Modeling Desorption Rates and Background Concentrations of Heavy Metals Using a One-Dimensional Approach
Abstract
1. Introduction
2. Materials and Methods
2.1. Cartagena Bay: A Reference System for Estuarine Conditions
2.2. Mathematical Model
2.2.1. Definition of the Physical Problem
2.2.2. Governing Equations and Boundary Conditions
2.2.3. Numerical Solution Under Variable Boundary Conditions
3. Results
3.1. Estimation of Molecular Diffusion (T1), Desorption (T2), and Sedimentation (T3)
3.2. Numerical Experiments
4. Discussion
4.1. Temporal Evolution of Background Concentrations Estimated by the Model
4.2. Dimensionless Analysis and HHM Dynamics
4.3. Model Assumptions, Limitations, and Ecological Implications
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix B
Appendix C
References
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Parameter | Description | Unit | Value | Reference |
---|---|---|---|---|
HHM background concentration | g L−1, mg kg−1 (dw) * | see Table 2 | calculated | |
Drag coefficient | / | 2 × 10−3 | [39] | |
Dissolved-phase HHM concentration | g L−1, mg kg−1 (dw) * | / | calculated | |
Cm | Suspended-sediment mass concentration | g L−1 | / | [40] |
Particulate-phase HHM concentration | g L−1, mg kg−1 (dw) * | / | calculated | |
Initial particulate HHM at precipitation | g L−1 | / | assumed | |
Suspended-sediment volumetric concentration | / | 10−4–10−5 | assumed | |
d50 | Median grain diameter of sediment | m | / | measured |
D | Sediment thickness | m | 0–1.6 ** | calculated |
F | Porosity–tortuosity factor | / | / | calculated |
HHMs | Harmful heavy metals | g L−1, mg kg−1 (dw) * | varies | measured |
Coefficient of equilibrium distribution | / | / | assumed | |
m | Exponent in the relationship of Sc and n | / | / | literature |
N | Number of computational nodes | / | 100 | assumed |
n | Porosity | / | 0.4 | [34] |
Q | Molecular diffusion flux | kg m−2 s−1 | varies | calculated |
S | Salinity | / | 0.06–35.7 | assumed |
Schmidt number | / | 10–100 | [6] | |
t | Time | s | 0–8.64 × 108 s | assumed |
T1 | Molecular diffusion rate | yr | 0.3–3 | calculated |
T2 | Desorption rate | yr | 3.15 (for γ = 5 × 10−8) | calculated |
T3 | Sediment rate | yr | >31 | calculated |
T4 | Turbulent exchange rate | yr | / | calculated |
Friction (dynamic) velocity | m s−1 | 0–0.01 | assumed | |
Settling velocity of sediments due to gravity | m s−1 | 10−5 | assumed | |
Y | Dimensionless vertical coordinate | / | 0–1 | calculated |
Vertical level within the substrate | m | 0–1.6 | calculated | |
Roughness parameter | m | / | literature | |
Inverse Schmidt number | / | 0.01–0.1 | [36] | |
γ | Desorption coefficient | s−1 | 5 × 10−8–1 × 10−9 | [41] |
Vertical grid size in dimensionless coordinates | / | 1/(N − 1) | calculated | |
θ | Tortuosity | / | / | [35] |
Karman constant | / | 0.41 | literature | |
ν | Kinematic molecular viscosity of water | m2 s−1 | 10−6 | constant |
Sediment–particle density | kg m−3 | 2650 | [39] | |
Molecular diffusion coefficient (water only) | m2 s−1 | / | [17] | |
Molecular diffusion coefficients (with sediments) | m2 s−1 | / | calculated |
Case | Description | mg kg−1 (dw) | Observation |
---|---|---|---|
1 | γ = 5 × 10−8 1/s | 1.4–1.7 | Long-term equilibrium at z = 0 |
2 | γ = 10−8 1/s | 1.0–1.2 | Slower equilibrium from low γ |
3 | increasing over 28 yr | 2.0–2.4 | Closest to observed CB field data |
4 | Variable sediment input * | 2.0–2.2 | Dynamic but consistent at z = 0 |
- | Average Hg (model) | 0.2 ± 1.7 | Variability across all cases |
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Gonzalez Cano, W.T.; Lonin, S.; Kim, K. Modeling Desorption Rates and Background Concentrations of Heavy Metals Using a One-Dimensional Approach. Toxics 2025, 13, 421. https://doi.org/10.3390/toxics13060421
Gonzalez Cano WT, Lonin S, Kim K. Modeling Desorption Rates and Background Concentrations of Heavy Metals Using a One-Dimensional Approach. Toxics. 2025; 13(6):421. https://doi.org/10.3390/toxics13060421
Chicago/Turabian StyleGonzalez Cano, Wendy Tatiana, Serguei Lonin, and Kyoungrean Kim. 2025. "Modeling Desorption Rates and Background Concentrations of Heavy Metals Using a One-Dimensional Approach" Toxics 13, no. 6: 421. https://doi.org/10.3390/toxics13060421
APA StyleGonzalez Cano, W. T., Lonin, S., & Kim, K. (2025). Modeling Desorption Rates and Background Concentrations of Heavy Metals Using a One-Dimensional Approach. Toxics, 13(6), 421. https://doi.org/10.3390/toxics13060421