# Transport of Thiophanate Methyl in Porous Media in the Presence of Titanium Dioxide Nanoparticles

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}) is recognized as an NP with unique optical, thermal, electrical, and magnetic properties and is widely used as an adsorbent material. Due to the extensive use of pesticides, their removal from the aquatic environment has gained widespread attention from the scientific community. In the present work, the transport of pesticide thiophanate methyl (TM), as well as the cotransport of TM and TiO

_{2}nanoparticles, in a water-saturated column packed with quartz sand under various water conditions were investigated. Several ionic strengths (1, 10, 50, and 100 mM) and pH values (3, 5, 7, and 10) were examined. The results from the transport experiments were fitted and analyzed with the use of the ColloidFit software, while the results from the cotransport experiments were fitted with a modified version of a recently developed mathematical cotransport model. The results of this study suggested that the lowest mass recovery rate was for the cotransport experiments with the addition of NaCl. Furthermore, it was shown that TM has a weak affinity for sand but a relatively strong affinity for TiO

_{2}at high ionic strength and acidic pH, probably accounting for the reduced mass recovery of TM in cotransport experiments.

## 1. Introduction

_{2}) is insoluble in water, very stable, with a high refractive index. As a result of its excellent properties to filter UV radiation, inhibit corrosion, and exhibit excellent antimicrobial activity, TiO

_{2}has found uses in food coloring, paints, inks, coatings, and personal products (toothpaste, face powders) and is commonly found in rutile, anatase, and brookite crystalline forms [18,19]. Due to the incorporation of TiO

_{2}NPs in consumer products, their potential release into the environment is increasing exponentially and may cause adverse health effects to humans and aquatic organisms.

_{2}nanoparticles for TM removal under different pH and ionic strength conditions has not been previously examined. The present study focuses mainly on the effect of TiO

_{2}nanoparticles on the removal of the TM pesticide in water-saturated porous media and explores the behavior of TiO

_{2}and pesticide cotransport. Furthermore, the experimental data collected in this study were successfully fitted with a cotransport numerical model previously published in the literature, which was properly modified to account for the irreversible sorption of TM onto TiO

_{2}nanoparticles. Finally, columns packed with quartz sand were used as a typical filtration system.

## 2. Materials and Methods

_{2}) anatase (Aldrich 637254-50G, purity N 99.9%, size < 25 nm, St. Louis, MO, USA). The required TiO

_{2}NPs suspensions were prepared by mixing 0.1 g of TiO

_{2}powder in 1000 mL of Milli-Q distilled deionized water (ddH

_{2}O). The suspensions were then placed in an ultrasonic bath (sonication bath Elmasonic S 30/(H), Elma Schmidbauer GmbH, Singen, Germany) for 30 min to achieve a uniform dispersion of TiO

_{2}NPs.

_{2}O to the volumetric flask mark. Subsequently, the TM stock solution was sonicated for 10 min.

^{3}and a size range from 400 to 800 μm. The quartz sand was cleaned with 0.1 M HNO

_{3}and 0.1 M NaOH by following previously established procedures [33,34]. All batch experiments (static and dynamic) were conducted in 20 mL Pyrex glass screw-cap tubes (Fisher Scientific, Waltham, MA, USA) under controlled conditions at four different pH values (pH = 3, 5, 7, and 10) and at four different ionic strengths (Is = 1, 10, 50, and 100 mM) with initial TM concentration C

_{0}= 10 mg/L, at room temperature. For each batch experiment, 20 screw-cap tubes were used (10 for the static and 10 for the dynamic group). Each tube contained 14 mL of TM solution with 14 g of quartz sand. For the static experiments, the glass screw-cap tubes were stowed in a tube holder, whereas for the dynamic experiments, the glass screw-cap tubes were placed in a typical rotator (Selecta, Agitador orbit), which was revolving at 12 rpm in order to maintain a thorough mixing of the quartz sand and the TM suspension. At preselected times (5, 15, 30, 45, 60, 90, 120, 150, 180, and 240 min), one screw-cap tube was taken at random from each of the two groups (static and dynamic). Subsequently, the collected samples were centrifuged at 30,000 rpm for 10 min in a microcentrifuge to settle any possible suspended particles.

_{2}O. The experimental procedures, as well as the sample collection methodology employed, are described in earlier works [37,38]. Two series of flow-through experiments were performed under controlled conditions for four different pH values (pH = 3, 5, 7, and 10) and at four different ionic strengths (Is = 1, 10, 50, and 100 mM) at room temperature. For the first set of experiments, the injected fluid contained only TM (10 mg/L), whereas in the second set of experiments, the injected fluid contained both TM (10 mg/L) and TiO

_{2}NPs (100 mg/L). The solution ionic strength was adjusted with the addition of NaCl, while the solution pH was adjusted to the desired value with the addition of either 0.1 M HCl or 0.6 M NaOH. The size and the dynamic zeta potential of the NPs were determined with a zeta sizer (Nano ZS90, Malvern Instruments, UK).

_{2}NPs in the collected samples were determined by UV-Vis double-beam spectrophotometry (model UV-1900, Shimadzu) at a wavelength of 262 nm for TM and 287 nm for TiO

_{2}NPs. Three calibration curves were constructed. One calibration curve for the samples containing only TM, and two containing both TM and TiO

_{2}(one containing TM and traces of TiO

_{2}, and the other containing TiO

_{2}and traces of TM), which were used for the cotransport experiments where both TM and TiO

_{2}concentrations were determined.

_{H}) of the suspended TiO

_{2}NPs were measured with a zeta sizer (Nano ZS90, Malvern Instruments, Southborough, MA, USA). The zeta sizer employs Dynamic Light Scattering to measure the random movement of particles due to collisions by the molecules of the surrounding fluid (Brownian motion) and correlates this to obtain the size of the suspended particles. The zeta potential of TiO

_{2}of the initial solution measured was ζ = −35.6 mV. The measured ζ and d

_{H}values for TiO

_{2}in the various experiments conducted here are listed in Table 1.

## 3. Mathematical Modeling

#### 3.1. Governing Partial Differential Equations

_{n}/L

^{3}], or attached to the solid matrix, ${\mathrm{C}}_{\mathrm{n}*}$ [M

_{n}/M

_{sm}]. Solute concentrations are represented by ${\mathrm{C}}_{\mathrm{s}}$ [M

_{s}/L

^{3}]. Solutes may sorb onto suspended nanoparticles, ${\mathrm{C}}_{\mathrm{ns}}$ [M

_{s}/M

_{n}], or sorb onto the solid matrix, ${\mathrm{C}}_{\mathrm{s}*}$ [M

_{s}/M

_{sm}], or sorb on nanoparticles already attached to the solid matrix, ${\mathrm{C}}_{\mathrm{n}*\mathrm{s}*}$ [M

_{s}/M

_{n}]. Note that the subscripts n, s, and ns represent nanoparticles, solutes, and nanoparticle-solute complexes, respectively. Additionally, M

_{n}represents the mass of nanoparticles, M

_{s}is the mass of solutes, and M

_{sm}is the mass of the solid matrix.

_{sm}/L

^{3}] is the bulk density of the solid matrix; ${\mathrm{D}}_{\mathrm{n}}$ [L

^{2}/t] is the hydrodynamic dispersion coefficient of the suspended nanoparticles; ${\mathrm{U}}_{\mathrm{n}}$ [L/t] is the interstitial velocity; and ${\mathrm{F}}_{\mathrm{n}}$ [M

_{n}/L

^{3}t] is a general form of the nanoparticle source configuration.

_{n}/M

_{sm}], and/or irreversible, ${\mathrm{C}}_{\mathrm{n}*}^{\left(\mathrm{i}\right)}$ [M

_{n}/M

_{sm}] manner. Therefore, the corresponding nanoparticle accumulation term in Equation (1) can be expressed as [41]:

^{2}/t] is the longitudinal hydrodynamic dispersion coefficient of the suspended solutes; ${\mathrm{D}}_{\mathrm{ns}}$ [L

^{2}/t] is the longitudinal hydrodynamic dispersion coefficient of nanoparticle-solute complexes; and ${\mathrm{F}}_{\mathrm{s}}$ [M

_{v}/L

^{3}t] is a general form of the virus source configuration.

_{n}/M

_{sm}] is the reversible sorbed solute concentration onto the solid matrix and ${\mathrm{C}}_{\mathrm{s}*}^{\left(\mathrm{i}\right)}$ [M

_{n}/M

_{sm}] is the irreversible sorbed solute concentration onto the solid matrix. The reversible term on Equation (6) is given by given [40,42]:

_{s}/M

_{n}] is the reversibly attached concentration of solute-nanoparticle complexes onto the solid matrix, and ${\mathrm{C}}_{\mathrm{n}*\mathrm{s}*}^{\left(\mathrm{i}\right)}$ [M

_{s}/M

_{n}] is the irreversibly attached concentration of solute-nanoparticle complexes onto the solid matrix. The reversible accumulation term present in Equation (9) is given by [1,41,46]:

^{3}M

_{sm}/M

_{n}

^{2}t] is the rate coefficient of solute sorption onto nanoparticles already attached to the solid matrix; ${\mathrm{r}}_{\mathrm{n}*\mathrm{s}*-\mathrm{s}}$ [1/t] is the rate coefficient of solute desorption from solute-nanoparticles complexes attached to the solid matrix; ${\mathrm{r}}_{\mathrm{ns}-\mathrm{n}*\mathrm{s}*}$ [1/t] is the rate coefficient of solute-nanoparticle complex attachment onto the solid matrix; and ${\mathrm{r}}_{\mathrm{n}*\mathrm{s}*-\mathrm{ns}}$ [1/t] is the rate coefficient of solute-nanoparticle complex detachment from the solid matrix. Furthermore, the irreversible accumulation term of Equation (9) can be given from:

^{6}/M

_{n}

^{2}t] is the rate coefficient of solute sorption onto suspended nanoparticles; ${\mathrm{r}}_{\mathrm{ns}-\mathrm{s}}$ [1/t] is the rate coefficient of solute desorption from suspended nanoparticles. Furthermore, it is assumed that for nanoparticle facilitated transport, the formation of ${\mathrm{C}}_{\mathrm{n}*\mathrm{s}*}$ depends only on ${\mathrm{C}}_{\mathrm{n}*}^{\left(\mathrm{r}\right)}$, which implies that solutes do not interact with irreversibly attached nanoparticles onto the solid matrix.

^{3}] describes the source physical geometry; and ${\mathrm{G}}_{\mathrm{i}}\left(\mathrm{t}\right)$ [M

_{i}/t] is the mass release function for a point source of species i. More information about different expressions of source configuration and also about the necessary initial and boundary conditions can be found in the work of Katzourakis and Chrysikopoulos [39].

#### 3.2. The Fitting Process

_{2}experiments, the mathematical model developed here (Equations (1)–(4), (7), and (10)–(13)) was solved numerically, and in conjunction with Pest, the required fittings were performed.

_{2}breakthrough curves collected from the TM-TiO

_{2}cotransport experiments were also fitted with ColloidFit, and the parameters determined are: ${\mathrm{D}}_{\mathrm{n}}$, ${\mathrm{r}}_{{\mathrm{n}-\mathrm{n}*}^{\left(\mathrm{r}\right)}}$, ${\mathrm{r}}_{{\mathrm{n}*}^{\left(\mathrm{r}\right)}-\mathrm{n}}$, and ${\mathrm{r}}_{{\mathrm{n}-\mathrm{n}*}^{\left(\mathrm{i}\right)}}$. This simplified approach is based on the assumption that, due to their size, the TiO

_{2}nanoparticles are practically not affected by the presence of the TM solutes. This approach is similar to that proposed by Katzourakis and Chrysikopoulos [41]. Finally, the TM breakthrough curves from the TM-TiO

_{2}cotransport experiments were fitted with Equations (1)–(4), (7), and (10)–(13).

#### 3.3. Additional Theoretical Calculations

_{r}[-]) for both TM and TiO

_{2}NPs at the column outlet was determined with the application of the following mathematical relationship [35]:

^{3}] is the aqueous phase concentration of either TM or TiO

_{2}NPs; t

_{p}[t] is the broad pulse duration; ${\mathrm{m}}_{0}$ [tM/L

^{3}] is the zeroth absolute temporal moment that quantifies the total mass in the concentration distribution curve [46]:

^{3}] is the aqueous phase concentration of either TM or TiO

_{2}NPs, L [L] is the length of the packed column; and t [t] is time. All M

_{r}estimates were obtained using Equations (14) and (15), as determined by the software ColloidFit [47].

## 4. Results and Discussion

_{0}= 10 mg/L, at room temperature, are presented in Figure 2. Clearly, the experimental data suggested that during static conditions, neither the pH nor Is significantly affected the sorption of TM onto quartz sand. As expected, under dynamic conditions, the amount of TM sorbed onto quartz sand increased slightly with time due to agitation, but the sorption of TM onto quartz sand was insensitive to both pH and Is variations. These findings are in agreement with the work by Flores et al. [49], who reported that the sorption of TM onto montmorillonite is insignificant (<5%), and the work by Wauchope et al. [50], who reported that TM does not sorb strongly onto soil particles.

_{0}) and the corresponding fitted curves as a function of time are presented in Figure 3 for the transport experiments in water-saturated columns packed with quartz sand. The effect of four different ionic strength values (Is = 1, 10, 50, and 100 mM) is shown in Figure 3a–d, whereas the effect of four different pH values (pH = 3, 5, 7, and 10) is shown in Figure 3e–h. All breakthrough curves were successfully fitted with the nonlinear least squares regression software ColloidFit. The experimental conditions, together with the estimated mass recoveries and the fitted parameters, for each case considered in this study, are listed in Table 2.

_{2}cotransport experiments, for several different ionic strengths (Is = 1, 10, 50, and 100 mM) and pH values (pH = 3, 5, 7, and 10) as a function of time, are presented in Figure 4 and Figure 5, respectively. Note that the mass recovery values for ΤΜ were considerably lower in the presence of TiO

_{2}compared to the single transport experiments, where M

_{r}= 100% was observed. The measured zeta potentials for TiO

_{2}in the various experiments, which are listed in Table 1, suggested that the zeta potential for TiO

_{2}was affected during the various experiments. The observed negative increase in the zeta potential, and thus an increase in stability, was not only due to the increase in pH but also due to possible TM sorption onto TiO

_{2}. The observed reduced mass recovery of TM during the cotransport with TiO

_{2}could also be explained by the possible sorption of TM onto TiO

_{2}nanoparticles. Previous studies have shown that fungicides can act as capping agents for metal nanoparticles. Malandrakis et al. [54] demonstrated such a capping effect of ZnO nanoparticles when applied in combination with the fungicide boscalid against the plant pathogen Alternaria alternata. A similar interaction between TM and silver nanoparticles was reported in a study by Zheng et al. [55], who developed a colorimetric array for the detection of TM adsorbed onto silver nanoparticles. The fitted parameter values for TiO

_{2}and TM concentrations are listed in Table 2. The mathematical model presented in this work successfully fitted the experimental breakthrough data. It should be noted, however, that the experiments for Is = 50 and 100 mM (see Figure 5g,h) caused extreme retention of TiO

_{2}inside the column (M

_{r}< 5%). Consequently, it was very hard for the cotransport model to produce meaningful and unique parameter values. Therefore, these two experimental data sets were excluded from the fitting process.

_{2}nanoparticles, increasing the ionic strength causes them to aggregate and increase their size. From Table 1, it is evident that for values of ionic strength in the range of 1 to 50 mM, the average hydrodynamic diameter size (d

_{H}) fluctuates around 351 nm, but for Is = 100 mM, the d

_{H}rapidly increases to 1004 nm. This is a consequence of particle aggregation that changes the physical characteristics of particle transport and dramatically reduces the mass recovery ratio M

_{r}. Aggregating nanoparticles require specialized models [56] for their simulation. This is the reason that the experimental data for high ionic strength values (Is = 50 & 100 mM) were excluded from the fitting process.

_{r}= 31.5% and for Is = 50 mM was M

_{r}= 34.3%, suggesting that TM removal from soil could be enhanced in the presence of TiO

_{2}nanoparticles. These observations are in agreement with the fitting results of this study, which indicated that increasing ionic strength contributes to the increase of both reversible, ${\mathrm{r}}_{{\mathrm{n}-\mathrm{n}*}^{\left(\mathrm{r}\right)}}$, and irreversible, ${\mathrm{r}}_{{\mathrm{n}-\mathrm{n}*}^{\left(\mathrm{i}\right)}}$, attachment rates. The effect of salt concentration on pesticide sorption is complex. Based on the diffuse double-layer theory, ions that form outer-sphere surface complexes show decreasing adsorption with increasing ionic strength, while ions that form inner-sphere surface complexes show little ionic strength dependence or show increasing adsorption with increasing ionic strength [57,58]. In previous studies, it has been observed that negatively charged TiO

_{2}nanoparticles are attached to positively charged sand [59]. Additionally, according to Chrysikopoulos and Fountouli [60], the presence of NaCl affected substantially the transport of TiO

_{2}nanoparticles, yielding a reduction in M

_{r}, which is also consistent with the results of the present study.

_{2}was enhanced (see Table 2), and the reversible attachment rate (${\mathrm{r}}_{{\mathrm{n}-\mathrm{n}*}^{\left(\mathrm{r}\right)}}$) for TiO

_{2}was decreased. Both of these observations are valid for all pH values examined in this study except for the experiment at pH = 10, where the results were exactly the opposite (TM mass recovery decreased, and ${\mathrm{r}}_{{\mathrm{n}-\mathrm{n}*}^{\left(\mathrm{r}\right)}}$ increased). This unexpected result might be due to the strong sorption rate of TM onto TiO

_{2}(${\mathrm{r}}_{\mathrm{s}-\mathrm{ns}}$) observed at pH = 10 (see Table 2). It should be noted that, with increasing the pH, the sorption rate of TM onto the solid matrix (${\mathrm{r}}_{{\mathrm{s}-\mathrm{s}*}^{\left(\mathrm{r}\right)}}$) was decreased (see Table 2). However, in the presence of TiO

_{2}nanoparticles, at high pH values the sorption rate of TM onto TiO

_{2}particles was increased. The sorption rate ${\mathrm{r}}_{\mathrm{s}-\mathrm{ns}}$ followed an increasing trend with increasing pH (see Table 2) and suggested that TiO

_{2}nanoparticles facilitated TM transport progressively more with increasing pH.

_{2}nanoparticles, all of the above factors, which are expected to enhance nanoparticle transport, are expected to also enhance the TM transport, while the inverse is also true.

## 5. Conclusions

_{2}and TM in a water-saturated column packed with quartz sand under various ionic strength and pH conditions, suggested that increasing the solution pH: (i) reduced the sorption rate of TM onto the solid matrix, (ii) reduced the attachment rate of TiO

_{2}nanoparticles onto the solid matrix, (iii) increased the sorption rate of TM onto TiO

_{2}nanoparticles, and (iv) increased the mass recovery of both TM and TiO

_{2}. On the contrary, increasing the ionic strength yielded: (i) increased sorption of TM onto the solid matrix, (ii) increased attachment rate of TiO

_{2}particles onto the solid matrix, and (iii) reduced mass recovery of both TiO

_{2}particles and TM solutes. Furthermore, for the cotransport case, under the experimental conditions of pH = 5.1 and Is = 100 mM, it was shown that the mass retention of TM by the packed column was highest or equivalent TM mass recovery was lowest (M

_{r}= 31.5%).

_{2}nanoparticles for Is = 100 mM yielded a 67.8% reduction in TM mass recovery, suggesting that TiO

_{2}nanoparticles can be used to enhance the removal of TM from the soil. Similarly, when considering the transport of TiO

_{2}nanoparticles, it was shown that increasing the ionic strength from 1 to 100 mM dramatically decreased their mass recovery, highlighting their sensitivity to ionic strength. Finally, it is evident from the current study that the solution pH and ionic strength can affect the TM transport characteristics, with the latter one having more profound effects in the presence of TiO

_{2}nanoparticles.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$\mathrm{C}$ | aqueous phase concentration, M/L^{3} |

${\mathrm{C}}_{\mathrm{n}}$ | aqueous phase concentration of suspended nanoparticles, M_{n}/L^{3}. |

${\mathrm{C}}_{\mathrm{n}*}$ | concentration of nanoparticles attached onto the solid matrix, M_{n}/M_{sm}. |

${\mathrm{C}}_{\mathrm{s}}$ | aqueous phase solute concentration, M_{s}/L^{3}. |

${\mathrm{C}}_{\mathrm{s}*}$ | concentration of solutes sorbed onto the solid matrix, M_{s}/M_{sm}. |

${\mathrm{C}}_{\mathrm{ns}}$ | concentration of suspended solute-nanoparticle complex, M_{s}/M_{n}. |

${\mathrm{C}}_{\mathrm{n}*\mathrm{s}*}$ | concentration of solute-nanoparticle complex attached onto the solid matrix, M_{s}/M_{n}. |

${\mathrm{C}}_{\mathrm{n}*}^{\left(\mathrm{i}\right)}$ | concentration of nanoparticles irreversibly attached onto the solid matrix, M_{n}/M_{sm}. |

${\mathrm{C}}_{\mathrm{n}*}^{\left(\mathrm{r}\right)}$ | concentration of nanoparticles reversibly attached onto the solid matrix, M_{n}/M_{sm}. |

${\mathrm{C}}_{0}$ | initial aqueous phase solute concentration, M_{s}/L |

d_{H} | hydrodynamic diameter, L |

D_{i} | hydrodynamic dispersion coefficient of species i, L^{2}/t. |

F_{i} | general form of the source configuration of species i, M_{i}/L^{3}t. |

G_{i}(t) | mass release function of species i (point source), M_{i}/t. |

Is | ionic strength, mM |

${\mathrm{K}}_{\mathrm{ns}}$ | rate of irreversible solute-nanoparticle complex attachment onto the solid matrix, 1/t |

L | length, L. |

m_{0} | zeroth absolute temporal moment, tM/L^{3} |

M_{n} | mass of nanoparticles, M_{n}. |

M_{sm} | mass of the solid matrix, M_{sm}. |

M_{s} | mass of solutes, M_{s}. |

M_{r} | ratio of recovered mass, [-] |

${\mathrm{r}}_{{\mathrm{n}-\mathrm{n}*}^{\left(\mathrm{i}\right)}}$ | rate of irreversible nanoparticle attachment onto the solid matrix, 1/t. |

${\mathrm{r}}_{{\mathrm{n}-\mathrm{n}*}^{\left(\mathrm{r}\right)}}$ | rate of reversible nanoparticle attachment onto the solid matrix, 1/t. |

${\mathrm{r}}_{n{*}^{\left(\mathrm{r}\right)}-\mathrm{n}}$ | rate of reversible nanoparticle detachment from the solid matrix, 1/t. |

${\mathrm{r}}_{{\mathrm{s}-\mathrm{s}*}^{\left(\mathrm{i}\right)}}$ | rate of irreversible solute sorption onto the solid matrix, 1/t. |

${\mathrm{r}}_{{\mathrm{s}-\mathrm{s}}^{\ast (r)}}$ | rate of reversible solute sorption onto the solid matrix, 1/t. |

${\mathrm{r}}_{{\mathrm{s}}^{*\left(\mathrm{r}\right)}-\mathrm{s}}$ | rate of reversible solute desorption from the solid matrix, 1/t. |

${\mathrm{r}}_{\mathrm{s}-\mathrm{ns}}$ | rate of solute sorption onto suspended nanoparticles, L^{6}/M_{n}^{2}t. |

${\mathrm{r}}_{\mathrm{ns}-\mathrm{s}}$ | rate of solute desorption from suspended nanoparticles, 1/t. |

${\mathrm{r}}_{\mathrm{s}-\mathrm{n}*\mathrm{s}*}$ | rate of solute sorption onto nanoparticles already attached onto the solid matrix, L^{3}M_{sm}/M_{n}^{2}t. |

${\mathrm{r}}_{\mathrm{ns}-\mathrm{n}*\mathrm{s}*}$ | rate of solute-nanoparticle complex attachment onto the solid matrix,1/t. |

${\mathrm{r}}_{\mathrm{ns}-\mathrm{s}}$ | rate of solute desorption from suspended nanoparticles, 1/t. |

${\mathrm{r}}_{\mathrm{n}*\mathrm{s}*-\mathrm{ns}}$ | rate of solute-nanoparticle complex detachment from the solid matrix, 1/t. |

t | time, t. |

t_{p} | source duration time period, t. |

U | interstitial velocity, L/t. |

W | characterizes the source physical geometry (point source), 1/L^{3}. |

x | Cartesian coordinate, L. |

Greek Letters | |

Θ | porosity, (L^{3} voids)/(L^{3} solid matrix). |

ζ | zeta potential, V |

ρ | bulk density of the solid matrix, M_{sm}/L^{3} |

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**Figure 1.**Chemical structure of thiophanate methyl [32].

**Figure 2.**TM normalized concentrations during the batch adsorption experiments onto quartz sand under: dynamic conditions and four different Is values (

**a**–

**d**), static conditions and four different Is values (

**e**–

**h**), dynamic conditions and four different pH values (

**i**–

**l**), and static conditions and four different Is values (

**m**–

**p**). Here the initial TM concentration is C

_{0}= 10 mg/L.

**Figure 3.**TM normalized breakthrough concentrations (symbols) at four different Is values (

**a**–

**d**) and four different pH values (

**e**–

**h**) collected at the exit of the water-saturated columns packed with quartz sand, together with the best fitted model simulations (solid curves).

**Figure 4.**Breakthrough data (symbols) for the cotransport of TM (triangles) (

**a**–

**d**) and TiO

_{2}(pentagons) (

**e**–

**h**), together with the corresponding fitted curves (solid curves), in a column packed with quartz sand, at 4 different ionic strengths (Is = 1, 10, 50, and 100 mM) as a function of time.

**Figure 5.**Breakthrough data (symbols) for the cotransport of TM (triangles) (

**a**–

**d**) and TiO

_{2}(pentagons) (

**e**–

**h**), together with the corresponding fitted curves (solid curves), in a column packed with quartz sand, at 4 different pH values (pH = 3, 5, 7, and 10) as a function of time.

Experimental Conditions * | TiO_{2} | ||
---|---|---|---|

pH | Ionic Strength (mM) | ζ (mV) | d_{H} (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 | ||||||||

M_{r} (%) | 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 |

t_{p} (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 |

D_{s} (cm/min) | 0.26 | 0.24 | 0.29 | 0.30 | 0.22 | 0.23 | 0.27 | 0.29 |

${\mathrm{r}}_{{\mathrm{s}-\mathrm{s}*}^{\left(\mathrm{r}\right)}}$ (1/min) | 0.0055 | 0.0032 | 0.0022 | 0.0019 | 0.0036 | 0.0038 | 0.0058 | 0.0060 |

${\mathrm{r}}_{{\mathrm{s}*}^{\left(\mathrm{r}\right)}-\mathrm{s}}$ (1/min) | 0.0204 | 0.0182 | 0.0136 | 0.0060 | 0.0117 | 0.0136 | 0.0165 | 0.0171 |

${\mathrm{r}}_{{\mathrm{s}-\mathrm{s}*}^{\left(\mathrm{i}\right)}}$ (1/min) | 0.00086 | 0 | 0 | 0 | 0.00037 | 0.00072 | 0.00090 | 0.00094 |

Cotransport parameter values for TM | ||||||||

M_{r} (%) | 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 |

t_{p} (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 |

D_{s} (cm/min) | 0.26 | 0.24 | 0.29 | 0.30 | 0.22 | 0.23 | 0.27 | 0.29 |

${\mathrm{r}}_{\mathrm{s}-\mathrm{ns}}$ (L^{6}/M_{n}^{2}t) | 0.00064 | 0.0020 | 0.0023 | 0.0071 | 0.9000 | 0.2870 | - | - |

${\mathrm{r}}_{\mathrm{ns}-\mathrm{s}}$ (1/min) | 0.0102 | 0.0296 | 0.0585 | 0.0654 | 0.7300 | 0.1780 | - | - |

${\mathrm{r}}_{\mathrm{n}*\mathrm{s}*-\mathrm{s}}$ (1/min) | 0.0085 | 0.0004 | 0.0786 | 0.0834 | 0.2820 | 0.0003 | - | - |

Cotransport parameter values for TiO_{2} nanoparticles | ||||||||

M_{r} (%) | 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 |

t_{p} (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 |

D_{n} (cm/min) | 0.26 | 0.23 | 0.29 | 0.30 | 0.22 | 0.5 | - | - |

${\mathrm{r}}_{{\mathrm{n}-\mathrm{n}*}^{\left(\mathrm{r}\right)}}$ (1/min) | 0.001 | 0.0008 | 0.0004 | 0.0007 | 0.0015 | 0.0044 | - | - |

${\mathrm{r}}_{{\mathrm{n}*}^{\left(\mathrm{r}\right)}-\mathrm{n}}$ (1/min) | 0.0185 | 0.0205 | 0.0111 | 0.0053 | 0.0127 | 0.0257 | - | - |

${\mathrm{r}}_{{\mathrm{n}-\mathrm{n}*}^{\left(\mathrm{i}\right)}}$ (1/min) | 0.0014 | 0.0009 | - | 0.0009 | 0.0089 | 0.0110 | - | - |

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**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Stefanarou, 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