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

: Several studies have shown the presence of ﬂuoride levels much higher than the 1.5 mg/L threshold concentration recommended by WHO in the spring waters and wells of the Ethiopian Rift Valley. Available deﬂuoridation techniques can be costly, present complicated technical aspects, and show limited effectiveness. Therefore, it is necessary to devise innovative, sustainable, and effective solutions. This study proposes an alternative method of intervention to the known techniques for removing ﬂuoride from water, particularly suitable for smaller rural communities. In particular, in this work, the possibility to use electromagnetic ﬁelds as a physical method for removing the excess ﬂuoride was investigated. The study was carried out by developing a multiphysics model used for studying and envisaging the design of a device. In this framework, the combination of this approach with the use of highly reactive smectite clay was numerically studied. The results obtained, although preliminary, indicate that the proposed system could signiﬁcantly impoverish the waters of the Rift Valley from ﬂuoride, with the consequence of obtaining a resource suitable for human consumption, in particular for rural communities. However, further theoretical investigations and experimental phases will be necessary to achieve the desired results. maximum efﬁciency in the removal ﬂuoride. we describe a theoretical model for the removal an electric ﬁeld and adsorption on smectite clay to demonstrate the synergy them. rural


Introduction
A recent WHO report [1] shows that one in three people in the world do not have access to safe drinking water, with a particularly high percentage in rural areas. Furthermore, many studies and research, and the consequent actions carried out so far, have been mainly aimed at accessibility to water for human consumption, but the experience of the pandemic has brought a very important lesson, namely the monetary and social costs that non-accessibility entails. In fact, we want to emphasize how much globalization has now linked populations around the world, and the COVID-19 pandemic is a very effective example of this. As described in the joint UNICEF-WHO report [2], we are now beginning to understand how important access to clean water is, not only for consumption (food and irrigation) but also for hygiene, i.e., a type of use which has proved to be fundamental to countering the pandemic. This will lead to a foreseeable significant increase in water demand compared to the parameters considered up to now. The above highlights the importance of having data and information available on the various types of existing aquifers in the various territories, their characteristics, and, finally, the protocols to be applied both for their exploitation and for safeguarding the resource. Based on these considerations, research aimed at studying new water treatment methods that are simple and that do not require advanced technologies or materials for their operation is therefore essential to allow a wider and more targeted use. The model proposed here has the purpose of depleting the fluorine from water, providing the possibility of an efficient use for other elements which are potentially harmful to human health (As, Cd, etc.) and that are present in ionic form. Fluorosis is endemic to approximately twenty developing and developed nations. India, China, and African countries of the Rift Valley region are the most severely affected [3].
The starting hypothesis of this work is based on the significant fluorine content of the geothermal springs present in the area of the Ethiopian Rift Valley; this content is in ionic form and these springs have an upward thrust which is sometimes considerable [4][5][6][7][8]. This suggests that, thanks to the Hall and Faraday effects, the ions dispersed in the hydrothermal water can be seized through magnetic or electric fields, at medium-high enthalpy, towards natural traps consisting of smectite clay, easily available in situ [9], in the tertiary volcanites, which make up most of the rocks outcropping in the Rift Valley border [8]. A sample of soil, collected in the tertiary basaltic lavas of the Muger region, with evident alteration, is the one that presented the best performance in the absorption of fluoride [9]. The parent rocks for the smectite-rich soils are scoriaceous basalts which produced the soil through surface alterations. The analysis of this sample [9] made it possible to identify, through X-ray powder diffraction (XRPD) analysis, the minerals present, mainly pyrophyllite, plagioclase, and smectite. Smectites are a group of phyllosilicate mineral species represented mainly by montmorillonite, beidellite, nontronite, saponite, and hectorite. Smectites are types of clay minerals that are common in soils developed in temperate regions. Soils rich in smectite are considered to be very effective at attenuating many organic and inorganic pollutants because of the high surface area and adsorptive properties of the smectites [10]. They adsorb anions by three different mechanisms: by electrostatic interaction with particle edges when these are positively charged [11,12], by exchanging structural OH groups at the edges and also on basal (planar) surfaces (e.g., [13]), and by accompanying multivalent cations at exchange positions [14].
The smectite clay available in these lithologies should not present particular difficulties to the exploitation. Conversely, zeolites, present in the pyroclastic rocks of the Rift Valley, have very high values of fluorine reaching the saturation of the zeolites themselves, and therefore cannot be taken into consideration for use in the system.
In the literature, several methods for fluoride removal from water are reported: coagulation and precipitation [15], adsorption [16], nanofiltration [17], reverse osmosis [18], membrane-based [19], electrodialysis [20], and crystallization [21]. Among these methods, with regard to defluoridation for obtaining drinking water, adsorption is one of the most suitable due to its low operational costs, relative ease of use, and its capacity to produce water of an excellent quality since it does not contaminate it with other undesirable components or generating sludges [22]. Several adsorbents have been tested for water defluoridation. These include graphene and carbon-based materials [23,24], modified alumina [25,26], porous MgO nanostructures [27], zeolites [28,29], Ce-Zn ceramic oxides [30], and even bio-based materials [31,32]. However, the combination of adsorption methods and physical fluoride removal strategies based on static electric fields has been poorly investigated. This work deals with the in silico investigation of a novel solution to impoverish fluoride-rich thermal waters. The proposed system allows modulating the various depletion stages, which could vary with varying conditions, in order to obtain the maximum efficiency in the removal of fluoride. In this paper, we describe a theoretical model for the removal of fluorine, coupling an electric field and adsorption on smectite clay to demonstrate the synergy between them. Furthermore, the designed system is modular, allowing a specific amount of water to be treated depending on the needs of a single rural community.

System Configuration
The simulated device consists of a parallelepiped-shaped container with two stainless steel plates facing each other and in contact with the outer surfaces of the device, i.e., not in contact with the aqueous medium. A constant voltage V 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.
a specific amount of water to be treated depending on the needs of a single rural community.

System Configuration
The simulated device consists of a parallelepiped-shaped container with two stainless steel plates facing each other and in contact with the outer surfaces of the device, i.e., not in contact with the aqueous medium. A constant voltage V0 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 = ww + ws) 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 ww ( Figure 1) and a layer of mineral (smectite clay) powder of a fixed thickness (ws, 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.

Mathematical Modeling and Equations
The ions motion mechanisms which are involved in the system are (i) the diffusion in the water and (ii) the migration induced by the electric field. Once the F − 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 V0 is

Mathematical Modeling and Equations
The ions motion mechanisms which are involved in the system are (i) the diffusion in the water and (ii) the migration induced by the electric field. Once the F − 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-Water 2022, 14, 167 4 of 11 known approximation, the ions' concentration fields are supposed to follow a Boltzmann's distribution (Equation (1)) [41]: where C i 0 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)): where ε is the dielectric permittivity of the solution, V is the electrostatic potential in volts, and υ is a factor of non-diluteness, which accounts for the steric and volume effects, defined as follows [34,35]: where a is the typical spacing between densely packed ions, reached at a critical potential V 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). Within the MPB model, the spatio-temporal migration dynamics of i-th ionic populations (therein F − 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]: where D n is the ion diffusion coefficient in water in m 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]: The molar balance for F − can be written following the mass continuity equation [44]: where the flux J n in the water can be defined using the Nernst-Planck equation [44]: Water 2022, 14, 167 5 of 11 while in the porous media it can be written as where D 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): where ε p is the porosity of the adsorbent material while τ f n is the tortuosity, defined as The adsorption equilibrium in the mineral was modeled using the Langmuir adsorption model [46]: where c n is the water concentration of F − 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 pmax n is the maximum adsorption capacity of the porous media (mol/kg), corresponding to the saturation limit.

Simulation Overview
The simulations were performed using the commercial FEM software COMSOL Multiphysics V5.5 (COMSOL, Inc., Burlington MA, USA). In particular, the MPB Equation (2) was solved using the Mathematics module coupled with Poisson's equation module while the drift-diffusion equation and adsorption in the porous media were implemented with the Transport of Diluted Species interface. The values of the parameters used for the simulation are reported in Table 1; some of these are derived from other works found in the literature and cited in column 4. The diffusion and dispersion coefficients of Na + 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.
The time useful to reduce the concentration to the limit of 1.5 mg/L was calculated using the function "levelcrossing" of Origin (v.9.0 PRO, OriginLab Corporation, USA). Initial concentration of F − in the water 5 mg/L; 10 mg/L

Results
To understand the device working principles by some examples, in Figure 2 the fluoride concentration (c F − ) profile along the system width for different times and applied voltages is reported. As can be seen from the first row of Figure 2, where the case of no applied voltage is presented, the only diffusion makes the ions move very slowly towards the mineral layer and the changes in the c F − profile are only due to adsorption. On the other side, looking at the second and the third rows of Figure 2, it is possible to observe, from the representation of the profile, that, applying raising voltages, the migration process is quicker and there is a faster decrease of c F − in the water.
This work aims to preliminarily demonstrate the feasibility of water defluoridation by an electric field aided adsorption-based system through the simulation of a device with the goal to reach a concentration of F − 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 n0 , 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 n0 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. Water 2021, 13, x 7 of 12

Discussion
This work aims to demonstrate the effectiveness of fluoride removal from drinking water, taking into account, as a case study, the applicability in the Ethiopian Rift Valley, where several springs with high concentrations of F − 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., Cl − , CO − 3 , SO 2− 4 ), 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.
Future work will consist of testing different adsorption materials and system configurations in order to find better and more efficient solutions.

Informed Consent Statement: Not applicable.
Data Availability Statement: The datasets generated for this study are available upon request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.