#
Evaluation of a Smectite Adsorption-Based Electrostatic System to Decontaminate F^{−} Rich Thermal Waters

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. System Configuration

_{0}is applied to these plates; thus, they act as external electrodes with the same voltage, but with a sign opposite to each other (V− and V+ in Figure 1). The length of these plates is equal to the length of the container (L, in Figure 1), while their distance (equal to the container width, w = w

_{w}+ w

_{s}) was varied during the study to analyze the fluoride removal process as a function of the distance between the electrodes, and so of the mass of water to treat, in relationship with a constant amount of adsorbent material in the system. The height of the container was not taken into account for symmetry reasons, using a 2D physics simulation of the system. Therefore, the results can be considered normalized for the unit of height. The container is filled with water for a width w

_{w}(Figure 1) and a layer of mineral (smectite clay) powder of a fixed thickness (w

_{s}, Figure 1), divided by a permeable septum. Fluoride in water was simulated as released by the dissolution of a salt, and NaF was chosen for the scope. The fluoride anions (F

^{−}, in Figure 1) present in the water are attracted by the positively charged plate, whereas the sodium cations (Na

^{+}, in Figure 1) move to the negatively charged surface. The mineral layer is positioned adjacent to the container surface where the positively charged plate is positioned, in order to enhance the motion of the F

^{−}towards the adsorbent material. A schematic representation of the simulated device is reported in Figure 1.

#### 2.2. Mathematical Modeling and Equations

^{−}anions reach the mineral layer, they first externally diffuse to the particles, then diffuse into the latter, and finally, they are adsorbed on the mineral surface. In the literature, the migration dynamic of an ion population to a charged surface, at which an electrostatic potential V

_{0}is applied, is typically given in terms of the dilute solution theory [33,34,35,36,37,38,39,40]. Provided that, with respect to the thermal energy, the potential is small enough, under this well-known approximation, the ions’ concentration fields are supposed to follow a Boltzmann’s distribution (Equation (1)) [41]:

_{i0}is the initial concentration of the i-th ion, z is the ion valence, e is the electron charge (C), k

_{B}is the Boltzmann constant (J × K

^{−1}), and T is the system temperature (in K). For values of voltage much higher than the thermal voltage (V

_{t}= k

_{B}T/ze), Equation (1) predicts an ionic concentration that exponentially blows up. As a consequence, the correspondent spatial charge distribution at the charged surface does not respect the physical limit due to the finite ion size, thus violating any steric principle. Therefore, in the literature, several models to modify the Poisson–Boltzmann (PB) equation have been proposed to deal with this problem. One of these models, which uses the mean-field approximation and works for low ion concentrations, was proposed by Kilic et al. [34]. The modified Poisson–Boltzmann (MPB) equation is as follows (Equation (2)):

_{c}, that is no more than a few times V

_{t}. This modification of the model was to ensure that the system can saturate to a maximum concentration value of counterions packed with typical spacing $a$ near a highly charged surface equal to C

_{imax}= a

^{−3}[42]. Thus, the amount of charge attracted to the charged surfaces cannot be infinite, avoiding the electrostatic potential to blow up locally, i.e., an effective, but finite, charge density distribution can be found from Equation (2).

^{−}and Na

^{+}) in the system can be studied by writing the macroscopic mass transport balances, which can be modeled through the following nonlinear electro migration–diffusion equations [35]:

^{2}/s, c

_{p}is the positive ion concentration, and ${c}_{n}$ is the concentration of the negative ion (F

^{−}in this case). It is also possible to define the ionic mobility μ using the Nernst–Einstein relationship [43]:

^{−}can be written following the mass continuity equation [44]:

_{n}in the water can be defined using the Nernst–Planck equation [44]:

_{Dn}is the coefficient of dispersion of the F

^{−}in the porous material in m

^{2}/s, F is the Faraday constant, and D

_{en}is the effective diffusion coefficient in m

^{2}/s. Based on the Millington and Quirk model [45], D

_{en}can be defined as reported in Equation (9):

_{p}is the porosity of the adsorbent material while τ

_{fn}is the tortuosity, defined as

^{−}at equilibrium (mol/m

^{3}), ${C}_{{p}_{n}}$ is the amount of F

^{−}adsorbed per unit mass of adsorbent (mol/kg), ${K}_{{L}_{n}}$ is the constant related to the free energy of adsorption (m

^{3}/mol), and ${c}_{pma{x}_{n}}$ is the maximum adsorption capacity of the porous media (mol/kg), corresponding to the saturation limit.

#### 2.3. Simulation Overview

^{+}and F

^{−}were considered equal for the two ions (D

_{n}= D

_{p}, D

_{Dn}= D

_{Dp}) and constant, neglecting the effects of the ion concentrations and local differences in temperature that in this case are not significant and can be neglected [42]. Regarding V

_{0}, this was varied between 0 and 9 V with variable steps in order to study the effect of the applied electrostatic potential. Another parameter that was changed was the initial concentration of F

^{−}in water for which two values were taken into account, 5 mg/L and 10 mg/L, according to the mean concentrations of the F

^{−}rich water to treat, as reported in the Introduction section. Additionally, the width of the device layer containing water was varied, keeping the mineral layer width constant to analyze the efficiency of the system in the defluoridation of higher volumes of water.

## 3. Results

^{−}in the water lower than 1.5 mg/L, the maximum threshold value suggested by WHO [48]. Taking into account this threshold, in Figure 3 the concentration distribution of F

^{−}as a function of the handling time is reported for different values of V

_{0}, c

_{n}

_{0}, and w

_{w}. The results are compared to the F

^{−}threshold limit to show the defluoridation rate and time. The times required to reduce the fluoride concentration below the limit for each case study are reported in Table 2. At first, it is possible to appreciate that the only diffusion without the application of any voltage, even if useful and effective, is a very slow process, taking several days to reach the target concentration. On the other hand, the application of a voltage can strongly enhance the ions’ migration [37], thus allowing them to be directed towards the positive pole and therefore towards the adsorbent material, smectite in our case. It can be noticed that the decrease in F

^{−}with time becomes faster and faster when the applied voltage increases up to 9 V. Comparing the two different c

_{n}

_{0}values analyzed, it is possible to state that, notwithstanding that a lower initial fluoride concentration requires a shorter defluoridation time, when V

_{0}increases, the differences in this treatment time fade away (see Table 2). Concerning the study of the device volume and of the ratio between the water to be treated and the mineral volumes, it can be noted that, as expected, by increasing the amount of fluorine-rich water, the defluoridation time also increases, but this detriment in the performance of the process can be easily compensated by increasing the applied voltage: for example, with w

_{w}equal to 20 cm, instead of 5 cm, the volume of defluorized water considerably increases from 50 L/m to 200 L/m, and an applied voltage higher than 3 V, instead of 0.3 V, is necessary to perform the treatment in less than 1 day.

## 4. Discussion

^{−}ions are used daily for human consumption. This was done by considering a new technique based on the synergies between the adsorption capacity of local Ethiopian smectite clay and electromagnetic fields. As shown in the previous section, the smectites identified here present a good adsorption capacity at equilibrium; however, the deionization process would be very slow, due to the slow diffusion of ions in the static water, from the liquid bulk to the surface of the smectite solid particles. Coupling this process with low-voltage static electric fields results in a consistent enhancement of the whole deionization treatment, as ions are forced to migrate to the charged electrodes at greater rates. In principle, an electric field can produce a separation of ions even in the absence of the mineral layer; however, the ion removal would be much lower, and flowing water, with multiple passages, would be necessary in order to obtain the target final concentration. In the studied system, the quantity of mineral to be used must be chosen with respect to the amount of water to be treated and to the F

^{−}starting concentration, as adsorption is the only process responsible for the ion removal from water (the number of ions which arrive to the positively charged surface is negligible, and the mineral is supposed to be initially fluoride-free, as was experimentally determined [9]). The possible presence, in the water, of other anions (e.g., ${\mathrm{Cl}}^{-}$, ${\mathrm{CO}}_{3}^{-}$, ${\mathrm{SO}}_{4}^{2-}$), even in high concentrations, is not expected to significantly modify the electric field intensity (the ion migration rate does not change), and can be faced by just considering the adsorption selectivity and selecting a proper ratio between water and adsorbent: for example, considering the most critical situation simulated here (w

_{w}=20 cm and c

_{n0}= 10 mg/L), only 38% of the smectite total adsorption capacity would be necessary to reduce the F

^{−}concentration to 1.5 mg/L. This is sufficient in most real applications according to the literature [49,50,51]. Considering that the adsorption process is supposed to reach equilibrium conditions, desorption is not possible, even if the voltage application is stopped, since we are considering juvenile waters with approximately constant concentrations in each source. The low voltages tested in this work confirm that the system can be installed and put into operation without using substantial economic resources for the electrical supply, thus representing an appealing opportunity for rural communities of the Ethiopian Rift Valley. Moreover, the device body could be constructed using cheap materials like PVC. Furthermore, the modularity of the system allows an optimum adaptation to the needed quantities of water to be treated and to reasonable processing times.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- World Health Organization 1 in 3 People Globally Do Not Have Access to Safe Drinking Water—UNICEF, WHO. Available online: https://www.who.int/news/item/18-06-2019-1-in-3-people-globally-do-not-have-access-to-safe-drinking-water-unicef-who (accessed on 2 August 2021).
- UNICEF; WHO. The Measurement and Monitoring of Water Supply, Sanitation and Hygiene (WASH) Affordability: A Missing Element of Monitoring of Sustainable Development Goal (SDG) Targets 6.1 and 6.2; WHO: Geneva, Switzerland, 2021; pp. 1–121. [Google Scholar]
- Jagtap, S.; Yenkie, M.K.; Labhsetwar, N.; Rayalu, S. Fluoride in Drinking Water and Defluoridation of Water. Chem. Rev.
**2012**, 112, 2454–2466. [Google Scholar] [CrossRef] [PubMed] - Kloos, H.; Tekle Haimanot, R. Distribution of Fluoride and Fluorosis in Ethiopia and Prospects for Control. Trop. Med. Int. Health
**1999**, 4, 355–364. [Google Scholar] [CrossRef][Green Version] - Abiye, T. Groundwater dynamics in the East African rift system. In Sustainable Groundwater Resources in Africa; CRC Press: Boca Raton, FL, USA, 2009; pp. 93–106. ISBN 0203859456. [Google Scholar]
- Rango, T.; Bianchini, G.; Beccaluva, L.; Tassinari, R. Geochemistry and Water Quality Assessment of Central Main Ethiopian Rift Natural Waters with Emphasis on Source and Occurrence of Fluoride and Arsenic. J. Afr. Earth Sci.
**2010**, 57, 479–491. [Google Scholar] [CrossRef] - Ayenew, T. The Distribution and Hydrogeological Controls of Fluoride in the Groundwater of Central Ethiopian Rift and Adjacent Highlands. Environ. Geol.
**2008**, 54, 1313–1324. [Google Scholar] [CrossRef] - Tekle-Haimanot, R.; Melaku, Z.; Kloos, H.; Reimann, C.; Fantaye, W.; Zerihun, L.; Bjorvatn, K. The Geographic Distribution of Fluoride in Surface and Groundwater in Ethiopia with an Emphasis on the Rift Valley. Sci. Total Environ.
**2006**, 367, 182–190. [Google Scholar] [CrossRef] [PubMed] - Errico, M.; Desogus, F.; Mascia, M.; Tola, G.; Dendena, L. Soil Adsorption Defluoridation of Drinking Water for an Ethiopian Rural Community. Chem. Pap.
**2006**, 60, 460–465. [Google Scholar] [CrossRef] - Schulze, D.G. Clay Minerals. In Encyclopedia of Soils in the Environment; Elsevier: Amsterdam, The Netherlands, 2005; pp. 246–254. [Google Scholar]
- van Olphen, H. A Tentative Method for the Determination of the Base Exchange Capacity of Small Samples of Clay Minerals. Clay Miner.
**1951**, 1, 169–170. [Google Scholar] [CrossRef] - Van Olphen, H. Rheological Phenomena of Clay Sols in Connection with the Charge Distribution on the Micelles. Discuss. Faraday Soc.
**1951**, 11, 82–84. [Google Scholar] [CrossRef] - Theng, B.K.G.; Russell, M.; Churchman, G.J.; Parfitt, R.L. Surface Properties of Allophane, Halloysite, and Imogolite. Clays Clay Miner.
**1982**, 30, 143–149. [Google Scholar] [CrossRef] - Dohrmann, R.; Kaufhold, S.; Lundqvist, B. Handbook of Clay Science; Elsevier: Amsterdam, The Netherlands, 2013; Volume 5, ISBN 9780080993645. [Google Scholar]
- Huang, H.; Liu, J.; Zhang, P.; Zhang, D.; Gao, F. Investigation on the Simultaneous Removal of Fluoride, Ammonia Nitrogen and Phosphate from Semiconductor Wastewater Using Chemical Precipitation. Chem. Eng. J.
**2017**, 307, 696–706. [Google Scholar] [CrossRef] - Siaurusevičiūtė, I.; Albrektienė, R. Removal of Fluorides from Aqueous Solutions Using Exhausted Coffee Grounds and Iron Sludge. Water (Switz.)
**2021**, 13, 1512. [Google Scholar] [CrossRef] - Bouhadjar, S.I.; Kopp, H.; Britsch, P.; Deowan, S.A.; Hoinkis, J.; Bundschuh, J. Solar Powered Nanofiltration for Drinking Water Production from Fluoride-Containing Groundwater—A Pilot Study towards Developing a Sustainable and Low-Cost Treatment Plant. J. Environ. Manag.
**2019**, 231, 1263–1269. [Google Scholar] [CrossRef] - Owusu-Agyeman, I.; Reinwald, M.; Jeihanipour, A.; Schäfer, A.I. Removal of Fluoride and Natural Organic Matter Removal from Natural Tropical Brackish Waters by Nanofiltration/Reverse Osmosis with Varying Water Chemistry. Chemosphere
**2019**, 217, 47–58. [Google Scholar] [CrossRef] [PubMed] - Pan, J.; Zheng, Y.; Ding, J.; Gao, C.; van der Bruggen, B.; Shen, J. Fluoride Removal from Water by Membrane Capacitive Deionization with a Monovalent Anion Selective Membrane. Ind. Eng. Chem. Res.
**2018**, 57, 7048–7053. [Google Scholar] [CrossRef] - Aliaskari, M.; Schäfer, A.I. Nitrate, Arsenic and Fluoride Removal by Electrodialysis from Brackish Groundwater. Water Res.
**2021**, 190, 116683. [Google Scholar] [CrossRef] [PubMed] - Jiang, K.; Zhou, K.G. Recovery and Removal of Fluoride from Fluorine Industrial Wastewater by Crystallization Process: A Pilot Study. Clean Technol. Environ. Policy
**2017**, 19, 2335–2340. [Google Scholar] [CrossRef] - Pillai, P.; Dharaskar, S.; Pandian, S.; Panchal, H. Overview of Fluoride Removal from Water Using Separation Techniques. Environ. Technol. Innov.
**2021**, 21, 101246. [Google Scholar] [CrossRef] - Guan, C.; Lv, X.; Han, Z.; Chen, C.; Xu, Z.; Liu, Q. The Adsorption Enhancement of Graphene for Fluorine and Chlorine from Water. Appl. Surf. Sci.
**2020**, 516, 146157. [Google Scholar] [CrossRef] - Ruan, Z.; Tian, Y.; Ruan, J.; Cui, G.; Iqbal, K.; Iqbal, A.; Ye, H.; Yang, Z.; Yan, S. Synthesis of Hydroxyapatite/Multi-Walled Carbon Nanotubes for the Removal of Fluoride Ions from Solution. Appl. Surf. Sci.
**2017**, 412, 578–590. [Google Scholar] [CrossRef] - He, Y.; Zhang, L.; An, X.; Wan, G.; Zhu, W.; Luo, Y. Enhanced Fluoride Removal from Water by Rare Earth (La and Ce) Modified Alumina: Adsorption Isotherms, Kinetics, Thermodynamics and Mechanism. Sci. Total Environ.
**2019**, 688, 184–198. [Google Scholar] [CrossRef] - Liu, J.; Yue, X.; Lu, X.; Guo, Y. Uptake Fluoride from Water by Starch Stabilized Layered Double Hydroxides. Water
**2018**, 10, 745. [Google Scholar] [CrossRef][Green Version] - Borgohain, X.; Boruah, A.; Sarma, G.K.; Rashid, M.H. Rapid and Extremely High Adsorption Performance of Porous MgO Nanostructures for Fluoride Removal from Water. J. Mol. Liq.
**2020**, 305, 112799. [Google Scholar] [CrossRef] - Gao, Y.; Li, M.; Ru, Y.; Fu, J. Fluoride Removal from Water by Using Micron Zirconia/Zeolite Molecular Sieve: Characterization and Mechanism. Groundw. Sustain. Dev.
**2021**, 13, 100567. [Google Scholar] [CrossRef] - Ghomashi, P.; Charkhi, A.; Kazemeini, M.; Yousefi, T. Removal of Fluoride from Wastewater by Natural and Modified Nano Clinoptilolite Zeolite. J. Water Environ. Nanotechnol.
**2020**, 5, 270–282. [Google Scholar] [CrossRef] - Vences-Alvarez, E.; Flores-Arciniega, J.L.; Flores-Zuñiga, H.; Rangel-Mendez, J.R. Fluoride Removal from Water by Ceramic Oxides from Cerium and Manganese Solutions. J. Mol. Liq.
**2019**, 286, 110880. [Google Scholar] [CrossRef] - Kim, W.; Singh, R.; Smith, J.A. Modified Crushed Oyster Shells for Fluoride Removal from Water. Sci. Rep.
**2020**, 10, 5759. [Google Scholar] [CrossRef] - Mohan, D.; Sharma, R.; Singh, V.K.; Steele, P.; Pittman, C.U. Fluoride Removal from Water Using Bio-Char, a Green Waste, Low-Cost Adsorbent: Equilibrium Uptake and Sorption Dynamics Modeling. Ind. Eng. Chem. Res.
**2012**, 51, 900–914. [Google Scholar] [CrossRef] - Bizeray, A.M.; Howey, D.A.; Monroe, C.W. Resolving a Discrepancy in Diffusion Potentials, with a Case Study for Li-Ion Batteries. J. Electrochem. Soc.
**2016**, 163, E223–E229. [Google Scholar] [CrossRef] - Kilic, M.S.; Bazant, M.Z.; Ajdari, A. Steric Effects in the Dynamics of Electrolytes at Large Applied Voltages. I. Double-Layer. Charging. Phys. Rev. E—Stat. Nonlinear Soft Matter Phys.
**2007**, 75, 021503. [Google Scholar] [CrossRef][Green Version] - Kilic, M.S.; Bazant, M.Z.; Ajdari, A. Steric Effects in the Dynamics of Electrolytes at Large Applied Voltages. II. Modified Poisson-Nernst-Planck Equations. Phys. Rev. E—Stat. Nonlinear Soft Matter Phys.
**2007**, 75, 061909. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ehlinger, V.M.; Crothers, A.R.; Kusoglu, A.; Weber, A.Z. Modeling Proton-Exchange-Membrane Fuel Cell Performance/Degradation Tradeoffs with Chemical Scavengers. JPhys Energy
**2020**, 2, 044006. [Google Scholar] [CrossRef] - Crothers, A.R.; Darling, R.M.; Kushner, D.I.; Perry, M.L.; Weber, A.Z. Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part III. Transport in Vanadium Redox-Flow-Battery Separators. J. Electrochem. Soc.
**2020**, 167, 013549. [Google Scholar] [CrossRef] - Chung, M.H. Numerical Method for Analysis of Tertiary Current Distribution in Unsteady Natural Convection Multi-Ion Electrodeposition. Electrochim. Acta
**2000**, 45, 3959–3972. [Google Scholar] [CrossRef] - Chu, K.T.; Bazant, M.Z. Nonlinear Electrochemical Relaxation around Conductors. Phys. Rev. E—Stat. Nonlinear Soft Matter Phys.
**2006**, 74, 011591. [Google Scholar] [CrossRef][Green Version] - Lin, C.; Popov, B.N.; Ploehn, H.J. Modeling the Effects of Electrode Composition and Pore Structure on the Performance of Electrochemical Capacitors. J. Electrochem. Soc.
**2002**, 149, A167. [Google Scholar] [CrossRef][Green Version] - Li, B. Continuum Electrostatics for Ionic Solutions with Non-Uniform Ionic Sizes. Nonlinearity
**2009**, 22, 811–833. [Google Scholar] [CrossRef][Green Version] - Lodi, M.B.; Fanari, F.; Fanti, A.; Desogus, F.; Getaneh, W.; Mazzarella, G.; Valera, P. Preliminary Study and Numerical Investigation of an Electrostatic Unit for the Removal of Fluoride from Thermal Water of Ethiopian Rift Valley. IEEE J. Multiscale Multiphysics Comput. Tech.
**2020**, 5, 72–82. [Google Scholar] [CrossRef] - Welch, R.S.; Wilkinson, C.J.; Mauro, J.C.; Bragatto, C.B. Charge Carrier Mobility of Alkali Silicate Glasses Calculated by Molecular Dynamics. Front. Mater.
**2019**, 6, 121. [Google Scholar] [CrossRef] - Danilov, D.; Notten, P.H.L. Mathematical Modelling of Ionic Transport in the Electrolyte of Li-Ion Batteries. Electrochim. Acta
**2008**, 53, 5569–5578. [Google Scholar] [CrossRef] - Millington, R.J.; Quirk, J.P. Permeability of Porous Solids. Trans. Faraday Soc.
**1961**, 57, 1200–1207. [Google Scholar] [CrossRef] - Belhachemi, M.; Addoun, F. Comparative Adsorption Isotherms and Modeling of Methylene Blue onto Activated Carbons. Appl. Water Sci.
**2011**, 1, 111–117. [Google Scholar] [CrossRef][Green Version] - Lu, R.; Leaist, D.G. Mutual Diffusion in Solutions of Alkali Metal Halides: Aqueous LiF, NaF and KF at 25 °C. J. Chem. Soc. Faraday Trans.
**1998**, 94, 111–114. [Google Scholar] [CrossRef] - WHO. World Health Organization guidelines for drinking-water quality. In WHO Chronicle; WHO: Geneva, Switzerland, 2011; Volume 1, ISBN 978 92 4 154761 1. [Google Scholar]
- Mudzielwana, R.; Gitari, M.W. Removal of Fluoride from Groundwater Using MnO
_{2}Bentonite-Smectite Rich Clay Soils Composite. Groundw. Sustain. Dev.**2021**, 14, 100623. [Google Scholar] [CrossRef] - Zhang, Z.; Tan, Y.; Zhong, M. Defluorination of Wastewater by Calcium Chloride Modified Natural Zeolite. Desalination
**2011**, 276, 246–252. [Google Scholar] [CrossRef] - Hamdi, N.; Srasra, E. Removal of Fluoride from Acidic Wastewater by Clay Mineral: Effect of Solid–Liquid Ratios. Desalination
**2007**, 206, 238–244. [Google Scholar] [CrossRef]

**Figure 2.**Fluoride concentration (mg/L) in the system as a function of time (t) for w

_{w}= 5 cm and c

_{n}

_{0}= 10 mg/L and applied voltage of 0 V (first row), 0.5 V (second row), and 1 V (third row).

**Figure 3.**Fluoride concentration in water as a function of time and applied voltage V

_{0}for (

**a**) ${w}_{w}=5\mathrm{cm}$, ${c}_{n}{}_{0}=5\mathrm{m}\mathrm{g}/\mathrm{L}$; (

**b**) ${w}_{w}=5\mathrm{cm}$, ${c}_{n}{}_{0}=10\mathrm{m}\mathrm{g}/\mathrm{L}$; (

**c**)${w}_{w}=10\mathrm{cm}$, ${c}_{n}{}_{0}=5\mathrm{m}\mathrm{g}/\mathrm{L}$; (

**d**)${w}_{w}=10\mathrm{cm}$, ${c}_{n}{}_{0}=10\mathrm{m}\mathrm{g}/\mathrm{L}$; (

**e**)${w}_{w}=20\mathrm{cm}$, ${c}_{n}{}_{0}=5\mathrm{m}\mathrm{g}/\mathrm{L}$; and (

**f**)${w}_{w}=20\mathrm{cm}$; ${c}_{n}{}_{0}=10\mathrm{m}\mathrm{g}/\mathrm{L}$. The dashed line indicates the F

^{−}threshold value discussed previously.

Parameter | Description | Value | Reference |
---|---|---|---|

T | Temperature of the solution | 37 °C | |

$\epsilon $ | Dielectric constant of the solution | 78 | [42] |

$a$ | Spacing between densely packed ions | 0.35 nm | [34,35] |

${D}_{n}$ | F^{−} diffusion coefficient in water | 1.35 × 10^{−}^{9} m^{2}/s | [47] |

${\u03f5}_{p}$ | Smectite clay layer porosity | 0.33 | [9] |

${\rho}_{p}$ | Smectite clay layer density | 1590 kg/m^{3} | [9] |

${D}_{Dn}$ | Coefficient of dispersion of F^{−} in the porous material | 7× 10^{−10} m^{2}/s | [9] |

${K}_{L}{}_{n}$ | Langmuir free energy adsorption constant | 4.5391 m^{3}/mol | [9] |

${c}_{pmax}{}_{n}$ | Langmuir maximum adsorption capacity | 0.01476 mol/kg | [9] |

${V}_{0}$ | Applied electrostatic potential | 0–9 V | |

L | Device length | 1 m | |

w_{w} | Water filled device width | 5–20 cm | |

w_{s} | Smectite filled device width | 1 cm | |

${c}_{n}{}_{0}$ | Initial concentration of F^{−} in the water | 5 mg/L; 10 mg/L |

**Table 2.**Time required to reduce the fluoride concentration below the limit of 1.5 mg/L as a function of applied voltage V

_{0}, c

_{no}, and w

_{w}.

Defluoridation Time (h) | ||||||
---|---|---|---|---|---|---|

V_{0} | c_{n0} = 5 mg/Lw _{w} = 5 cm | c_{n0} = 10 mg/Lw _{w} = 5 cm | c_{n0} = 5 mg/Lw _{w} = 10 cm | c_{n0} = 10 mg/Lw _{w} = 10 cm | c_{n0} = 5 mg/Lw _{w} = 20 cm | c_{n0} = 10 mg/Lw _{w} = 20 cm |

0 V | >48 | >48 | >48 | >48 | >48 | >48 |

0.1 V | >48 | >48 | >48 | >48 | >48 | >48 |

0.2 V | 27.8 | 39.2 | >48 | >48 | >48 | >48 |

0.3 V | 18.7 | 25.3 | >48 | >48 | >48 | >48 |

0.5 V | 11.2 | 14.7 | 41.1 | >48 | >48 | >48 |

1 V | 5.6 | 7.1 | 20.6 | 26.0 | >48 | >48 |

3 V | 1.9 | 2.3 | 6.9 | 8.5 | 26.3 | 32.5 |

5 V | 1.1 | 1.4 | 4.1 | 5.1 | 15.8 | 19.5 |

9 V | 0.6 | 0.8 | 2.3 | 2.8 | 8.8 | 10.8 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Fanari, F.; Lodi, M.B.; Getaneh, W.; Fanti, A.; Desogus, F.; Valera, P.
Evaluation of a Smectite Adsorption-Based Electrostatic System to Decontaminate F^{−} Rich Thermal Waters. *Water* **2022**, *14*, 167.
https://doi.org/10.3390/w14020167

**AMA Style**

Fanari F, Lodi MB, Getaneh W, Fanti A, Desogus F, Valera P.
Evaluation of a Smectite Adsorption-Based Electrostatic System to Decontaminate F^{−} Rich Thermal Waters. *Water*. 2022; 14(2):167.
https://doi.org/10.3390/w14020167

**Chicago/Turabian Style**

Fanari, Fabio, Matteo Bruno Lodi, Worash Getaneh, Alessandro Fanti, Francesco Desogus, and Paolo Valera.
2022. "Evaluation of a Smectite Adsorption-Based Electrostatic System to Decontaminate F^{−} Rich Thermal Waters" *Water* 14, no. 2: 167.
https://doi.org/10.3390/w14020167