Environ. Sci. Technol. 1997, 31, 3110-3119
Temporal, Spatial, and Resolution Constraints for in Situ Sampling Devices Using Diffusional Equilibration: Dialysis and DET MICHAEL P. HARPER, WILLIAM DAVISON,* AND WLODEK TYCH Institute of Environmental and Biological Sciences, Lancaster University, Lancaster LA1 4YQ, U.K.
The techniques of dialysis and diffusional equilibration in thin films (DET) are used to measure solute concentrations in sediment porewaters. Their performance was assessed using two-dimensional modeling with a view to establishing their limitations and providing guidelines for their application in the field and the subsequent interpretation of results. Three alternative types of supply to the samplers were considered: (i) where porewater solute concentrations are well buffered by desorption from or dissolution of the solid phase; (ii) where there is no resupply to the porewater apart from diffusion; (iii) where there is a partial resupply to the porewater from the sediment solid phase. Using typical sampler designs (DET gels 0.4 mm thick and peeper cells 6 mm deep), the times for 99% equilibration in the buffered case were calculated as 18 min and 36 h for DET and dialysis peepers, respectively. For the purely diffusive case, 99% equilibration times are 78 h (DET) and 1380 days (dialysis peepers). Experimentally observed equilibration times (∼ hours for DET, up to 2-3 weeks for peepers) lie between the modeled buffered and diffusive case values and are consistent with the modeled partial resupply from solid phase to porewater. The equilibration time is inversely proportional to the solute diffusion coefficient and increases with peeper cell depth or gel layer thickness. To ensure minimum equilibrium times in multiple depolyments, DET devices should be separated by >2 cm and peepers by >16 cm. Porewater concentration maxima and gradients are underestimated by both techniques, resulting in underestimations of vertical fluxes calculated from Fick’s first law. DET performs better for a given width of a porewater maximum. As concentration maxima become wider, the fidelity of measured profiles is improved. The fidelity of peeper profiles is limited largely by the cell size and separation, and that of DET by slicing interval and gel/filter thickness. Peeper cell depth does not affect the measured peak concentrations, but increasing DET gel thickness underestimates measured peak concentrations. To minimize back-equilibration times for DET analysis, diffusional path lengths and eluent volumes should be as small as possible.
Introduction Dialysis and diffusional equilibrium in thin film gels (DET) are techniques, used to separate solutes from natural waters, * Author to whom correspondence should be addressed. E-mail:
[email protected]; telephone: 01524 593935; fax: 01524 593985.
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that rely on the attainment of diffusional equilibrium between a sampling medium (acrylamide gels for DET, deionized water or electrolyte solution for dialysis) and the natural water. In DET, a thin (typically 0.4 or 0.8 mm) polyacrylamide hydrogel is covered with a 0.45-µm cellulose nitrate filter and encased in a perspex holder prior to deployment. Once in place, dissolved species diffuse through the filter into the gel by molecular diffusion until equilibrium is achieved. After removal, the concentration of a solute in the gel (and by inference in the natural water) is determined by backequilibration with a known volume of an eluent, which is subsequently analyzed using an appropriate analytical technique. For dialysis, the principle is similar except that the sampling solution is analyzed directly. Dialysis has been used extensively over the past 20 years (1-4), whereas the use of DET is relatively recent (5-7). Both techniques have been primarily used to separate solutes from the porewaters of near-surface sediments where steep concentration gradients can occur (8). Sediment peepers use dialysis to equilibrate a large number of separated cells arranged vertically. They are deployed in situ. DET assemblies usually comprise gel and filter sandwiched between two perspex plates, with the filter exposed to the sediment through a 10 × 1 cm window (long axis vertical) in the perspex front plate (6). Deployment is either in situ or in sediment cores. After equilibration, the assembly is retrieved, the filter is discarded, and either the gel is sliced quickly or the solute is chemically ‘fixed’ as an immobile solid phase immediately after retrieval. The gel is then either analyzed directly using a beam technique (at a maximum resolution of 100 µm) or more commonly sliced at g1-mm resolution. In the latter case, back-equilibration with a known volume of an eluent (water if mobile, acid if immobilized) enables the average concentration in each slice to be calculated. The objective in measuring solute concentrations near the sediment-water interface is often to measure accurately concentration gradients for use in calculating fluxes using a modified version of Fick’s first law (9, 10):
J ) -φDs
∂C ∂x
(1)
where J is the vertical flux, φ is the sediment porosity, Ds is the effective solute diffusion coefficient within porewaters, and ∂C/∂x is the vertical concentration gradient. The reliability of fluxes calculated from eq 1 is dependent on the accuracy of concentration gradients and, therefore, on the accuracy of measured concentrations. The fidelity of measured concentration profiles with respect to porewater concentrations is consequently crucial for accurate flux calculations. That flux estimations based on discrete concentration profiles are likely to be systematically inaccurate is well understood (10, 11), but the magnitude of the problem remains largely unquantified. To assess profile fidelity, we need to understand the processes that limit it and derive methods to quantify it. The aim is to establish practical guidelines for sampling strategies and enable proper interpretation of results and quantification of errors for workers applying these techniques in the field. Constraints on the Fidelity of Measured Profiles. A number of processes act to reduce measured profile fidelity. Concentrations of an analyte within peeper cells or gel slices are averaged during analysis, so any structure on a scale equal to or less than the resolution of the technique will be lost (profile averaging). A less obvious factor that influences the magnitude of the error introduced by averaging concentrations is the vertical position of the peeper cells or gel slices
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FIGURE 1. Lateral diffusion in a gel. A persistent square peak (1 mm wide) in a porewater profile (a) is in contact with a gel. Solutes diffuse into the gel both horizontally and vertically along concentration gradients away from the high concentrations. Consequently, the horizontally averaged concentration profile in the gel (b) even at equilibrium is a ‘relaxed’ form of the original. with respect to porewater concentration profiles (the phase shift). For example, whether a peak concentration in a porewater profile is coincident with a peeper cell (in phase) or between cells (out of phase) can markedly affect the fidelity of the measurement. In one respect, DET is at a disadvantage in having a continuous sampling medium. Due to the process of lateral diffusion (illustrated in Figure 1) the concentration profile in the gel will be a ‘degraded’ form of that in the porewater, even at equilibrium. The absence in the gel of the sources and sinks responsible for vertical structure in the porewater means that concentration gradients are not fully maintained in the gel. This process also occurs with peepers, but separated cells limit its effect. Further changes occur in the gel after removal from the sediment due to the relaxation of profiles in the absence of external sources. Sampling using DET takes advantage of the gel matrix restricting transport within the gel to molecular diffusion. Concentration profiles within the gel, therefore, only relax slowly, allowing subsampling by slicing at millimeter intervals. However, the degree of relaxation depends on the time elapsed between retrieval and either slicing or fixing and on the shape of the profile (6). When sampling redox-sensitive metals (Fe, Mn), oxygen contamination will also affect fidelity (12) but is not considered here. Assessing Technique Performance. By modeling twodimensional (2D) transport in sampling media and sediments, we have investigated the performance of diffusional equilibration techniques in terms of both profile fidelity and equilibration times. Changes in concentration profiles within the samplers during deployment, retrieval, handling, and analysis are modeled. The transport of species through thinfilm gels has previously been demonstrated to obey Fick’s laws of diffusion (6). Although solute transport in sediments can be complicated by bioturbation or bioirrigation, these have been neglected in order to investigate the basic processes. For one-dimensional (1D) diffusional transport in sediments, we can use the model proposed by Berner (9), neglecting porewater advection or bioturbation/bioirrigation effects:
FIGURE 2. Edge effects in a DET sampler. This overhead view shows concentration contours (as a percentage of the original porewater concentration) in a horizontal plane around a DET assembly after 2 h deployment. Compared to 1D diffusion (a planar DET assembly of infinite extent), concentration gradients are steeper, fluxes are greater, and equilibration times are reduced.
(
)
∂Ds Ds ∂φ ∂C ∂C ∂2 C ) Ds 2 + + ∂t ∂z φ ∂z ∂z ∂z
(2)
where C is the dissolved porewater concentration, φ is the sediment porosity, Ds is the solute diffusion coefficient, and z is the vertical distance below the sediment-water interface. This can be reduced to eq 3 when changes in porosity and the diffusion coefficient with respect to depth are negligible:
∂2 C ∂C ) Ds 2 ∂t ∂z
(3)
For the sake of simplicity, a 1D approach is often used to model what is a three-dimensional system. For example, concentration data are generally available as vertical depth profiles, horizontal homogeneity is assumed, and 1D models can be used to model vertical transport (9, 13). However where 1D models are used to investigate interactions between samplers and sediments, an infinite planar sampling surface is implicitly assumed, and concentration gradients within samplers cannot be investigated. Realistically, a sampler of finite size is surrounded by ‘infinite’ sediment. The finite size introduces edge effects where solutes diffuse from sediment beyond the edge of the samplers (illustrated in Figure 2), producing steeper concentration gradients in the porewaters as compared to the 1D case. Solute Resupply from Sediment. The flux of solute to the sampler is supplied from the porewater by diffusive transport, with a degree of resupply from the sediment solid phase. The extent to which resupply ‘buffers’ porewater concentrations varies, and any number of cases could be considered. This work considers the two extreme cases and one intermediate case: (a) The buffered case where the flux from the sediment solid phase to porewaters (by desorption or dissolution) or local convective transport effectively buffers porewater concentrations even over short time scales. The sampler is, therefore, in contact with sediment porewater characterized
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by a persistent concentration profile. Zn and Cd have recently been shown to conform to this case in a freshwater sediment (14). (b) The diffusive case where there is no resupply from the solid phase (i.e., the total mass of solute in the aqueous system is conserved). Concentration gradients will therefore diminish over time. The only supply to the sampler is by diffusion through the porewaters. This assumption is supported by recent studies (14, 15) that have shown that the flux of certain species to peepers or gel samplers can, depending on the time scale of resupply, be limited by diffusion through the sediment. (c) The partial resupply case where there is some resupply from the solid phase, but the porewater concentration in contact with the sampler is not necessarily persistent. The resupply is governed by a first-order (de)sorption reaction between the solid and dissolved phases.
Methods Model Formulation. Solute transport in both sediment and sampling medium is assumed to be by molecular diffusion according to the 2D equivalent of eq 3:
∂C ) D∇2C ∂t
(4)
where ∇2C is the second spatial derivative of solute concentration within the sampling medium or sediment, and D is the appropriate diffusion coefficient. For diffusion within gels and peeper cells, this is taken to be the appropriate free ion diffusion coefficient (Do) given by Li and Gregory (17). Diffusion coefficients through the filter and gel are the same, as found experimentally by Davison et al. (16). The effective diffusion coefficient within sediments (Ds) is less than Do due to the increased diffusional path length or tortuosity (θ) of the sediment. Li and Gregory give the relationship between the two as
Ds )
Do θ2
(5)
For this work values of Do ) 5 × 10-6 cm2 s-1 and θ2 ) 1.5 were used. The former is representative for metals (Fe, Mn, Cu, Zn, Ni) at temperatures of approximately 10 °C. The latter value is given by Sweerts et al. (18) as typical of a sediment with high organic content and high (0.6 < φ < 0.95) porosity such as those of near-surface sediments in productive lakes. Recent work (19) suggests that this may be an overestimate. The choice of Do is to some extent arbitrary, so the sensitivity of the models was tested using a range of values from 10-6 to 10-5 cm2 s-1. For simplicity, sediment porosity (φ) was taken to be 1. Resupply from the sediment solid phase to the porewater is implicitly assumed in the buffered case and excluded in the diffusive case. The partial resupply case explicity considers the possibility of resupply by desorption from solid surface sites according to the model of Nyffeler et al. (20). If Cs is the concentration of a solute sorbed to the solid phase and only the solutes in the porewater are subject to diffusional transport, then the rates of change of C and Cs are given by eq 6. The first-order rate constants for desorption from and sorption to the solid phase are k-1 and k1. The term Cp is the concentration of particles (the ratio of mass of particles to volume of porewater, in a given volume of total sediment) and is taken to be 0.5 g cm-3. R (eq 6a) is an optional source term introduced in a portion of the domain sediment to generate a vertical porewater concentration profile.
∂C ) -k1C + k-1CpCs + D∇2C + R ∂t
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∂Cs k1C - k-1Cs ) ∂t Cp
(6b)
The model for the partial resupply case is eq 6, that for the buffered and diffusive cases is eq 4. The differences between these latter cases are in the model domain and the initial/ boundary conditions. Model Domain. Three factors determine the geometry of model domains. The first two are the sampler design (DET or peeper) and dimensions and which case (buffered, diffusive, or partial resupply) is being modeled. The third is the information required from the simulation, in general, either (a) the equilibration time for the sampler with the porewater or (b) the fidelity of the measured concentration profile with respect to the porewater concentration profile. In all cases, the diffusive and partial resupply cases include sediment, the buffered case does not. Each combination of these factors requires a different model domain. The details for each case are given below. In our description of sampler geometries and model domains, we have used the following coordinate system: Z is the vertical axis (i.e., the distance below the sediment-water interface); X and Y the horizontal axes perpendicular and parallel, respectively, to the front of the sampler. Any dimension or distance given is followed by its orientation according to this coordinate system. DET. For sediment porewater sampling using DET assemblies, a gel of thickness ∆g (typically 0.4 mm) is covered by a 0.13 mm (X) thick filter and exposed to the sediment through a 1 × 10 cm (Y × Z) window (6). Determining equilibration time, where the sediment is assumed to be vertically uniform, is best achieved by modeling the horizontal plane (X × Y) through the DET assembly. In this way ‘edge effects’, which result in faster equilibration times for the diffusive case, are taken into account. Diffusion in from the sides effectively means concentration gradients are steeper than with 1D models, reducing the overall time to equilibrium. The model domain and boundary conditions for the diffusive and partial resupply cases are depicted in Figure 3a. As the area of sediment included in the domain was variable, dimensions have not been given. The domain for the buffered case (inset) consists of just the gel and the filter. To investigate profile fidelity, it was necessary to consider the vertical transport and distribution of species in the gel and sediment. A vertical plane (X × Z) was chosen running through the center of the gel perpendicular to the plane of the gel holder. Concentrations in the horizontal axis parallel to the perspex holder (Y) were therefore assumed to be uniform. The model domain for the diffusive and partial resupply cases are depicted in Figure 3b with that for the buffered case inset. Peepers. The peeper model is based on a design similar to that described by Carignan et al. (3). The domain for the diffusive and partial resupply cases is shown in Figure 4 with that for the buffered case inset. The depth (X) of the cells is ∆c (typically 6 mm) and, as with DET, the area of sediment included is variable. Unlike DET, a vertical model (X × Z) domain is used for investigating both equilibration times and profile fidelity. A vertical plane for equilibrium times was chosen as the cell dimensions suggest that the edge effects vertically (between cells) will be more significant in reducing equilibrium times than those horizontally (at the ends of cells). Initial and Boundary Conditions. The initial and boundary conditions are given in Table 1. Co is the initial concentration. The function f(z,σ) is defined (eq 7) to give a vertical Gaussian-shaped peak in porewater concentration, with varying dispersion coefficient, σ (analogous to standard deviation in a normal probability distribution): 2
2
f(z,σ) ) ke-((z - zo) /2σ )
(7)
FIGURE 4. Model domains for peeper, comprising a vertical plane perpendicular to the front of the assembly. The number of cells used in the model varied between 5 and 10. Inset is the buffered case domain, where P is the boundary condition for determining equilibration times and Q is that for investigating fidelity. P and Q are defined in Table 1.
Results and Discussion
FIGURE 3. Model domains for DET partial resupply and diffusive cases: (a, top) horizontal plane through assembly (the perspex block is not part of the domain); (b, bottom) vertical plane perpendicular to assembly. Insets show the domains for the buffered cases. The axes X, Y, and Z refer to the coordinate system described in the text. The initial and boundary conditions, including those for P and Q, are given in Table 1. The thickness (X) of the gels is ∆g; that of the filter is 0.13 mm. f(z,σ) is given a maximal value of 1 by scaling the constant k, and zo is the vertical coordinate of the peak maximum (zero in most cases). Cs,o is the initial value of Cs and is calculated from Co (eq 8) by rearranging eq 6b, assuming that the sediment is in sorptive equilibrium before deployment of the sampler (i.e., ∂C/∂t ) 0). Kd is the distribution coefficient between the sorbed and dissolved phases:
Cs,o )
1 k1 C ) KdCo Cp k-1 o
(8)
The boundary conditions are generally ∇C ) 0 (i.e., the concentration gradient at the domain boundaries is zero). The only exceptions to this are for the buffered case where the filter boundary (representing the interface between the filter and sediment) has the condition C ) 1 (for investigating equilibration times ) or C ) f(z,σ) (for investigating fidelity). The models were solved using the finite element method by the Partial Differential Equation Toolbox for Matlab. All models were run to equilibrium where it existed (for buffered and partial resupply case scenarios) or to a point where all structure has degraded (for the diffusive case). The model parameters and domains (such as Do, θ, ∆g, ∆c, area of sediment) were varied systematically.
Equilibrium Times and Spatial Depletion. The times to achieve mean concentrations in the DET gel or peeper cell of between 95% and 99% of those in the porewaters (the 95 and 99% equilibration times) are given in Table 2. For the buffered case (where the porewater concentration in contact with the sampler is constant), these times are the same as predicted by 1D models (16), and samplers clearly equilibrate quickly. The diffusive case (where no sources exist in the sediment and supply is by diffusion only) represents the ‘worst case’ in terms of equilibration times. Here the difference between 2D and 1D models is marked with equilibration occurring much faster in the former case, due to the edge effects discussed earlier. The partial resupply case (where resupply occurs from the sediment, but at a rate insufficiently fast to buffer the porewater concentrations), results in times that are between the buffered and diffusive cases, but much closer to the former. This is especially true for peepers, where the equilibration time is long enough for a resupply process with a given rate constant to be a more significant source of supply to the sampler than for DET. Our selections of the rate constants k1 and k-1 (chosen such that k-1 ) 10-7 s-1 and Kd ) 105 cm3 g-1) that yield the equilibration times in Table 2 are inevitably arbitrary. If they increase, then the resupply term becomes more significant, and the equilibrium time approaches that for the buffered case. In practice, the rate constants are unlikely to be known, although it should be possible to fit these parameters for time series data on concentrations in samplers. The equilibration time is inversely proportional to Do, i.e., if Do is doubled, equilibrium times are halved. The time for samplers to achieve diffusional equilibration is also dependent on the geometry of the sampling medium, particularly the cell depth. This finding agrees with previous modeling of dialysis samplers (1, 2) that showed that the equilibration time is strongly dependent on cell depth. Making peeper cells or DET gels flush with the sampler surface will not affect equilibration times at all in the buffered case or significantly
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TABLE 1. Model Domains, Boundary, and Initial Conditionsa buffered domain
G+F horizontal (DET) vertical (peeper) P: C ) 1 otherwise ∇C ) 0 Co ) 0
boundary conditions initial conditions
domain
diffusive Equilibrium Time G+F+S horizontal (DET) vertical (peeper) ∇C ) 0
Co ) 0 (sampler) Co ) 1 (sediment) Resolution G+F+S vertical ∇C ) 0
G+F vertical Q: C ) f(z,σ) otherwise ∇C ) 0 Co ) 0
boundary conditions initial conditions
Co ) 0 (sampler) Co ) f(z,σ) (sediment)
partial resupply G+F+S horizontal (DET) vertical (peeper) ∇C ) 0 ∇ Cs ) 0 Co ) 0 (sampler) Co ) 1, Cs,o ) Kd (sediment) G+F+S vertical ∇C ) 0 ∇ Cs ) 0 Co ) 0 (sampler) Co ) 1, Cs,o ) Kd (sediment)
a G, F, and S represent gel, filter, and sediment. Horizontal and vertical refer to the plane of the model domain. The boundary conditions P and Q refer to the labels on Figures 3 and 4. The function f(z,σ) is defined by eq 7. Sampler refers to either the gel and filter (DET) or to the cell and filter (peepers).
TABLE 2. Times to 95% (99% in Brackets) of Porewater Concentrations (m, minutes; h, hours; d, days) and Approximate Depletion Distances beyond which Porewater Concentrations Remain >99% of Initial Concentrations after Typical Deployment Times (24 h for DET, 1 month for Peepers) DET buffered case diffusive case (2D) diffusive case (1D) partial resupply case (1D) diffusive case (2D) diffusive case (1D)
Times 12 m (18) 15 h (78) 27 h (660) 41 m (65)
Distances 10 mm 14 mm
dialysis peepers 23 h (36) 56 d (1380) 157 d (3914) 30 h (47) 80 mm 90 mm
in the diffusive case. In the partial resupply case, equilibration times will be reduced. We have compared the equilibration times calculated from systematically varying the gel thickness or cell depth to the times, te, calculated using the Einstein relationship (eq 9):
L2 ) 2Dte
(9)
Here, L represents the diffusive distance, D is the diffusion coefficient, and te is the time. For the buffered case, taking L to be the gel + filter thickness or cell depth, the 95% (99%) equilibration times are approximately equal to 2.5te (4te) for DET and 2.3te (3.6te) for peepers. The difference in the coefficients between DET and peepers is attributable to a significant proportion of the diffusive distance in DET (the filter) being occluded from the percentage definition of equilibration. For the 1D diffusive case, 95% (99%) equilibration times are approximately 390te (9500te) for both DET and peepers. The equilibration times for the buffered and 1D diffusive cases can therefore be calculated using eq 9 and are proportional to the square of the diffusional medium depth. For the partial resupply and 2D diffusive cases, the Einstein relationship is not a useful predictor of equilibration time as there is no linear relationship between te and the 95% or 99% equilibration times given by the model. According to our arbitrary partial resupply case, 95% (99%) equilibration times are less than 13te (20te) for DET (with gel thicknesses g0.2 mm) and less than 3.5te (5te) for peepers (with cell depths g3 mm), and that for the 2D diffusive case the times in hours are approximately 400L (2200L), where L is in centimeters. According to our buffered case, samplers can be placed close to one another without interferences; for the partial
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resupply case, porewater concentrations more than a few millimeters removed from the sampler are not depleted. For the diffusive case, as the sampler approaches equilibration all concentration gradients will disappear, but prior to this, horizontal concentration gradients exist in proximity to the sampler. It follows that if two devices are placed too close they both deplete the same volume of porewater, increasing the time to equilibrium. Approximate radial (2D) and linear (1D) distances beyond which the porewaters remain effectively undepleted (concentrations >99% after deployment times of 24 h for DET and 1 month for peepers) are given in Table 2. As with the equilibrium times, there is a considerable difference between the 1D and 2D diffusive cases. The results show that the initial stages of equilibration (to 95%) are rapid as compared to the increase from 95 to 99% (especially in the diffusive supply cases). This is because as equilibrium is approached, the flux to the membrane is controlled by slow diffusion over large distances across shallow concentration gradients. It follows from the difference in their equilibration times that DET will be sensitive to (i.e., re-equilibrate to) short-term (hourly) changes in porewater concentrations, while peepers will respond only to long-term (daily) changes. Carignan (21) observed that peeper equilibration times of 20 days were adequate for most sediments, and the results of Teasdale et al. (1) suggest a similar time scale. These experimentally observed times lie between the buffered and diffusive 2D cases in Table 2. This suggests that there may be significant resupply from the sediment solid phase to the porewaters as observed from the in situ measurement of fluxes (14). However, differing assumptions such as fast mixing within cells (15) could reduce modeled equilibrium times and obviate the need to invoke a resupply term. Measured Profile Fidelity. The existence of concentration gradients in porewaters implies that there must be some localized sources and sinks responsible for maintaining these gradients. For the partial resupply case, local sources and sinks are incorporated into the model. The buffered case represents the combined effect of sources and sinks by a steady-state Gaussian depth profile; in the diffusive case, the Gaussian profile is a fossil structure left from some extinct source. In the diffusive case, the profile structure will degrade over time, but this case is worth preliminary consideration as it represents a worst case scenario so far as resolution is concerned. For DET, an average concentration in the gel was calculated for each of a large number of horizontal strips to approximate to a continuous vertical profile of concentration within the gel (the ‘sampler profile’). this continuous sampler profile cannot in practice be measured: instead the gel is usually
context of resolution and will not be considered further. While it is obvious that a purely diffusive supply cannot produce concentration gradients in measured profiles, it has still been used as a model for assessing equilibration times. However, if resupply must occur to partially buffer porewater concentration gradients, it must also act to reduce equilibrium times. Partial Resupply Case. The shapes of porwater profiles produced by the partial resupply case model are dependent primarily on the response time, T, of the (de)sorption process given by eq 10. When T is 200 s (2 days), porewater gradients occur over ∼1 mm (6 cm). Due to its greater spatial resolution, DET provides details of processes operating over time scales too fast to discern from peeper measured profiles, and it is possible using this model to derive rate constants from the breadth of porewater peaks:
T) FIGURE 5. Concentration changes over time in a DET gel for the diffusive case, starting with a Gaussian porewater peak, σ ) 1. Times given in minutes. sliced at fine (1-mm) intervals and the concentration in each slice averaged. This was simulated by averaging the concentration profile over 1-mm intervals to produce a ‘measured profile’. The concentrations in the filter were not included in these calculations as this is discarded prior to slicing, although the filter is in contact with the porewater and is therefore likely to contain the best preserved section of the profile. Both the sampler and measured profiles could be compared to the original porewater profile. For dialysis, treatment of the results was similar but determined by peeper geometry. The concentrations in peeper cells at equilibrium were averaged to obtain a measured profile comprising 6-mm averages with 4-mm gaps. Diffusive Case. Figure 5 shows gel concentrations for the diffusive case, which build up to a maximum of 1 mm) gels give relatively poor fidelity and are unsuitable for high resolution (∼mm) sampling, although they may still resolve detail better than peepers. Deeper cells do not affect peeper fidelity. Once a DET device is removed from the sediment, it is in disequilibrium as the porewater profile is no longer in contact with the gel assembly. Concentration gradients within the gel will therefore relax over time by lateral diffusion until the gel is sliced or fixed. Figure 9 shows the relaxation in peak
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FIGURE 8. Peak concentration in a gel as a proportion of peak porewater concentration plotted against gel thickness for Gaussian shaped profiles characterized by different σ (values in figure legend). A gel thickness of zero indicates the concentration at the boundary between the gel and filter.
FIGURE 9. Peak concentration in a 0.4 mm thick gel as a proportion of peak orewater concentration plotted against relaxation time. A relaxation time of zero gives the equilibrium peak gel concentration. Cases are given for Gaussian shaped peaks, characterized by different σ (values in figure legend). height for four different gel profiles, characterized by different σ. As with lateral diffusion, the rate of relaxation is dependent on peak width with narrow peaks decaying faster. After 30 s relaxation time (sufficient time for gels in incubated cores to be retrieved and fixed), there is little relaxation evident for any of the peaks in Figure 9. After 1 min (sufficient time for retrieval and fixing from in situ deployment), only the σ ) 0.5 and 0.25 mm peaks are significantly depeleted. After 5-10 min, only the widest peak is well preserved. These results are consistent with those of previous workers (6), who predicted significant relaxation in narrow (6 mm wide for DET (sliced at 1-mm resolution) and >45 mm wide for peepers. If a higher resolution is used for DET (for example, using PIXE to sample at 100-µm intervals (5), then the shaded area would reduce in size and approach the sampler profile. The limit on DET fidelity (i.e., assuming infinitely high resolution subsampling of the gel) for a given
FIGURE 11. Sampler (solid line) and measured peak concentrations (shaded area) as a proportion of porewater peak concentration. The measured concentration for a given peak width will lie within the shaded area, depending on phase shift. gel thickness is therefore the sampler profile. The only way the DET sampler profile fidelity can be improved is by reducing gel and filter thickness, taking advantage of thinner gels requires higher resolution measured profiles. For example a 0.2-mm gel sliced at 1-mm intervals would imply a measured peak concentration g90% that of the porewater concentration for peaks >5 mm wideslittle better than the 0.4-mm gel. For peepers, a decrease in cell width and intercell spacing would improve the fidelity of the measured profile. In particular, less distance between cells would raise the lower boundary of the shaded area in Figure 11b. Elution of DET Samples. DET gel samples must fully equilibrate with the eluent if concentrations are to be calculated correctly. Elution times are principally a function of diffusional path lengths and the degree of mixing in the solution. Figure 12 plots the concentration in a piece of gel against time for two cases. Case A is for a 10 × 1 × 0.4 mm piece of gel at the bottom of a centrifuge vial covered with 25 mm depth of eluent. Case B is for a similar slice of gel from a DET assembly covered with 3.4 mm of eluent. If the eluent is continuously mixed, 99% equilibration occurs in 2 cm (DET assemblies with 0.4 mm thick gels) or >16 cm (peepers with 6 mm deep cells). These standard DET assemblies can therefore be deployed in sediment cores with diameters as small as 7 cm. However, both distances of depletion and equilibrium times will vary according to differences in basic parameters such as porosity, tortuosity, and diffusion coefficients (equilibrium time is inversely proportional to the diffusion coefficient) as well as the dimensions of the DET assembly. The faster equilibration times of DET assemblies as compared to peepers implies that they will respond better to perturbations in porewater concentrations. Measured concentration profiles may not accurately reflect porewater profiles due to systematic errors compounding the usual handling and analysis errors. Our partial resupply case results indicate that the presence of a sampler modifies the porewater concentration profile adjacent to that sampler. For peepers and DET measured peaks of greater than approximately 6 mm in width, this effect does not significantly reduce the fidelity of measured profiles. Our subsequent conclusions are based on the buffered case, which represents the ‘best case’ for profile fidelity, and are unaffected by the extent to which the sampling medium is recessed below the front of the sampler. For typical designs of DET assemblies (0.4 mm thick gels, sliced at 1-mm resolution) and peepers (6 mm cells, 4 mm apart, giving a resolution of 1 cm), measured peak concentrations will be at least 90% of peak porewater concentrations for porewater features of width >6 mm (DET) and 45 mm (peepers). DET measured profiles can approach sampler profiles, that is, the actual concentration in the gel, by increasing the spatial resolution of the final analysis. To ensure that the sampler profile more accurately reproduces the porewater profile, gel and/or filter thickness must be reduced. The fidelity of the profile measured by peepers can be improved by reducing the vertical dimensions of cells and their separation. Peeper designs that comprise adjacent sets of cells that are staggered to provide a vertically continuous sampling medium will improve performance but will also
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reflect any horizontal heterogeneity in the sediment. In certain contexts, where mean concentrations are required, the averaging effect of peepers may be at an advantage over DET deployments which measure very localized profiles. For small porewater features, profiles can be misleading. For example, a peak could be apparently well defined by four points with DET but be significantly degraded as compared to the porewater profile. The degree of degradation is inversely proportional to peak width. The extent of underestimation may be dramatic: using DET a 1 mm wide porewater peak could be measured at 30% of its true peak concentration and double its width, depending on phase shift. A 5 mm wide peak could be virtually missed entirely using a peeper. Therefore, measured profile concentration gradients will result in underestimates of vertical fluxes calculated using eq 1. DET has greater accuracy at much higher resolution than peepers, is easy to use, has a quicker response, and is preferable provided sufficient analyte is present in the gel. However, if a peeper could be constructed with 1-mm cells separated by
