Per- and polyfluoroalkyl substances (PFAS) represent a class of persistent, toxic pollutants that pose serious threats to ecosystems and human health due to their resistance to degradation and widespread contamination. Understanding their behavior in saturated soils is critical for accurate risk assessment and remediation planning. This study presents a comprehensive modeling framework based on the tempered one-sided stable density (TOSD) distribution to simulate PFAS adsorption kinetics, equilibrium isotherms, and nonideal transport processes in geomedia. By integrating physical principles with empirical data, the TOSD-based models offer a unified approach capable of capturing complex dynamics across multiple scales.
The foundation of this work lies in the recognition that PFAS adsorption is inherently heterogeneous due to variations in soil composition, including organic carbon content, clay mineralogy, metal oxide abundance, and pore structure. These factors lead to multi-rate adsorption/desorption processes that cannot be adequately described by conventional single-rate models. To address this, a TOSD-isotherm model was developed using a tempered fractional derivative formulation. The equation Cs = k Cw E₁,⁺¹(–Cw) generalizes traditional isotherm models such as Freundlich and Langmuir by incorporating both power-law and exponential regimes through adjustable parameters. When applied to experimental data from Li et al. (2019) and Cao et al. (2017), the model successfully reproduced linear, power-law, and truncated power-law behaviors observed in various PFAS-soil systems. Parameter analysis revealed that the index decreases with increasing chain length—consistent with stronger hydrophobic interactions—and that functional groups like sulfonates significantly enhance adsorption capacity.
For kinetic modeling, the TOSD-kinetic model was derived from the assumption that the rate of adsorption follows a TOSD-distributed process. The resulting expression Ct = C₀(C₀ – Ce)t⁻¹E₁,₂(–t) captures the transition from early-time power-law decay to late-time exponential stabilization. Applied to kinetic data from Li et al. (2019) and Wei et al. (2017), the model provided superior fits compared to biexponential equations, particularly in representing the shift in adsorption rate over time. The truncation parameter was found to correlate with system heterogeneity, while the time index varied systematically with soil type, suggesting a strong influence of geochemical properties on mass transfer dynamics. These results confirm that PFAS adsorption is not a uniform process but rather governed by a spectrum of rates influenced by environmental conditions.
In the context of solute transport, the TOSD-transport model was formulated to account for diffusive mass transfer between advective flow zones and immobile domains.Cytokeratin 8/18 Antibody Data Sheet The governing equation ∂Ca/∂t + ∂/∂t[et Ca] = v ∂Ca/∂x + D ∂²Ca/∂x² embeds memory effects via the TOSD kernel, enabling simulation of heavy-tailed breakthrough curves.Podoplanin Antibody In Vitro Testing against column experiments from Brusseau et al.PMID:35080663 (2019a), Lv et al. (2018), and Guelfo et al. (2020) demonstrated excellent agreement with measured data. The model accurately captured extended elution tails in PFOS and PFOA transport, especially in media with high organic carbon content or reactive surfaces. The time index α ranged from 0.25 to 0.95, indicating variable degrees of anomalous diffusion, while the truncation parameter β reflected the time scale of mass exchange. Notably, the model outperformed standard two-site and mobile-immobile models in semi-log plots, where tailing behavior is most evident.
Comparative analysis confirmed that the TOSD framework provides greater generality and physical consistency than existing models. Unlike multi-rate approaches requiring numerous fitting parameters, the TOSD models achieve high accuracy with minimal complexity. Moreover, their mathematical structure ensures scalability across spatial and temporal dimensions. Extensions to distributed-order and vector TOSD forms allow adaptation to non-stationary heterogeneity and directional transport in aquifers. Overall, this study establishes the tempered one-sided stable density as a universal law governing PFAS fate in saturated soils, offering a powerful, physics-based tool for predicting contaminant behavior under diverse environmental conditions.MedChemExpress (MCE) offers a wide range of high-quality research chemicals and biochemicals (novel life-science reagents, reference compounds and natural compounds) for scientific use. We have professionally experienced and friendly staff to meet your needs. We are a competent and trustworthy partner for your research and scientific projects.Related websites: https://www.medchemexpress.com