Non-Steady-State Fickian Diffusion Models Decrease the Estimated Gel Layer Diffusion Coefficient Uncertainty for Diffusive Gradients in Thin-Films Passive Samplers
Samuel D. Hodges, David G. Wahman, Levi M. Haupert, Huong T. Pham, Margaret K. Bozarth, Michael B. Howland, Julian L. Fairey
Abstract
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 R 2 ≥ 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 cm 2 ·s –1 (agarose) and 9.5 to 14.7 × 10 –6 cm 2 ·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 cm 2 ·s –1 (agarose) and 12 to 19 × 10 –6 cm 2 ·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 cm 2 ·s –1 (agarose) and 14.0 ± 0.3 × 10 –6 cm 2 ·s –1 (APA), respectively.