Environ. Sci. Technol. 2002, 36, 349-354
Measurement and Dynamic Modeling of Trace Metal Mobilization in Soils Using DGT and DIFS HELMUT ERNSTBERGER,† W I L L I A M D A V I S O N , * ,† H A O Z H A N G , † ANDREW TYE,‡ AND SCOTT YOUNG‡ Department of Environmental Science, IENS, Lancaster University, Lancaster, LA1 4YQ, U.K., and School of Life and Environmental Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K.
The technique of diffusive gradients in thin-films (DGT) accumulates metals on a Chelex resin after their diffusive transport through a hydrogel. It lowers metal concentrations in soil solution adjacent to the device and induces resupply of metal associated with the solid phase. DGT devices were deployed in an alluvial gley soil for 21 different time periods between 4 h and 19.5 d. The accumulated masses of Cu, Cd, Ni, and Zn were used to calculate the distribution coefficient for labile metal, Kdl, and adsorption and desorption rate constants. Calculations were performed using a dynamic numerical model of DGTinduced fluxes in soils (DIFS). It assumes first-order exchange between solid phase and solution and diffusional transport in both the soil solution and the hydrogel. The DIFS model fitted changes in accumulated mass with time very well. Values of Kdl calculated from DIFS of 100 (Cd), 250 (Cu), 150 (Ni), and 150 (Zn) were larger than values of distribution coefficients estimated by exchange with Ca(NO3)2 but similar to those estimated by isotopic exchange (Cd and Zn only). These results suggest that the solidphase pool of metal affected by the removal of labile metal by DGT, which operates on a time scale of minutes, is similar to the solid-phase pool of metal that can isotopically exchange with solution on a time scale of 2 d. Response times of minutes were consistent with interaction rates with surfaces, and desorption rate constants agreed with other reported values. An appraisal of the DIFS model demonstrated the importance of the labile pool size in the solid phase for controlling supply to a sink, such as DGT or a plant. As values of Kdl and kinetic parameters are obtained using DGT with minimal soil disturbance and by a similar mechanism to that involved in plant uptake, they may be pertinent to bioavailability studies.
Introduction Knowledge about the interaction of solutes with solid phases in soils largely comes from measurements made under conditions that differ substantially from the in situ conditions. Adsorption/desorption studies are performed in dilute * Corresponding author telephone: +44 (0)1524 593935; fax: +44 (0)1524 593985; e-mail:
[email protected]. † Lancaster University. ‡ University of Nottingham. 10.1021/es010917d CCC: $22.00 Published on Web 01/04/2002
2002 American Chemical Society
suspensions (1, 2), while sequential extraction procedures systematically change the chemical environment (3-5). All these measurements advance understanding, but their applicability to processes occurring under undisturbed natural conditions is uncertain. In addition to macroscopic studies, a variety of spectroscopic and microscopic tools have been used to investigate surface reactions of heavy metals with soil components. Dynamic models of soil/solute systems that embrace processes such as plant uptake need quantitative relationships for the distribution of species between solid and solution phases (6, 7). Distribution coefficients (Kd) are the simplest and most widely used parameters. When obtained using experimentally contrived particle concentrations, distribution coefficients may not be representative of in situ conditions (8). Moreover, when Kd values are determined using chemical extractants to quantify the solid-phase component, they may not adequately quantify the partition occurring in situ, which will relate to a kinetically labile fraction. DGT (diffusive gradients in thin-films) measurements of trace metal fluxes to a resin sink have been shown to be good surrogates for assessing plant uptake (9, 10). These in situ measurements depend on labile trace metal concentrations in soil solution and their resupply from the solid phase. The contribution from the solid phase is determined by the capacity of the solid-phase reservoir and the rate of transfer to solution. The derivation of these capacity and kinetic parameters from DGT measurements requires a model of the soil system and the DGT device. The DIFS (DGT-induced fluxes in soils) model provides a numerical simulation of this dynamic system (11, 12). It assumes a single pool of particles whose interactions with reactive trace metals are described by a linear distribution coefficient (Kdl) between labile metal present in the solid phase and metal in the solution. The kinetics of the interaction are taken into account by adsorption and desorption rate constants (k1 and k-1), while transport throughout the system is diffusion controlled. DIFS has been developed and used to advance conceptual understanding of the dynamic response of soils to perturbations that locally lower concentrations, including resins and plants (11, 12), but it has not been tested systematically. This paper assesses the capability of DIFS to model DGT-derived data by making DGT measurements over a range of deployment times. The derived Kdl and kinetic parameters for the undisturbed soil system are compared to more conventional measurements.
Principles of DGT and DIFS The DGT plastic device houses a resin-gel layer that is separated from the soil by a diffusion gel layer and a protective membrane. The resin gel incorporates Chelex-100 resin that strongly binds labile trace metal species that diffuse through the diffusion layer. This leads to the formation of a linear concentration gradient in the diffusion-gel layer (Figure 1). The gradient depends on the thickness of the diffusion layer (∆g) and the interfacial concentration of labile trace metal species (Ci). It determines the flux (F(t)) of metal toward the resin gel according to Fick’s first law (eq 1):
F(t) ) φdDd
Ci(t) ∆g
(1)
where φd is the porosity of the diffusion gel and Dd is the diffusion coefficient of the labile trace metal species in the diffusion layer. Thus, DGT acts as a sink that induces a welldefined flux of trace metals from the soil to the DGT probe. VOL. 36, NO. 3, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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soil solution concentration (Csoln) provides a ratio (R) that gives an indication of the extent of the depletion of soil solution concentrations at the DGT interface (eq 5):
R)
FIGURE 1. Processes induced by deployment of a DGT probe (exploded view) in a soil slurry. The mass (M) of metal is accumulated by diffusion across the diffusion layer of exposed interfacial area (A). Further explanations are given in the text. F may change during the DGT deployment if Ci changes. The accumulation of trace metals by the resin gel tends to deplete trace metals in the soil solution adjacent to the DGT interface (Figure 1). With increasing deployment time, trace metals in soil solution may become progressively depleted further away from the interface. Resupply of trace metals from particles to soil solution counteracts the depletion. The depletion is most pronounced when there is no resupply from the solid phase. The concentration of particulate, labile, trace metal (Cls) available for release and the kinetics of the adsorption and desorption processes will determine the efficiency with which trace metal concentrations are sustained in soil solution relative to their initial level. DGT continuously accumulates metal on the resin gel during deployment. The total mass of metal (M) accumulated per unit area over the deployment time (T) is given by integrating the flux over the deployment time (eq 2): T
M)
∑F(t) dt
(2)
t)0
The time-averaged interfacial concentration (CDGT) can be calculated from the directly measurable quantity M (eq 3): T
∑C (t) dt i
CDGT )
t)0
) T
M∆g φdDdT
(3)
M is determined analytically by measurement of the eluent concentration (Ce) after elution of the resin gel (volume, Vgel) with 1 M HNO3 (volume, VHNO3), using an elution factor (fe) (eq 4):
M)
Ce(VHNO3 + Vgel) feA
(4)
Comparison of CDGT with the independently measured initial 350
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CDGT Csoln
(5)
A linear concentration gradient that will determine the magnitude of F is established in the diffusion layer within minutes of insertion. The concentration gradient at the resin gel/diffusive gel boundary is initially zero, as there is no metal initially in the diffusive layer. The gradient increases as the diffusion layer is supplied with metal from the soil. Depending on the capacity of the solid phase to resupply metal to the soil solution and the rate of this resupply, the flux will tend to decrease with time. CDGT and R provide integrated measurements of these changes over the deployment time. Therefore, the value of R is dependent on the deployment time of the DGT device in the soil. The DIFS model quantifies the dependence of R on resupply of trace metals from solid phase to solution, coupled to diffusional supply to the interface and across the diffusion layer to the resin gel, by solving a pair of linked partial differential equations describing dissolved and sorbed trace metal concentrations in the soil and DGT device (11). DIFS is a one-dimensional (1D) model operating along the axis perpendicular to the DGT interface. It uses Kdl (eq 6) and the response time (Tc) (eq 7) to describe adsorption/desorption kinetics (Figure 1).
Cls Csoln
(6)
1 k1 + k-1
(7)
Kdl ) Tc )
Tc defines the time needed for the partitioning components of Kdl to reach 63% of their equilibrium value (8). DIFS requires data for Csoln, soil porosity (φs), diffusion layer porosity (φd), diffusion layer thickness (∆g), particle concentration (Pc), effective diffusion coefficient in the soil (Ds), diffusion coefficient in the diffusion layer (Dd), and deployment time (T). Two of the three parameters Kdl, Tc, and R are supplied as inputs, and DIFS calculates the other parameter. Distributions of solution and solid-phase concentrations through the DGT-soil system are calculated for any chosen time. In this work, DGT devices were deployed for different times. At each time, CDGT (eq 3) was measured directly and R was calculated (eq 5). The two unknowns, Kdl and Tc, were derived from the best model fit of plots of R versus deployment time (T). Even though theoretically two measurements at appropriately spaced T are sufficient, a large number of data points is desirable to assess the goodness of fit between model and measurements over a large range of deployment times.
Methods DGT Devices. Cylindrical DGT devices were prepared using polyacrylamide gels with 0.12% cross-linker and Chelex-100 resin according to the procedure detailed elsewhere (13). The interfacial area (A) in contact with the soil is 3.14 cm2, and ∆g ) 0.101 cm (diffusion gel layer 0.86 mm + membrane 0.15 mm). It has been previously established that φd ) 0.95 (13). Dd has been shown to approximate closely to D0, the diffusion coefficient of the free aqua complexes of the trace metals (14). Dd values were 5.89 × 10-6 cm2 s-1 (Cd), 6.02 × 10-6 cm2 s-1 (Cu), 5.58 × 10-6 cm2 s-1 (Ni), and 5.87 × 10-6 cm2 s-1 (Zn).
FIGURE 2. Dependence of experimental measurements of R for Cd, Cu, Ni, and Zn on time. The lines show the optimal DIFS model fits, resulting in values for Kdl (mL/g) and Tc (s) shown. Deployment in Soil Slurry. The soil was one of a series (soil G, Fladbury) used in a 2-yr time series study of metal availability (15). It was a pelo-vertic alluvial gley soil with pH 5.8 and field capacity of 35.0% (weight percent of water/ oven-dry weight; this applies also for the moisture contents reported below). The soil had been spiked with metals 3 yr previously to give the following total metal contents (natural + spike): 3.31 mg/kg Cd, 161 mg/kg Cu, 121 mg/kg Ni, and 417 mg/kg Zn. Eight small plastic pots were each filled with 50 g of soil (moisture content 47.3%). Soil slurries were prepared by addition of 23 mL of deionized water to each pot, resulting in 115% moisture content. From this, Pc ) 0.869 g/mL and φs ) 0.753 were calculated, assuming a standard particle density ) 2.65 g/mL. Ds in the slurry was calculated using the relationship Ds ) D0/(1 - 2 ln φs) (16). Ds values were 3.76 × 10-6 cm2 s-1 (Cd), 3.84 × 10-6 cm2 s-1 (Cu), 3.56 × 10-6 cm2 s-1 (Ni), and 3.75 × 10-6 cm2 s-1 (Zn). The slurries were prepared on the day before DGT deployments to give some time for soil solutions to equilibrate with soil solids. DGT devices were carefully inserted to ensure complete contact with the soil slurry. Twenty-one DGT devices were deployed for times between 4 h and 19.5 d, all at 18 ( 2 °C. Upon retrieval, the DGT devices were jet-washed with deionized water to remove soil particles and then dissembled. The resin gels (Vgel ) 0.15 mL) were eluted with 1 M HNO3 (VHNO3 ) 1 mL) in closed microvials. The concentration of trace metals in the eluent (Ce) was measured by ICP-MS (Varian Ultramass) within various calibration ranges after appropriate dilution and using Rh as internal standard. An elution factor, fe ) 0.8, was used for the studied metals as found previously (13). M, CDGT, and R were calculated with eqs 3-5 using time-weighted averages of soil solution concentrations (Csoln). The Chelex capacity of a DGT device, estimated as 1.6 µmol of divalent ion/cm2, was not exceeded after 19.5 d. Soil Solutions. Soil solutions were sampled approximately every second deployment (totaling 11 samples) in order to monitor any temporal changes in trace metal concentrations (Csoln). After retrieval of the DGT device, the slurry was stirred, and a fraction (ca. 5-10 mL) was transferred into a 25-mL PTFE tube and centrifuged at 2000 rpm for 10 min. The supernatant was taken up with a plastic syringe and filtered
into microvials using 13 mm diameter, 0.45 µm pore size, disposable polysulfone filter assemblies (Whatman Puradisk) and acidified using 2 µL of 1 M HNO3 in each 100 µL. Soil solutions were analyzed by ICP-MS with Rh as internal standard using a MicroMist low uptake (200 µL/min) nebulizer and Cinnabar low-volume spray chamber (Glass Expansion). Over the whole deployment, trace metal concentrations declined by 25% for Zn (P ) 0.01), 17% for Ni (P ) 0.01), 6% for Cd (P ) 0.05), and 5% for Cu (statistically insignificant). At the P ) 0.05 level, the decline in soil solution concentration became statistically significant for Zn after 5 d, for Ni after 11 d, and for Cd after 15 d of deployment. Mixing the layer depleted by the DGT device with bulk soil could only account for a decline in bulk soil solution concentrations of, at most, 3%. The relatively larger decline in Zn and Ni soil solution concentrations probably reflects a slow reequilibration that occurs after raising the soil moisture content above saturation. The time-weighted averages of soil solution concentrations evaluated for the longest deployment time of 16.7 µg/L Cd, 66 µg/L Cu, 0.55 mg/L Ni, and 1.21 mg/L Zn were used as input parameters for DIFS. Exchangeable trace metals were extracted with 0.1 M Ca(NO3)2 prepared from Ca(NO3)2‚4H2O (99%; ACS reagent). A total of 25 mL was added to 5 g of soil (47.3% moisture content) in a PTFE tube and put on a rotating shaker for 5 d. Following centrifugation at 3000 rpm for 10 min, 5 mL of the extract was taken up with a syringe, filtered through Whatman Puradisks, and acidified with 100 µL of 1 M HNO3. Trace metals in the extract were determined by ICP-MS after 50-fold dilution using Rh as internal standard and expressed as concentration per mass of particulates. A distribution coefficient was calculated by dividing the extracted metal concentration on the solid phase over the soil solution concentration obtained after hydration of the soil for 24 h. Exchangeable Cd and Zn were also determined by isotopic exchange using established procedures (17) and expressed as distribution coefficients.
Results and Discussion Figure 2 shows experimental results and optimally fitted model lines for Cd, Cu, Ni, and Zn. The good fits of the modeled responses to the data justify the use of the simplest VOL. 36, NO. 3, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Experimental data and model simulation of R for Zn with error margins. (a) Tc is changed to produce a maximum 30% deviation in R from the best model fit. The model output is most sensitive to changes in Tc at short deployment times. (b) Kdl is changed to produce a maximum 30% deviation in R from the best model fit. The model output is most sensitive to changes in Kdl at long deployment times. possible model and suggest that any changes that may occur in the system during the deployment do not impact on the major resupply process. The largest values of R were observed for Zn, followed by Ni ) Cd > Cu, indicating that the ability of the soil to sustain initial soil solution concentrations decreases in that order. R declined more markedly with time for Zn, Ni, and Cd than for Cu. For Cu then, Ci must be nearly constant, indicating near steady-state conditions at the interface. This case is characterized by a large response time (Tc ) 3000 s). The decline of R is most pronounced at faster sorption kinetics (low Tc, as illustrated for Zn). The quality of the fits is sensitive to both Kdl and Tc. Figure 3 demonstrates the sensitivity of the model line to both parameters for the case of Zn. Changing Tc from its best fit value affects the model simulation of R at short deployment times (Figure 3a). A maximum +30% deviation in R from the best fit line is achieved by changing Tc to e60 s, with smaller values than 60 resulting in identical model simulation lines. A -30% deviation in R from the best fit line arises when Tc ) 1183 s. The legend in Figure 3a gives the corresponding
desorption rate constants and therefore provides a lowest limit for the value of k-1. Contrastingly, changing Kdl from its optimum value affects the model simulation of R at long deployment times (Figure 3b). When changing Kdl while Tc is fixed, a +30% deviation in R from the best fit line (Kdl ) 150 mL/g; Tc ) 300 s) arises for Kdl ) 287 mL/g. A -30% deviation in R arises when Kdl ) 61 mL/g. Changing Kdl also affects the fitted value of k-1 (Figure 3b). The resulting variation in k-1 covers a much smaller range than that resulting from a change in Tc (Figure 3a). The good agreement of the optimal model fit to the data shows that the uncertainty range in Kdl is much smaller than the range presented in this sensitivity analysis. The accuracy of the D0, Pc, and φd values used in the model also affects the model output. A sensitivity analysis monitoring the response of R to changes in D0, Pc, and φd was conducted previously (11), which has demonstrated that a 10% change in any of these parameters results in a less than 4% change in R. DGT measurement precision should not be a problem, even at short times. In experiments with a different soil, DGTmeasured Cd from probes deployed in different pots for the same time (22 h) had a relative standard deviation (RSD) of 1.6%. Similarly, Cd concentration in soil solution had a RSD ) 4.0% when soil solutions were sampled at the same time from different pots (4 replicates). Other workers have found the RSD of DGT measurements in soils to be better than 8% (18). Values of Kdl, the response time Tc, the adsorption rate constant k1, and the desorption rate constant k-1 derived from DGT measurements by DIFS modeling are presented in Table 1. Values of Kd measured by isotopic exchange and by treatment with Ca(NO3)2 are presented for comparison. Values obtained by isotopic exchange are higher than those based on Ca(NO3)2 extraction. These findings are consistent with previous reports (17). Ca(NO3)2 is believed to remove virtually all the Zn or Cd from exchangeable sites, but only a fairly small proportion of the chemisorbed metals are expected to be released due to the change in ionic strength. By contrast, the isotopic exchange method allows measurement of all the metal that is in labile equilibrium with the solution phase. This can include a larger proportion of the chemisorbed metal. The isotopic exchange experiment was conducted 1 yr prior to the DGT experiment and Ca(NO3)2 extraction, raising the possibility that the soil metal pools changed over that period. Values for the exchangeable solidphase pool (Cs) determined in a Ca(NO3)2 extraction carried out at the time of isotopic exchange experiments agreed well with values obtained 1 yr later (Table 1), demonstrating that the exchangeable pool of metals did not change over the 1-yr period. The Kdl value for Zn determined by DGT was larger than the Kd obtained by isotopic exchange, whereas the DGTdetermined Kdl for Cd was remarkably close to the value determined by isotopic exchange. The agreement of the DGT and isotopic exchange measurements suggests that they
TABLE 1. List of Parameters (Explained in the Text) Modeled by DIFS for Cd, Cu, Ni, and Zna Kdl, DGT (mL/g) Kd, isotopic exchangeb (mL/g) Kd, Ca(NO3)2 exch (mL/g) Tc (s) k1 (s-1) k-1 (s-1) Cs, Ca(NO3)2 exch (mg/kg) Cs, Ca(NO3)2 exchb (mg/kg)
Cd
Cu
Ni
Zn
100 125 27 700 1.41 × 10-3 1.6 × 10-5 0.48 0.55
250 nmc 5 3000 3.32 × 10-4 1.5 × 10-6 0.34 nm
150 nm 26 800 1.24 × 10-3 9.5 × 10-6 15.8 nm
150 51 26 300 3.31 × 10-3 2.5 × 10-5 37.8 31.7
a Values of K obtained by isotopic exchange and by extraction with Ca(NO ) are included. d 3 2 measured.
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b
Experiments conducted 1 yr earlier. c nm, not
FIGURE 4. DIFS model output for Zn, simulating the behavior of Csoln and Cls in the vicinity of the DGT interface during deployment. Values of Kdl and Tc used in panel c correspond to the optimized best fit, as used in Figure 2. The other panels examine the effect of systematically changing Kdl and Tc. measure similar solid-phase pools. Although there are differences, they are not large when it is considered that the isotopic exchange measurements were made 1 yr prior to the DGT measurements. In that time, solution concentrations had declined due to aging effects and due to the different moisture content of the soil. These results suggest that the solid-phase pool of metal affected by the removal of labile metal by DGT, which operates on a time scale of minutes, is similar to the solid-phase pool of metal that can isotopically exchange with solution on a time scale of 2 d. It is difficult to rationalize the relatively large difference as compared to the other metals between Kdl measured for Cu by DGT and the values obtained by Ca(NO3)2 exchange. By comparison with the other metals, the Ca(NO3)2 exchangeable Kd appears to be more out of line than the DGTdetermined Kdl. A possible explanation is that a larger proportion of Cu than of the other metals is bound to the
solid phase by selective sites that do not allow exchange with Ca. However, the lower R values obtained for Cu than the other metals (Figure 2) raise the possibility of bias associated with the DGT measurements. DGT does not measure trace metals bound on colloids or kinetically inert trace metal complexes in soil solution. However, these species are included in the measurement of Csoln. Moreover, the diffusion coefficients used are based on simple ions and may be overestimates for labile organically complexed trace metals supplied to the resin. Both of these effects would tend to result in R values smaller than the true values. However, if R values for Cu were uniformly higher than those measured, the modeled Kdl values would also be higher. For Cd, Ni, and Zn, the measured values of Tc ranged from 5 to 13 min (Table 1), with Cu again being atypical with a value of 50 min. The longer time might indicate release from sites other than at the surface. Generally short response VOL. 36, NO. 3, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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times (less than hours) have been suggested as characteristic for soils and sediments (8). Response times of the interaction of Zn with a variety of marine particles (19) range from 11 to 260 s (corrected to the same particle concentration), in close agreement with our value of 300 s. Response times for Cd calculated from rate constants quoted in the same study (19) range from 34 to 2100 s, embracing our value of 700 s. It is difficult to compare the values for the rate constant for metal release, k-1, (Table 1) with those of other workers. Even though the kinetics of sorption on soils or mineral phases is an active area of research (20), there is a lack of first-order desorption rate constants for trace metals in soils. In part this is due to other kinetic models (Elovich equation, parabolic diffusion model) being given preference over the one-site kinetic model (21, 22). Experiments that investigated the rate of partition of radiolabeled Zn with marine particles provided a value of k-1 of 2 × 10-5 s-1, in very good agreement with the DGT-measured value of 2.5 × 10-5 (Table 1) (23). In a study conducted with a variety of marine particles (19), k-1 values for Zn ranged from 8.1 × 10-7 to 2.3 × 10-5 s-1 and for Cd ranged from 3.5 × 10-6 to 1.2 × 10-5 s-1, with the higher values being close to our measured values. Two-site first-order desorption rate constants for Cd on iron and manganese oxides range from 10-2 to 2 × 10-6 s-1 (24) embracing the value of 1.6 × 10-5 s-1 we found.
Appraisal of DIFS DIFS was generally able to model the experimental results well. However, for Ni and Zn, the initial decline in Rmeasured is steeper than Rmodeled (Figure 2). This may be an indication that the approach to equilibrium is inaccurately modeled using a single pair of forward and reverse rate constants. Possibly multiple pools of sorption sites characterized by different affinity and sorption kinetics should be used. A steeper measured decline in R with T could be caused by fast supply from a solid-phase pool with low capacity (low Kdl), while at long deployment times the slower supply from pools with large capacity could dominate. DIFS provides an opportunity to appreciate how capacity and kinetic factors govern the transfer to a sink, be that a Chelex resin or a plant. The modeled distributions of the solution and solid-phase concentrations of Zn through the diffusive layer and soil with respect to distance from the interface are shown at 6 h, 3 d, and 20 d (Figure 4c). The effects on these distributions of changing the values of Kdl and Tc are shown in the rest of the figure. When response times are short (rapid resupply; Figure 4a,b), dissolved concentration profiles closely reflect the particulate concentration profiles at any time during the deployment (see inset figures). At low Kdl values, when the size of the particulate reservoir is small, there is a substantial progressive depletion with time. A large particulate reservoir (Kdl ) 10000 mL/g) sustains dissolved concentrations relatively well throughout the deployment. At longer response times (Tc ) 300 s, the actual case for Zn; Figure 4c), the ability of particles to supply trace metals in the necessary time diminishes. Consequently, depletion of dissolved metals is more pronounced than depletion of the solid phase (see inset) at shorter times (6 h) but not for longer times. The dissolved concentration profiles at short times (6 h) are controlled by Tc, with almost identical profiles for both small and large Kdl. However, for long times at low Kdl, the solid-phase reservoir again controls the supply, and it becomes progressively depleted. At Kdl g 10 000 mL/g, insignificant depletion of particulate metal yields a steadystate dissolved concentration profile throughout the deployment that is insensitive to further increases in Kdl (Figure 4d), indicating kinetic control of dissolved concentrations at all times. Further increases in response time restrict the resupply from the solid phase even more, resulting in extended depletion zones, with an eventual tendency toward 354
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diffusion only profiles for extreme values of Tc (Figure 4e). Therefore, when kinetics are fast (Tc e ca. 10 s), Kdl controls dissolved concentration profiles. Above this threshold value of Tc, slower kinetic supply exerts increasing influence over dissolved concentration profiles for short times. Kdl provides the ultimate control at long times. These conclusions are derived from a model that considers the simplest possible kinetic and capacity control in a framework of diffusional transport. Generally, then, for studies on time scales exceeding 1 d, the pool size of available metal is more important than the kinetics of supply from solid phase to solution. Figure 4 shows how Csoln and Cls for Zn change with time in the vicinity of the DGT probe during deployment. The distance of depletion extends significantly away from the interface after 20 d (>5% depletion at x < 0.6 cm, see Figure 4c). When the depletion distance is small as compared to the radius (1 cm) of the probe, only diffusion perpendicular to the probe contributes significantly to the total flux, and a 1D model is valid. However, for large depletion distances, angular diffusion to the edge of the probe can be significant. This effect is only appreciable for long deployment times when depletion distances are large. Therefore, it will not affect the value of Tc, which is only sensitive to initial measurements, but it could result in a slight overestimation of Kdl.
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Received for review May 1, 2001. Revised manuscript received September 14, 2001. Accepted September 28, 2001. ES010917D
