Non-Steady-State Fickian Diffusion Models Decrease the Estimated Gel Layer Diffusion Coefficient Uncertainty for...

Mass transport in diffusive gradients in thin-film passive samplers is restricted to diffusion through a gel layer of agarose or agarose cross-linked polyacrylamide (APA). The gel layer diffusion coefficient, D_Gel, is typically determined using a standard analysis (SA) based on Fick's first law from two-compartment diffusion cell (D-Cell) tests. The SA assumes pseudo-steady-state flux, characterized by linear sink mass accumulation-time profiles with a typical threshold R² ≥ 0.97. In 72 D-Cell tests with nitrate, 63 met this threshold, but the SA-determined D_Gel ranged from 10.1 to 15.8 × 10^-6 cm²·s^-1 (agarose) and 9.5 to 14.7 × 10^-6 cm²·s^-1 (APA). A regression model developed with the SA to account for the diffusive boundary layer had 95% confidence intervals (CIs) on D_Gel of 13 to 18 × 10^-6 cm²·s^-1 (agarose) and 12 to 19 × 10^-6 cm²·s^-1 (APA) at 500 rpm. A finite difference model (FDM) developed based on Fick's second law with non-steady-state (N-SS) flux decreased uncertainty in D_Gel tenfold. The FDM-captured decreasing source compartment concentrations and N-SS flux in the D-Cell tests and, at 500 rpm, the FDM-determined D_Gel ± 95% CIs were 14.5 ± 0.2 × 10^-6 cm²·s^-1 (agarose) and 14.0 ± 0.3 × 10^-6 cm²·s^-1 (APA), respectively.