DGT Data Analysis

The concentration of metal accumulated on the binding gel in the DGT device (M) was determined according to Equation (1).

$$\mathcal{M} = \mathbb{C} \left( V\_{\text{acid}} + V\_{\text{gel}} \right) / \text{fc} \tag{1}$$

where: *C* is the metal concentration eluted from the binding gel measured by ICP-MS

*V*acid is the volume of acid used for elution (*V*acid = 1 mL),

*V*gel is the volume of resin gel (*V*gel = 0.16 mL), *f* e is the elution factor (*f e* = 0.8).

Once M was calculated, the interfacial DGT concentration (CDGT) was calculated using Equation (2),

$$\mathbf{C\_{DGT}} = \mathbf{M} \Delta \mathbf{g} / \mathbf{D} \mathbf{A} \mathbf{t} \tag{2}$$

where: Δg is the diffusive layer thickness (0.8 mm) plus the thickness of the filter membrane (0.14 mm), which is 0.94 mm,

D is the diffusion coefficient of metal at a given temperature (cm2 S<sup>−</sup>1),

A is the area of the exposed membrane (A = 3.14 cm2),

t is the deployment time (in seconds).

The diffusion coefficients of the metal of interest (Ds) were calculated using Equations (3)–(5).

$$\mathbf{P}\mathbf{c} = \mathbf{m} / \mathbf{V} \tag{3}$$

$$\Phi = \text{Dp} / (\text{Pc} + \text{Dp}) \tag{4}$$

$$\text{Ds} = \text{D}\_0 \mid \left(1 - \ln \phi^2\right) \tag{5}$$

where: *m* is the total mass of all soil particles;

V the pore water volume in a given volume of total soil (cm3),

Dp is the density of soil particles (2.65g cm<sup>−</sup>3) in soil,

Do is the diffusion coefficient of the metal ion at 20 <sup>±</sup> <sup>1</sup> ◦C, (cm<sup>2</sup> <sup>S</sup><sup>−</sup>1),

Ds is the diffusion coefficient in sediment (cm<sup>2</sup> S<sup>−</sup>1).

The input parameters used in the 2D DFIS model to calculate RDIFF, were particle concentration (Pc) and soil porosity (φ). Pc (g cm−3) was determined using Equation (3) and soil porosity (φ) was determined using Equation (4), and the diffusion coefficient in sediment (Ds) was calculated using Equation (5).

Effective solution concentrations, CE, were derived using Equation (6).

$$\mathbf{C}\_{\rm E} = \mathbf{C}\_{\rm DGT} / R\_{\rm DFF} \tag{6}$$

where: CDGT was the metal concentration measured by the DGT technique (in mg/kg).

The effective concentration (CE) was used to estimate the potential metal concentration that can be absorbed by plants. The DGT technique is designed to mimic root uptake metal from soil. During DGT measurement, interface metal concentrations were measured to take into account the continuous depletion of metals, due to the uptake and the resupply process of metals from solid to solution phase. Metal depletion is indicated as a ratio (R) using the CDGT and independently measured solution (CSOL) concentrations (Equation (7)).

$$\mathcal{R} = \mathsf{C}\_{\text{DGT}} / \mathsf{C}\_{\text{SOL}} \tag{7}$$

$$\text{Tr} \mathbf{c} = \mathbf{C} \left( \mathbf{1} - \mathbf{R} / \mathbf{R} - \mathbf{d} \right)^2 \tag{8}$$

where: Tc (seconds) is the time taken to reach the equilibrium, Tc is determined using Equation (8).

Note: For samples with high porosity; C = 403, d = 0.0247 and for low porosity case C = 229, d = 0.0186 [7]. The soils for this study were treated as being low porosity.
