Non-Steady-State Fickian Diffusion Models Decrease the Estimated Gel Layer Diffusion Coefficient Uncertainty for Diffusive Gradients in Thin-Films Passive Samplers

Mass transport in diffusive gradients in thin-film passivesamplersis restricted to diffusion through a gel layer of agarose or agarosecross-linked polyacrylamide (APA). The gel layer diffusion coefficient, D (Gel), is typically determined using a standardanalysis (SA) based on Fick's first law from two-compartmentdiffusion cell (D-Cell) tests. The SA assumes pseudo-steady-stateflux, characterized by linear sink mass accumulation-time profileswith a typical threshold R (2) & GE; 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 x 10(-6) cm(2)& BULL;s(-1) (agarose) and 9.5 to 14.7x 10(-6) cm(2)& BULL;s(-1) (APA). A regression model developed with the SA to account for thediffusive boundary layer had 95% confidence intervals (CIs) on D (Gel) of 13 to 18 x 10(-6) cm(2)& BULL;s(-1) (agarose) and 12 to 19x 10(-6) cm(2)& BULL;s(-1) (APA) at 500 rpm. A finite difference model (FDM) developed basedon Fick's second law with non-steady-state (N-SS) flux decreaseduncertainty in D (Gel) tenfold. The FDM-captureddecreasing source compartment concentrations and N-SS flux in theD-Cell tests and, at 500 rpm, the FDM-determined D (Gel) & PLUSMN; 95% CIs were 14.5 & PLUSMN; 0.2 x 10(-6) cm(2)& BULL;s(-1) (agarose)and 14.0 & PLUSMN; 0.3 x 10(-6) cm(2)& BULL;s(-1) (APA), respectively. Diffusioncoefficient measurements in passive sampler gellayers typically assume a pseudo-steady-state flux. This study reportsthat non-steady-state flux occurs in diffusion cell tests with implicationsfor environmental compliance monitoring.

Automated summary

Mass transport in diffusive gradients in thin-film passive samplers is restricted by diffusion through a gel layer. The traditional standard analysis method has a large variation in the diffusion coefficient results, while a finite difference model provides more accurate results.