## Modelling Interactions Of Dgt With Soils And Sediments

When DGT is deployed in soils or sediments, a steady-state condition is never truly reached. Thus, time-dependent models are required to quantify the contribution of diffusional supply and release from the solid-phase to the accumulated mass of solute. The DGT-induced fluxes in soils and sediments (DIFS) model developed by Harper et al. [13,26]

provides a numerical simulation of the interaction between the DGT device and its deployment medium. It quantifies the dependence of R on the supply of trace metals from solid-phase to solution, coupled to diffusional supply to the interface and across the diffusion layer, by solving a pair of linked partial differential equations describing dissolved and sorbed solute concentrations in the soil or sediment and the DGT device. The model assumes that all pore spaces are filled with solution, which restricts its use to sediments and soils with moisture content at or above field capacity.

Initial calculations, based on a finite difference approach, considered two-dimensional diffusion and release processes in the soil perpendicular to the plane of the DGT device [13]. A simplified version of the original model, which considered only one dimension along the axis perpendicular to the DGT device, was made generally available [14]. The exchange of solute between solid-phase and solution is described by the first-order rate constants for binding, k1, and release, k_1 (Fig. 16.1). Although these constants are sometimes referred to as sorption and desorption rate constants, no mechanism, other than exchange between the solid-phase and solution, is assumed. A distribution coefficient for the labile solute, Kdl, is used to define the ratio of the concentration of exchangeable solute in the solid-phase, Cls, to that in solution:

Csoln

Another key parameter is the response time, Tc, which is the time needed for the disequilibria of solute induced by DGT to revert to 63% of the equilibrium value [27]. Tc is the reciprocal of the sum of the rate constants, which for most situations approximates to the inverse of the rate given by the product of k_1 and Kdl:

The model has been used to generate concentration profiles of solute in solution, in the solid-phase, through the soil or sediment, and within the diffusion layer (Fig. 16.2) [13,18,20]. The dependence of these profiles on the values of Kdl and Tc provides insight into their controlling influence on the DGT measurement. Generally, the concentration in solution within 1 mm of the DGT surface is sustained at high values for several days when Kdl is large and Tc is small, with little depletion of the solid-phase. However, when Kdl is small and Tc is large, the depletion of

Fig. 16.2. Dependence of the normalized concentration of a DGT active component, in the solution and solid-phase of a soil (with reported characteristics [18]), on time and distance from the surface of the diffusion layer. Simulated using DIFS with Kd — 150 mL g-1 and Tc — 300 s. At long times, the concentration in solution is determined by Kd, as kinetic effects become negligible. Thus, the normalized 20 days lines for both solution and solid-phase are identical.

Fig. 16.2. Dependence of the normalized concentration of a DGT active component, in the solution and solid-phase of a soil (with reported characteristics [18]), on time and distance from the surface of the diffusion layer. Simulated using DIFS with Kd — 150 mL g-1 and Tc — 300 s. At long times, the concentration in solution is determined by Kd, as kinetic effects become negligible. Thus, the normalized 20 days lines for both solution and solid-phase are identical.

the concentration in both solution and solid-phase rapidly extends away from the device. For the more common intermediate case, a rapid response (small Tc) helps to sustain the interfacial concentration, but only for relatively short deployment times (hours). The interfacial concentration's fraction of its initial value, R, is determined exclusively by Kdl at long deployment times (several days), when the controlling effect on the solution concentration is the extent of depletion of solute associated with the solid-phase.

The one-dimensional model is accurate for short deployment times or for cases when there is rapid and sustained supply from the solidphase. However, the model is less accurate when concentration gradients extend appreciably into the soil or sediment. Supply solely by diffusion represents the worst case and corrections based on a fuller two-dimensional calculation were provided with the model. To overcome these problems, the model has been reformulated within a mathematical framework that uses the finite element method (FEM) [28]. Significant advances include (a) a two-dimensional solution, (b) full flexibility in selection of DGT geometry and parameters, (c) incorporation of two-dimensional (planar) microniche sources of solutes and (d) an interactive, user-friendly interface. The accuracy of this new model, called 2D-DIFS, was tested using a three-dimensional solution and correction equations derived for the diffusion-only case. The performance and sensitivity of the model has been evaluated systematically using available DGT data [29].

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