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

Area of Science:

• Environmental Science
• Analytical Chemistry
• Chemical Engineering

Background:

• Mass transport in thin-film passive samplers relies on diffusion through gel layers (agarose or APA).
• The gel layer diffusion coefficient (D_Gel) is crucial for sampler performance.
• Standard analysis (SA) using Fick's first law often assumes pseudo-steady-state flux, limiting accuracy.

Purpose of the Study:

• To develop and validate a more accurate method for determining the gel layer diffusion coefficient (D_Gel).
• To assess the limitations of standard analysis (SA) in D-Cell tests.
• To implement a finite difference model (FDM) accounting for non-steady-state (N-SS) flux.

Main Methods:

• Conducted 72 two-compartment diffusion cell (D-Cell) tests using nitrate.
• Applied standard analysis (SA) based on Fick's first law and a regression model.
• Developed and utilized a finite difference model (FDM) based on Fick's second law, incorporating N-SS flux.

Main Results:

• SA determined D_Gel with significant variability (e.g., 10.1–15.8 × 10⁻⁶ cm²·s⁻¹ for agarose).
• Regression models with SA showed wide 95% confidence intervals for D_Gel (e.g., 13–18 × 10⁻⁶ cm²·s⁻¹ for agarose at 500 rpm).
• FDM reduced D_Gel uncertainty tenfold, yielding precise values (e.g., 14.5 ± 0.2 × 10⁻⁶ cm²·s⁻¹ for agarose at 500 rpm).

Conclusions:

• The finite difference model (FDM) significantly enhances the accuracy of D_Gel determination in passive samplers.
• FDM accounts for dynamic changes in concentration and flux, overcoming SA limitations.
• This improved method provides more reliable mass transport data for environmental monitoring.