Transport of Thiophanate Methyl in Porous Media in the Presence of Titanium Dioxide Nanoparticles
Abstract
:1. Introduction
2. Materials and Methods
3. Mathematical Modeling
3.1. Governing Partial Differential Equations
3.2. The Fitting Process
3.3. Additional Theoretical Calculations
4. Results and Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
aqueous phase concentration, M/L3 | |
aqueous phase concentration of suspended nanoparticles, Mn/L3. | |
concentration of nanoparticles attached onto the solid matrix, Mn/Msm. | |
aqueous phase solute concentration, Ms/L3. | |
concentration of solutes sorbed onto the solid matrix, Ms/Msm. | |
concentration of suspended solute-nanoparticle complex, Ms/Mn. | |
concentration of solute-nanoparticle complex attached onto the solid matrix, Ms/Mn. | |
concentration of nanoparticles irreversibly attached onto the solid matrix, Mn/Msm. | |
concentration of nanoparticles reversibly attached onto the solid matrix, Mn/Msm. | |
initial aqueous phase solute concentration, Ms/L | |
dH | hydrodynamic diameter, L |
Di | hydrodynamic dispersion coefficient of species i, L2/t. |
Fi | general form of the source configuration of species i, Mi/L3t. |
Gi(t) | mass release function of species i (point source), Mi/t. |
Is | ionic strength, mM |
rate of irreversible solute-nanoparticle complex attachment onto the solid matrix, 1/t | |
L | length, L. |
m0 | zeroth absolute temporal moment, tM/L3 |
Mn | mass of nanoparticles, Mn. |
Msm | mass of the solid matrix, Msm. |
Ms | mass of solutes, Ms. |
Mr | ratio of recovered mass, [-] |
rate of irreversible nanoparticle attachment onto the solid matrix, 1/t. | |
rate of reversible nanoparticle attachment onto the solid matrix, 1/t. | |
rate of reversible nanoparticle detachment from the solid matrix, 1/t. | |
rate of irreversible solute sorption onto the solid matrix, 1/t. | |
rate of reversible solute sorption onto the solid matrix, 1/t. | |
rate of reversible solute desorption from the solid matrix, 1/t. | |
rate of solute sorption onto suspended nanoparticles, L6/Mn2t. | |
rate of solute desorption from suspended nanoparticles, 1/t. | |
rate of solute sorption onto nanoparticles already attached onto the solid matrix, L3Msm/Mn2t. | |
rate of solute-nanoparticle complex attachment onto the solid matrix,1/t. | |
rate of solute desorption from suspended nanoparticles, 1/t. | |
rate of solute-nanoparticle complex detachment from the solid matrix, 1/t. | |
t | time, t. |
tp | source duration time period, t. |
U | interstitial velocity, L/t. |
W | characterizes the source physical geometry (point source), 1/L3. |
x | Cartesian coordinate, L. |
Greek Letters | |
Θ | porosity, (L3 voids)/(L3 solid matrix). |
ζ | zeta potential, V |
ρ | bulk density of the solid matrix, Msm/L3 |
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Experimental Conditions * | TiO2 | ||
---|---|---|---|
pH | Ionic Strength (mM) | ζ (mV) | dH (nm) |
3 | - | −25.1 | 315.6 |
5 | - | −25.7 | 317.0 |
7 | - | −28.0 | 326.6 |
10 | - | −42.3 | 567.3 |
7.5 | 1 | −36.0 | 389.3 |
7.5 | 10 | −41.0 | 278.0 |
5.4 | 50 | −29.9 | 386.3 |
5.1 | 100 | −27.0 | 1004.4 |
Experimental Conditions | pH | Ionic Strength (mM) | ||||||
---|---|---|---|---|---|---|---|---|
3 | 5 | 7 | 10 | 1 | 10 | 50 | 100 | |
Transport parameter values for TM | ||||||||
Mr (%) | 99.0 | 100 | 100 | 100 | 97.2 | 95.3 | 99.5 | 99.3 |
U (cm/min) | 0.53 | 0.54 | 0.54 | 0.54 | 0.53 | 0.54 | 0.55 | 0.54 |
tp (min) | 240 | 242 | 242 | 234 | 231 | 237 | 239 | 234 |
θ (-) | 0.38 | 0.38 | 0.39 | 0.38 | 0.38 | 0.37 | 0.37 | 0.38 |
Ds (cm/min) | 0.26 | 0.24 | 0.29 | 0.30 | 0.22 | 0.23 | 0.27 | 0.29 |
(1/min) | 0.0055 | 0.0032 | 0.0022 | 0.0019 | 0.0036 | 0.0038 | 0.0058 | 0.0060 |
(1/min) | 0.0204 | 0.0182 | 0.0136 | 0.0060 | 0.0117 | 0.0136 | 0.0165 | 0.0171 |
(1/min) | 0.00086 | 0 | 0 | 0 | 0.00037 | 0.00072 | 0.00090 | 0.00094 |
Cotransport parameter values for TM | ||||||||
Mr (%) | 92.9 | 95.2 | 98.6 | 90.9 | 57.9 | 54.3 | 34.3 | 31.5 |
U (cm/min) | 0.54 | 0.53 | 0.54 | 0.54 | 0.54 | 0.55 | 0.54 | 0.53 |
tp (min) | 231 | 229 | 232 | 237 | 235 | 228 | 222 | 224 |
θ (-) | 0.37 | 0.38 | 0.38 | 0.38 | 0.38 | 0.37 | 0.38 | 0.38 |
Ds (cm/min) | 0.26 | 0.24 | 0.29 | 0.30 | 0.22 | 0.23 | 0.27 | 0.29 |
(L6/Mn2t) | 0.00064 | 0.0020 | 0.0023 | 0.0071 | 0.9000 | 0.2870 | - | - |
(1/min) | 0.0102 | 0.0296 | 0.0585 | 0.0654 | 0.7300 | 0.1780 | - | - |
(1/min) | 0.0085 | 0.0004 | 0.0786 | 0.0834 | 0.2820 | 0.0003 | - | - |
Cotransport parameter values for TiO2 nanoparticles | ||||||||
Mr (%) | 92.8 | 94.6 | 100 | 100 | 61.5 | 53.3 | 3.29 | 2.81 |
U (cm/min) | 0.54 | 0.53 | 0.54 | 0.54 | 0.54 | 0.55 | 0.54 | 0.53 |
tp (min) | 231 | 229 | 232 | 237 | 235 | 228 | 222 | 224 |
θ (-) | 0.37 | 0.38 | 0.38 | 0.38 | 0.38 | 0.37 | 0.38 | 0.38 |
Dn (cm/min) | 0.26 | 0.23 | 0.29 | 0.30 | 0.22 | 0.5 | - | - |
(1/min) | 0.001 | 0.0008 | 0.0004 | 0.0007 | 0.0015 | 0.0044 | - | - |
(1/min) | 0.0185 | 0.0205 | 0.0111 | 0.0053 | 0.0127 | 0.0257 | - | - |
(1/min) | 0.0014 | 0.0009 | - | 0.0009 | 0.0089 | 0.0110 | - | - |
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Stefanarou, A.S.; Katzourakis, V.E.; Fu, F.; Malandrakis, A.A.; Chrysikopoulos, C.V. Transport of Thiophanate Methyl in Porous Media in the Presence of Titanium Dioxide Nanoparticles. Water 2023, 15, 1415. https://doi.org/10.3390/w15071415
Stefanarou AS, Katzourakis VE, Fu F, Malandrakis AA, Chrysikopoulos CV. Transport of Thiophanate Methyl in Porous Media in the Presence of Titanium Dioxide Nanoparticles. Water. 2023; 15(7):1415. https://doi.org/10.3390/w15071415
Chicago/Turabian StyleStefanarou, Anthi S., Vasileios E. Katzourakis, Fenglian Fu, Anastasios A. Malandrakis, and Constantinos V. Chrysikopoulos. 2023. "Transport of Thiophanate Methyl in Porous Media in the Presence of Titanium Dioxide Nanoparticles" Water 15, no. 7: 1415. https://doi.org/10.3390/w15071415