to the soil samples and were shaken continuously for 24 h. Then the supernatants were analyzed for B by inductively coupled plasma atomic emission spectroscopy (ICP-AES; Spectroflame, Spectro Analytical Instruments GmbH, Kleve, Germany).
Column Experiments
The displacement experiments were conducted in columns of 12 cm in length and 5.2 cm in diameter. The columns were uniformly packed with the soils in 1-cm increments. Each increment was tapped firmly to achieve homogeneous packing and uniform bulk density. Before water saturation, the columns were purged with CO2 to eliminate the effect of air entrapment. The background solution at pH 7 was slowly introduced from the bottom of the columns and the saturation process continued for 2 d. The columns were leached with the background solution until a steady state was reached with respect to solution composition, electrolyte concentration, and pH. The BTCs for B and Br– were generated at two flow rates, equivalent to pore-water velocities of 0.25 and 2.5 cm h–1. The breakthrough data for Br– were used to estimate the dispersion characteristics of the soils. The B and Br– concentrations in the input solutions were 2.5 and 5 mg L–1, respectively. The input water flow velocity was controlled by a peristaltic pump. It should be noted that the low velocity (0.25 cm h–1) corresponds to the water velocities observed in field conditions. The high velocity (2.5 cm h–1) was used to illustrate the impact of rate-limited adsorption on B transport in the soils. Miscible-displacement experiments were conducted with the flow-interruption technique (Brusseau et al., 1989; Johnson et al., 2003). Several flow interruptions were generated during the displacement of B and Br– through the soil columns, until the B concentration in the outflow was the same as that in the inflow solutions. As found by Communar and Keren (2006), the axial redistribution of Br– and B concentrations in homogeneous sandy loam and loamy sand soils was negligible, even when the flow interruption experiments involved a stagnation time of 120 h. This suggests that, if a shorter stagnation time were used, the effect of the axial molecular diffusion on the shape of BTCs generated at various concentration gradients would also be insignificant. Therefore, in these experiments, each interruption of water flux was performed after about 2.5 pore volumes had been leached, and the stagnation time for each flow interruption was 12 h. All of the column experiments were conducted in duplicate. Effluents were collected in a fraction collector. The leached volume was measured and the solution was analyzed for Br– and B. The Br– concentration in the effluents was determined by ion chromatography, and the B concentration by ICP-AES.
Model Simulations
To simulate the transient B transport in unsaturated loamy sand and sandy loam soils, we assumed that the initial water potential head hi for both soils was –1000 cm H2O. We further assumed that transient water flow in the initially wet–dry soils was caused by periodic irrigation, i.e., the water flux at the soil surface was subjected to cyclic changes. These changes in the water flux were described as
 | [14] |
where q* is the net water flux (qinf is the infiltration rate and qev is the water evaporation rate). According to Eq. [14], the duration of the infiltration stage tinf = 6 h, water redistribution takes place during the next 6 h (nighttime), and the water evaporation stage tev lasts for 12 h (daytime). The B and Br– concentrations in the irrigation water at each application were assumed to be the same as those in the column displacement experiments (i.e., 2.5 and 5 mg L–1, respectively).
The parameters of the van Genuchten–Mualem functions, (h) and K(), for the loamy sand and sandy loam soils were estimated with the Hydrus-1D software (Simunek et al., 1998), using a specific particle-size distribution (Table 1) and soil densities (Table 2). The water content (h) and the hydraulic conductivity K()functions shown in Fig. 1
were used to simulate the water flow in these soils. For the initial water (pressure) potential head of –1000 cm H2O, the initial water content i in the loamy sand and sandy loam soils was 0.0748 and 0.1579 m3 m–3, respectively. As h increased, the water content increased, but at any given water pressure, the water content in the loamy sand soil was lower than that in the sandy loam soil. Note that in the water (pressure) potential head range from –1000 to –40 cm, the hydraulic conductivity of the loamy sand soil was less than that of the sandy loam soil, whereas the opposite was true for h > –40 cm.
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Fig. 2. Boron adsorption isotherms for the loamy sand and sandy loam soils used in this study. The lines were calculated with Eq. [5], using the adsorption coefficients bm and k from Table 2.
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Fig. 3. Measured and simulated breakthrough curves for B transport in the loamy sand and sandy loam soils at pore-water velocity, u, of 0.25 and 2.5 cm h–1. Solid lines were obtained with the nonequilibrium (NE) model, using the adsorption and transport parameters from Table 2. The rate coefficient values in Table 2 were obtained by fitting the NE model to the high-velocity data.
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The parameters for the NE model were determined from the above-mentioned batch and column experiments. The coefficients bm and k were obtained from the B adsorption isotherms for the loamy sand and sandy loam soils, and the values were obtained from the Br– BTCs. Despite the differences in soil texture, the Br– BTCs (not shown) for the loamy sand soil were almost the same as those for the sandy loam soil, and their shape was independent of pore-water velocity. The Br– BTCs were unaffected by the flow interruption, indicating that any nonreactive solute transport in these two soils is ideal, which is consistent with the findings of Communar and Keren (2006) for similar soils. The Br– BTCs were analyzed using the classical CDE with a retardation factor R = 1 + KL/, where KL (L mg–1) is the distribution coefficient for a linear adsorption). The CDE with the retardation factor R of 1 gave good matches (r2 = 0.97) to the measured Br– BTCs for both soils. The optimized value of the pore-scale dispersivity for the loamy sand soil ( = 0.25 ± 0.11cm) was very close to that obtained for the sandy loam soil ( = 0.3 ± 0.08 cm). The rate coefficients were determined by fitting the NE model to the B BTCs obtained from the fast-velocity experiments using the optimized bm, k, and values. The flow interruption was simulated by using the NE model at q = 0 and De = Dm. Molecular diffusion coefficients, Dm, of 0.075 cm2 h–1 (Cussler, 1984) and 0.036 cm2 h–1 (Boudreau, 1997) were used for Br– and B, respectively. The effective molecular diffusion coefficient for unsaturated flow conditions was calculated by using the relationship of Millington and Quirk (1961):
 | [15] |
The simulations of transient water flow and solute transport in the unsaturated soils were executed for a soil profile of 2-m depth, by using the RE and the NE model with the above-mentioned parameters. To provide an accurate result, the numerical computations were performed with a variable grid size of 0.5 < 
z < 1 cm and a variable time increment of 0.001 < t < 0.05 h. Water contents (), water pressures (h), and Br– and B concentrations (c) were calculated as functions of time at various depths. All concentrations reported are relative concentrations, normalized to the input concentration (c0).
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RESULTS AND DISCUSSION
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The B adsorption isotherms used to estimate the adsorption parameters are shown in Fig. 2
for the loamy sand soil and sandy loam soils. Note that the best-fit values for B adsorption coefficients k (at pH 7) were approximately the same for these two soils (Table 2). However, the loamy sand soil, with the lower clay content, was characterized by a smaller bm value than the sandy loam soil (15.44 ± 1.86 vs. 32.40 ± 2.32 mg kg–1); consequently, it adsorbed less B than the sandy loam soil.
The measured and the simulated B concentrations for the loamy sand and sandy loam soils at two pore-water velocities (u = 2.5 and 0.25 cm h–1) are shown in Fig. 3
. The B transport was more retarded in the sandy loam soil than in the loamy sand soil because the adsorption capacity of the former was greater than that of the latter. For both soils, no change in B solution concentration occurred during the stagnation time with low pore-water velocity. With high pore-water velocity, however, each interruption of water flow was accompanied by a drop in the solution B concentration. The drop in B concentration decreased as the volume of solution leached through the columns increased, but remained observable at each flow interruption. For both soils, the B BTCs obtained under high velocity were shifted from those obtained at low velocity. Such a shift in the BTCs and the drop and restoration of B concentrations indicate that B transport was nonequilibrium under high-velocity flow. The tailing of the B BTCs under high-velocity flow, and the concentration drop and restoration caused by the interruption and resumption of water flow were well described (r2 = 0.93) by the NE model (Fig. 3). The best-fit values of for the loamy sand and sandy loam soils were 0.25 ± 0.16 and 0.41 ± 0.09 h–1, respectively. When these values were used, the NE model was able to successfully predict the B BTCs obtained with the slow flow. In these slow flow experiments, the column residence time t0 (=l/u) was 48 h, and the 0 = t0 values (the Damkohler number, which represents a ratio of hydraulic residence time to reaction time) for the loamy sand and sandy loam soils were 12 and 19.7, respectively. At these Damkohler numbers, the BTCs yielded by the NE model coincided with those from the LE model (Bahr and Rubin, 1987; Communar and Keren, 2006). Thus, B transport in these soils occurred under equilibrium conditions at the low pore-water flow velocity.
While the flow rate and the water content remained constant in the column displacement experiments, the solute transport will be affected by changes in the transport parameters: q, , and De in unsaturated soils under transient, nonmonotonic flow conditions. Thus, numerical simulations for solute transport under transient flow are generally more complicated than those for uniform steady-state flow conditions. Therefore, before performing the irrigation simulations, we verified the transient model by comparing our results with those of other numerical solutions (Huang et al., 1998; Diaw et al., 2001), and found good agreement for all simulations. The application of the Picard iteration methods for solving the RE and the NE model provided good conservation of mass balance for water content and solute concentration, respectively. Furthermore, use of the procedure suggested by Zhang et al. (2002) enables reduction of the convergence problems related to boundary conditions for water flux at the soil surface.
For the surface boundary condition (Eq. [9] with q*defined by Eq. [14]), the water-flow regimes in these soils were transient and nonmonotonic. The water fluxes calculated with the Darcy equation q = –K()[
h()/z – 1] for depths of 5, 10, 15, and 20 cm are shown in Fig. 4
for several irrigation cycles. Although the water fluxes were the same in both soils, the cyclic changes in water contents and in water pressures (Fig. 5
) for the loamy sand soil were different from those obtained for the sandy loam soil. These differences between the water contents and between the water pressures in the two soils are associated with the differences in the respective hydraulic properties (Fig. 1). Water evaporation reduced the water content and the water pressure (the water pressure became less negative) that resulted from the infiltration and drainage stages in the topsoil. The reduction in the water pressure at the soil surface caused the water to move upward and to compensate in part for the reduction of the water content. At the prevailing irrigation frequency and q* values, the water flux at a depth of 5 cm always remained positive, increasing from 0 to 0.08 cm h–1 during infiltration and decreasing again to zero during water evaporation. The water content at this depth increased with time but was subjected to cyclic changes of constant amplitude (Fig. 5). As a result, the local pore-water velocity, u = q/ changed accordingly. Note that the time-averaged u value of 0.18 cm h–1 obtained at z = 5 cm corresponded to that used in the low-velocity column experiments. As the number of irrigation cycles increased, the water front reached a depth (in our case, about 15–20 cm for both soils) at which the impact of the boundary condition on the cyclic changes in water content and water pressure became negligible (Fig. 5).
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Fig. 4. Cyclic changes of water flux at the soil surface and variation of water flux with time at various depths z in the loamy sand and sandy loam soils.
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Fig. 5. Variations of water content and water pressure h with time at various depths z for the loamy sand and sandy loam soils.
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To assess the impact of the transient, nonmonotonic flow on the transport of a nonreactive solute (Br–, for example), the simulations with the NE model were performed at = 0. Note that at this value (b/t = 0), the NE model converges to the classical CDE. The changes in relative Br– concentration calculated for the 5-, 10-, 15-, and 20-cm depths are plotted vs. time in Fig. 6
for the loamy sand and sandy loam soils. One can see that the characteristic features of Br– transport were approximately the same for the two soils; however, solute movement in the sandy loam soil was markedly slower than that in the loamy sand soil. The time required to obtain a complete Br– BTC in the sandy loam soil at any depth was approximately twice that for the loamy sand soil and, for this reason, the effect of the boundary condition on the redistribution of solute concentrations was smaller in the latter than in the former soil.
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Fig. 6. Relative Br– concentration vs. time at various depths for the loamy sand and sandy loam soils. The simulations with the nonequilibrium (NE) model were performed with a rate coefficent () = 0.
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The solute spreading in the unsaturated soils was controlled by convection and dispersion during the infiltration stage and by diffusion during the redistribution and evaporation stages. As was expected, the BTCs showed "stepwise" changes in the Br– concentration at small depths. Similar stepwise changes in the BTCs were reported by Wierenga (1977) and by Russo et al. (1989), but for pulse injection of a nonreactive solute. In our study, however, the time-based BTCs (Fig. 6) were obtained for the case when the solute was fed into the soils at each infiltration cycle, i.e., each step solute input was followed by water redistribution and evaporation cycles. Diminution of the water content during the evaporation stage caused the solute concentration in the vicinity of the soil surface to increase. The infiltration compensated only partly for this concentration increase, and it rose again during the evaporation stage.
It is important to note that although the influence of the boundary conditions on the shape of the BTCs became negligible at depths where the water-flow regime approached a steady state (i.e., where the stepwise changes in the BTCs became less noticeable), the actual solute concentrations appeared higher than the inlet solute concentration because of water evaporation. As a result, the relative Br– concentrations in the upper part of the BTCs exceeded unity at various soil depths (Fig. 6). To estimate the solute concentration overshoot at z = 0, one can use the simplified mass-balance equation, 0c0 = *c*, in which the volumetric water contents, 0 and *, corresponding to the beginning and the ending of the evaporation stage, respectively, are expressed through the introduced and the evaporated water volumes. Then, the relative solute concentration to the end of evaporation stage can be defined as
 | [16] |
where qinf, qev and tinf, tev are the fluxes and time periods corresponding to the infiltration and evaporation stages, respectively. It follows from Eq. [16] that before each subsequent infiltration, the relative solute concentration at the soil surface may be 25% higher than the inlet solute concentration. Note that the extent of overshooting predicted by Eq. [16] was the same for both soils and corresponded well to that obtained from the combined model (Fig. 6).
To assess the impact of mass-transfer rate limitation on B transport in unsaturated soils, the simulations were conducted with the rate coefficients (Table 2) obtained from the laboratory displacement experiments, and with two additional values: 0.05 and 10 h–1. The prediction by the NE model with = 10 h–1 was identical to that of the LE model under the given irrigation frequency and q* values. The B BTCs in Fig. 7
present the relative B concentration as a function of time, calculated at the depths of 5, 10, 15, and 20 cm for the loamy sand and sandy loam soils. As expected, the transport of B in the soils was retarded relative to the transport of the nonreactive (Br–) solute under the same hydrodynamic conditions. The B BTCs in the loamy sand soil were different from those in the sandy loam soil; these differences were associated with the differences between the adsorption and hydraulic properties of the two soils. As in the laboratory displacement experiments (Fig. 3), the B transport in the sandy loam soil (with B adsorption capacity bm of 32.40 mg kg–1) was more retarded than that in the loamy sand soil (with B adsorption capacitybm of 15.44 mg kg–1). For this reason and because of the difference between the nonreactive solute transport behaviors in the two soils (Fig. 6), the effect of the boundary condition on the redistribution of solute B concentrations in the sandy loam soil was more extended than that in the loamy sand soil. As found for the Br– transport, the influence of the boundary condition on the shape of the B BTCs became less noticeable at soil depth where the water-flow regime approached a steady state.
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Fig. 7. Relative B concentration vs. time at various depths in loamy sand soil and sandy loam soils, calculated for various values of the rate coefficient, , and local equilibrium (LE). Calculations were based on the parameters of Table 2 and the input B concentration of 2.5 mg L–1 in the irrigation water.
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As shown in Fig. 7, the shape of the B BTCs depended strongly on the rate-limited step for B adsorption by the soils. At a small of 0.05 h–1, the BTCs had a characteristically jagged shape, with alternating increases and decreases in the relative B concentrations in the outflows. Boron BTCs of similar shape were obtained from the high-velocity displacement experiments conducted with water flow interruption (Fig. 3). Whereas in the column displacement experiments the inlet B concentration was constant, the shape of the B BTCs under a transient flow regime (Fig. 7) was affected by the changes in the solution B concentration in the topsoil. The B adsorption tended to compensate for the increase of solution B concentration caused by water evaporation, but this compensation effect depended on the values. In fact, at a small , changes in solution B concentration followed the cyclic changes (decrease or increase) in water content, especially at a small depth, but with some delay because of a rate limitation on B adsorption. The jagged shape of the BTCs became less pronounced when values of 0.25 and 0.41 h–1 (Table 2) were used to simulate B transport in the loamy sand and sandy loam soils, respectively. Note that the B transport at these values was more retarded than that obtained at = 0.05 h–1. Under equilibrium adsorption, the solution B concentration in the topsoil changed immediately after any redistribution in water content. In such a case, the B mobility can be expressed by the retardation factor R = 1 + (/)(db/dc) that is directly proportional to the derivative db/dc, and inversely proportional to the volumetric water content. Thus, even under equilibrium adsorption, the B transport in unsaturated soils may be affected by changes in the water content and solution B concentration.
As in the case of Br–, the relative B concentrations (Fig. 7) exceeded unity in the upper part of the BTCs at all values. The overshoot of relative B solution concentrations in the loamy sand soil was the same as that in the sandy loam soil. Assuming that adsorption at the soil surface occurs under equilibrium conditions, the maximum B concentration in the solution can be estimated by using the following mass-balance equation: 0c0R0 = *c*R*, where R0 and R* are the B retardation factors corresponding to the beginning and the end of the evaporation stage, respectively (the other parameters are defined above). Note that the B concentration overshoot (Fig. 7) was approximately the same as that of the Br– concentration (Fig. 6), i.e., the ratio between retardation coefficients, R0/ R*, was close to 1 for both soils. This indicates that changes in retardation factors caused by a decrease or increase in the water content were compensated by a corresponding increase or decrease in solution B concentrations.
In light of the comparison between the concentration distributions obtained with the NE and LE models, it appears that for predicting the solution B concentrations under transient, nonmonotonic flow, the use of the nonequilibrium approach may be more appropriate. Although this conclusion is based on the assumptions of homogeneous soil (with physicochemical properties that remain constant as the depth changes) and frequent irrigations, our simulations are in agreement with the field data reported by Shani et al. (1992).
The results obtained revealed that deviation from adsorption equilibrium may lead to significant changes in solution B concentration, especially in the topsoil, where the water flow is explicitly transient and nonmonotonic. This highlights the requirement that nonequilibrium effects in the B adsorption–desorption process should be taken into consideration when assessing B concentrations in topsoil solutions.
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ACKNOWLEDGMENTS
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This research was supported in part by a grant from the Chief Scientist, Ministry of Agriculture and Rural Development, Israel, and the German–Israeli Foundation.
Received for publication November 14, 2005.
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REFERENCES
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- Anderson, D.A., J.C. Tannehill, and R.H. Pletcher. 1984.Computational fluid mechanics and heat transfer. Taylor and Francis, Philadelphia, PA.
- Bahr, J.M., and J. Rubin. 1987. Direct comparison of kinetic and local equilibrium formulations of solute transport affected by surface reactions. Water Resour. Res. 23:438–452.
- Boudreau, B. 1997. Diagenetic models and their implementation. Springer Verlag, Berlin.
- Bresler, E. 1973. Simultaneous transport of solute and water under transient unsaturated flow conditions. Water Resour. Res. 9:975–986.
- Brusseau, M.L., P.S.C. Rao, R.E. Jessup, and J.M. Davidson. 1989. Flow interruption: A method for investigating sorption nonequilibrium. J. Contam. Hydrol. 4:223–240.[CrossRef]
- Celia, M.A., E.T. Bouloutas, and R.L. Zarba. 1990. A general mass-conservative numerical solution for the unsaturated flow equation. Water Resour. Res. 26:1483–1496.
- Communar, G., and R. Keren. 2005. Equilibrium and nonequilibrium transport of boron in soil. Soil Sci. Soc. Am. J. 69:311–317.[Abstract/Free Full Text]
- Communar, G., and R. Keren. 2006. Rate-limited boron transport in soils: Effect of soil texture and solution pH. Soil Sci. Soc. Am. J. 70:882–892.[Abstract/Free Full Text]
- Communar, G., R. Keren, and F. Li. 2004. Deriving boron adsorption isotherms from soil column displacement experiments. Soil Sci. Soc. Am. J. 68:481–488.[Abstract/Free Full Text]
- Cussler, E.L. 1984. Diffusion: Mass transfer in fluid systems. Cambridge Univ. Press, Cambridge, UK.
- Diaw, E.B., F. Lehmann, and Ph. Ackerer. 2001. One-dimensional simulation of solute transfer in saturated–unsaturated porous media using the discontinuous finite elements method. J. Contam. Hydrol. 51:197–213.[CrossRef][ISI][Medline]
- Flury, M., M.V. Yates, and W.A. Jury. 1999. Numerical analysis of the effect of the lower boundary condition on solute transport in lysimeters. Soil Sci. Soc. Am. J. 63:1493–1499.[Abstract/Free Full Text]
- Goldberg, S., S.M. Lesch, and D.L. Suarez. 2000. Predicting boron adsorption by soils using chemical parameters in the constant capacity model. Soil Sci. Soc. Am. J. 64:1356–1363.[Abstract/Free Full Text]
- Huang, K., B.P. Mohanty, J. Leij, and M.Th. van Genuchten. 1998. Solution of the nonlinear transport equation using modified Picard iteration. Adv. Water Resour. 21:237–249.
- Johnson, G.R., K. Gupta, D.K. Putz, Q. Hu, and M.L. Brusseau. 2003. The effect of local-scale physical heterogeneity and nonlinear, rate-limited sorption/desorption on contaminant transport in porous media. J. Contam. Hydrol. 64:35–58.[CrossRef][ISI][Medline]
- Keren, R., and F.T. Bingham. 1985. Boron in water, soil, and plants. Adv. Soil Sci. 1:229–276.
- Keren, R., and U. Mezuman. 1981. Boron adsorption by clay minerals using a phenomenological equation. Clays Clay Miner. 29:198–204.[Abstract]
- Mezuman, U., and R. Keren. 1981. Boron adsorption by soils using a phenomenological adsorption equation. Soil Sci. Soc. Am. J. 45:722–726.[ISI]
- Millington, R.J., and J.M. Quirk. 1961. Permeability of porous solids. Trans. Faraday Soc. 57:1200–1207.
- Reedy, O.C., P.M. Jardine, G.V. Wilson, and H.M. Selim. 1996. Quantifying the diffusive mass transfer of nonreactive solute in columns of fractured saprolite using flow interruption. Soil Sci. Soc. Am. J. 60:1376–1384.[ISI]
- Russo, D., W.A. Jury, and G.L. Butters. 1989. Numerical analysis of solute transport during irrigation: 1. The effect of hysteresis and profile heterogeneity. Water Resour. Res. 25:2109–2118.
- Shani, U., L.M. Dudley, and R.J. Hanks. 1992. Model of boron movement in soils. Soil Sci. Soc. Am. J. 56:1365–1370.
- Simunek, J., M. Sejna, and M.Th. van Genuchten. 1998. The Hydrus-1D software package for simulating water flow and solute transport in two-dimensional variably saturated media. Version 2.0. IGWMC-TPS-70. Int. Ground Water Modeling Ctr., Colorado School of Mines, Golden.
- van Genuchten, M.Th. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892–898.[ISI]
- Wierenga, P.J. 1977. Solute distribution profiles computed with steady state and transient water movement models. Soil Sci. Soc. Am. J. 41:1050–1055.
- Zhang, X., A.G. Bengough, J.W. Crawford, and I.M. Young. 2002. Efficient methods for solving water flow in variably saturated soils under prescribed flux infiltration. J. Contam. Hydrol. 260:75–78.
- Zurmühl, T. 1998. Capability of convection–dispersion transport models to predict transient water and solute movement in undisturbed soil columns. J. Contam. Hydrol. 30:101–128.[CrossRef][ISI]
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G. Communar and R. Keren
Boron Adsorption by Soils as affected by Dissolved Organic Matter from Treated Sewage Effluent
Soil Sci. Soc. Am. J.,
February 15, 2008;
72(2):
492 - 499.
[Abstract]
[Full Text]
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ABSTRACT
INTRODUCTION
