## Abstract

The ability of heavy metals to accumulate in living organisms, combined with the fact that they are not biodegradable, necessitates an expansion and improvement of the existing water purification methods. An effective mixing of contaminated water with heavy metals and magnetic nanoparticles is crucial for water treatment applications. In the present work, electromagnetic and shear mixing are combined to explore optimization mixing strategies. Mixing is studied through simulations under various initial conditions for two streams that are loaded with nanoparticles and one contaminated water stream that lies between the nanoparticle streams. In the present work, magnetic mixing is superimposed with a time-modulated gradient external magnetic field. The results show that as the radius ratio between the nanoparticles and the heavy metals increases, the external magnetic field is more effective insofar as the mixing of the nanoparticles is concerned. Moreover, for simulations where the radius ratio is higher than or equal to 10, an effective mixing is achieved. By comparing the velocity ratios, a better mixing is achieved in the case of higher velocity ratios. Also, minor effects on mixing are observed by comparing the ratios *V*_{p}/*V*_{c} = 10 and *V*_{p}/*V*_{c} = 20.

## HIGHLIGHTS

We study the mixing optimization of heavy metal contaminated water with magnetic nanoparticles.

The study is performed using Computational Fluid Dynamics (CFD).

Magnetic mixing is combined with a time-varying gradient magnetic field.

Mixing efficiency is enhanced as the radius ratio between nanoparticles and heavy metals increases.

Mixing is affected by the velocity ratio of contaminated water over the nanoparticle current.

## INTRODUCTION

Heavy metals are particularly pathogenic for human health since they are non-biodegradable, non-metabolizable and tend to accumulate in environmental systems (Karvelas *et al.* 2018). During the last few decades, progress has been made in the field of nanotechnology, and extended knowledge has been acquired on the synthesis, characterization and possible applications of magnetic nanoparticles that can be employed in the process of water purification (Bönnemann *et al.* 2008). Besides the experimental approach, numerical simulations at the nanoscale for water purification have been developed (Sofos *et al.* 2019a, 2019b). The term adsorption is referred to as the process in which pollutants in solution transfer onto the solid adsorbent, which is frequently used for water and wastewater purification (Qu *et al.* 2013; Wang & Zhuang 2017). Water purification from heavy metals can be performed by using the adsorption method where the heavy metal ions are adsorbed on the surface or active site of adsorbents (Podstawczyk *et al.* 2015). The adsorption method is found to depend on several factors. Among them are the synthesis of nanoparticles such as the size and the coatings of them. Moreover, the pH of the surrounding medium, the temperature (Somorjai *et al.* 2006), the adsorbent dose and the initial concentration of the ions are significantly affecting the adsorption method (Liosis *et al.* 2021).

The contribution of magnetic nanoparticles to the adsorption process arises from their large surface area, which increases the available contact surface, and also from the considerable number of surface atoms, which leads to an increased amount of active sites (Bronstein *et al.* 2008) and reduces the amount of adsorbent dose and retention time (Beni & Esmaeili 2020). In addition, a majority of the existing research focuses on the magnetic nanoparticles of iron oxide due to its supermagnetic properties, high corrosion and low toxicity (Liu *et al.* 2011; Kargin *et al.* 2020). The magnetic saturation (*M*_{s}) of Fe_{3}O_{4} nanoparticles is 92–100 (emu/g) with a critical diameter value (*D*_{cr}), and for a value below *D*_{cr}, more energy is required to create a domain wall than to support the external magnetostatic energy of the single domain state (Estelrich *et al.* 2015). Magnemite nanoparticles become supermagnetic when the size of the nanoparticles is under 20 nm (Ling *et al.* 2015). The above similar physical properties arise from the alike crystal structure. In general, as the size of Fe_{3}O_{4} nanoparticles decreases, the saturation magnetization also decreases (Gholizadeh 2017).

Several studies have focused on the enhancement of micromixing either experimentally or numerically. The flow rate and the external magnetic field are usually numerically investigated (Zhu & Nguyen 2012; Nouri *et al.* 2017; Karvelas *et al.* 2020). Moreover, interesting results can be found with regard to the factors behind effective mixing, driving and collecting magnetic nanoparticles (Karvelas *et al.* 2017b, 2021; Asghari *et al.* 2018; Liosis *et al.* 2020).

In the present study, a water stream that is contaminated by heavy metals and two streams with Fe_{3}O_{4} nanoparticles are the inlets of the microfluidic duct. Numerical simulations are performed in order to investigate the optimum mixing of the streams, so as to create the ideal conditions for the possible adsorption of heavy metal ions. Hence, a magnetic field where its permanent and gradient components are temporarily varied is employed for the mixing and driving of Fe_{3}O_{4} particles and heavy metal ions under various velocities, initial concentrations and also radius ratios.

The methodology for the simulations of water flow and nanoparticle motion is described in the methods section. Then, the results of the numerical study are discussed, placing emphasis on the influence of the various inlet ratios and magnetic frequency. Finally, the most important conclusions are summarized in the last section.

## METHODS

The slow water flow in the micromixer duct is expected to be laminar and steady state. The mixing efficiency depends on the velocity ratio but is not affected by the incoming angles of flow streams (Karvelas *et al.* 2019). Therefore, a simplified geometry is employed, which consists of a squared cross-section (inlet–outlet of the micromixer) with equal height and width, along with length five times bigger than the other sides (Kamali *et al.* 2014). The three water streams enter the micromixer from different inlets, mix with one another and leave the domain from the common outlet, as shown in Figure 1.

The OpenFoam platform is used for a computational grid that consists of 40,000 hexaedra for the calculation of incompressible Navier–Stokes equations that are solved in the Eulerian frame, for the pressure, *p*, and velocity, *u*, together with a model for the discrete motion of particles in a Lagrangian frame (Weller *et al.* 1998). The equations are evolved in time by using the Euler's time marching method.

In this work, the radius ratio of *R*_{particles}/*R*_{Heavy metals} was studied for achieving mixing effectiveness. The radius of the heavy metals (*R*_{Heavy metals}) was equal to 0.424 (nm) for the simulations. Hence, the maximum diameter of nanoparticles must be below 85 nm for the simulations in order to remain at the nanoscale. Moreover, monodisperse size distribution was used for each simulation in an attempt to approach the experimental model in a better way. In this model, monodisperse distribution was employed to prevent the agglomeration of nanoparticles, which was achieved by using surfactants as colloidal stabilizers (Bönnemann *et al.* 2008). Mixing optimization depends on the external magnetic field, and when applied to paramagnetic nanoparticles, can oscillate under the action of the magnetic force when an alternating uniform magnetic field is applied (Liosis *et al.* 2020). Additionally, the physical and mechanical properties of Fe_{3}O_{4} have an impact on particle–particle collisions, and, thus, they have been numerically embedded in the simulations. The values of these properties found from the literature correspond to a density equal to 5,180 kg/m^{3} (Teja & Koh 2009), Poisson's ratio equal to 0.31 and Young's modulus 200 × 10^{9} Pa (Chicot *et al.* 2011). Heavy metal properties are varied for each potential heavy metal element (Cd, Cr, Cu, Ni, Zn and Pb), and, therefore, the mean values of density, Poisson's ratio and Young's modulus used for the simulations were calculated and found to be 8,563 kg/m^{3}, *v* = 0.323 and 123 × 10^{9} Pa, respectively. Details of the numerical models, force and moment terms used in equations may be found in Tijskens *et al.* (2003) and Karvelas *et al.* (2017a).

The adsorption capacity is strongly related to metal ion concentration (Yoo *et al.* 2020), since the adsorbent dosage determines the adsorbent capacity for a given initial concentration (Shaker 2015). According to previous related works, the initial concentration ratio *C*_{nanoparticles}/*C*_{heavy_metals} varies and can be found either as <1 or as >1 (Gong *et al.* 2012; Zhang *et al.* 2019). The relative results show that fast (0.5 min) mixing is established for an initial concentration ratio up to 2.5 (Zhang *et al.* 2019). Hence, the concentration ratio at the inlet of the nanoparticles per second over the heavy metals per second at their inlet is selected as equal to 2, as in our previous work (Karvelas *et al.* 2020). In order to achieve effective mixing, the radius of the nanoparticles has been studied, initially for a better understanding of the effect of the magnetic field on the motion of the nanoparticles and secondly to investigate the possible active sites by calculating the specific surface area of the nanoparticles. During the adsorption process, the removal rates of heavy metal ions first increase rapidly with time and those of the active sites gradually decrease. The driving force weakens as a result of slow removal rates (Shaker 2015), and, therefore, slow shearing for Fe_{3}O_{4} nanoparticles and heavy metals is introduced in the microfluidic duct with variable inlet velocity ratios.

The equilibrium of the adsorption process is established when an adsorbate-containing phase comes into contact with the adsorbent for a sufficient period of time (Limousin *et al.* 2007). The time where the equilibrium is established varies in the literature from 100 min (Shaker 2015) to 0.5 min (Zhang *et al.* 2019) due to several ‘main’ factors such as pH, temperature, initial concentrations (heavy metals and the adsorbent dosage), particle size, contact time and also due to ‘secondary’ factors such as ionic strength (Mohseni-Bandpi *et al.* 2016) and zeta potential (Ji 2014). To achieve equilibrium, the length and the inlet flow rate must be taken into account. Τhe length of the micromixer that has been chosen according to the literature is sufficient for mixing, but the specific length, in combination with the inlet flow rate, will not be able to achieve equilibrium (before particles and heavy metals exit from the common outlet). Nevertheless, the assumption that has been made is that the flow conditions inside the micromixer will not change as long as we increase its length. Since an efficient mixing is achieved and keeping in mind that the flow conditions inside the micromixer will not change, the length of the duct for adsorption equilibrium can be established after the clarification of the flow conditions and the selected heavy metal that is going to be adsorbed. Moreover, after a desirable navigation of the Fe_{3}O_{4} nanoparticles and the mixing effectiveness, the application of an external magnetic field is not necessary anymore, and due to the slow shearing conditions, it is expected that the contact time will be maximized.

*et al.*2019a, 2019b) are suppressed. The governing equations of the fluid phase are given by Karvelas

*et al.*(2017a),where

*t*is the time and

*v*is the kinematic viscosity of the water. The motion equations of each single particle in the discrete frame are based on Newton's law and may read as follows:where the index

*i*stands for the

*i*th-particle with diameter

*d*,

_{i}*u*and

_{i}*ω*are its transversal and rotational velocities, respectively, and

_{i}*m*is its mass. The mass moment of the inertia matrix is

_{i}*I*and the terms ∂

_{i}*u*/∂

_{i}*t*and ∂

*ω*/∂

_{i}*t*correspond to the linear and angular accelerations, respectively.

*F*is the magnetic force, while

_{mag,i}*F*and

_{nc,i}*F*are the normal and tangential contact forces, respectively. F

_{tc,i}_{drag,i}stands for the hydrodynamic drag force, and

*F*is the total force due to buoyancy.

_{grav,i}*T*is the magnetic torque, while

_{mag,i}*M*and

_{drag,i}*M*are the drag and contact moments, respectively. An external magnetic field is considered, which consists of a time-dependent part

_{con,i}*B*

_{y}=

*B*

**sin(2**

_{0}*πft*), where

*B*

_{0}is its magnitude,

*f*is its frequency and a magnetic gradient

*G*is aligned in the

_{y}*y*-direction, all of which act together. Since the magnetic field acts mainly along the

*y*-direction,

*B*and

_{x}*B*can be ignored, and the corresponding magnetic actuation force is mostly along the

_{z}*y*-direction (Liosis

*et al.*2020).

## RESULTS AND DISCUSSION

A series of simulations are performed for Fe_{3}O_{4} nanoparticles under electromagnetic and shear conditions for wastewater treatment applications. The simulations are carried out for achieving optimum mixing under various initial conditions such as velocity, initial concentration and radius ratios of the contaminated water (*V*_{c}) and the nanoparticle solution (*V*_{p}) streams at various frequencies of the permanent and gradient magnetic fields. The most important parameter for driving magnetic nanoparticles has been found to be the external magnetic field magnitude (Karvelas *et al.* 2017a). The specific surface area is equal to the surface area/volume = 3/Radius (Ghasemi *et al.* 2018) and is calculated from the radius of the nanoparticles (42.4 nm, 4.24 nm and 0.424 nm). Hence, as the radius decreases, the specific surface area increases, which can lead to better water purification from heavy metal ions. Simulation parameters, as well as the boundary conditions, are tabulated in Table 1.

Simulation parameters . | ||
---|---|---|

Dimensions of the micromixer geometry | Length (L): 5 × 10^{−4} m, Height (H): 1 × 10^{−4} m, Width (W): 1 × 10^{−4} m | |

Radius of Fe_{3}O_{4} nanoparticles | 42.4 (nm), 4.24 (nm), 0.424 (nm) | |

Radius of heavy metals | 0.424 (nm) | |

Density of Fe_{3}O_{4} nanoparticles | 5,180 (kg/m^{3}) | |

Density of heavy metals | 8,563 (kg/m^{3}) | |

Nanoparticles per second | 3,000 | |

Heavy metals per second | 1,500 | |

Permanent magnetic field (B_{0}) | 10 T | |

Gradient magnetic field (G) | 10 T/m | |

Frequency (f) | 0.1, 1, 3, 5 (Hz) | |

. | Boundary conditions . | |

Boundary . | Velocity (U) (m/s)
. | Pressure (p) (pa)
. |

Contaminated water – heavy metals (V_{c}) | (5, 1, 0.5, 0.25) × 10^{−5} | Zero gradient |

Nanoparticles (V_{p}) | 5 × 10^{−5} | Zero gradient |

Outlet | Zero gradient | 0 |

Walls | 0 | Zero gradient |

Simulation parameters . | ||
---|---|---|

Dimensions of the micromixer geometry | Length (L): 5 × 10^{−4} m, Height (H): 1 × 10^{−4} m, Width (W): 1 × 10^{−4} m | |

Radius of Fe_{3}O_{4} nanoparticles | 42.4 (nm), 4.24 (nm), 0.424 (nm) | |

Radius of heavy metals | 0.424 (nm) | |

Density of Fe_{3}O_{4} nanoparticles | 5,180 (kg/m^{3}) | |

Density of heavy metals | 8,563 (kg/m^{3}) | |

Nanoparticles per second | 3,000 | |

Heavy metals per second | 1,500 | |

Permanent magnetic field (B_{0}) | 10 T | |

Gradient magnetic field (G) | 10 T/m | |

Frequency (f) | 0.1, 1, 3, 5 (Hz) | |

. | Boundary conditions . | |

Boundary . | Velocity (U) (m/s)
. | Pressure (p) (pa)
. |

Contaminated water – heavy metals (V_{c}) | (5, 1, 0.5, 0.25) × 10^{−5} | Zero gradient |

Nanoparticles (V_{p}) | 5 × 10^{−5} | Zero gradient |

Outlet | Zero gradient | 0 |

Walls | 0 | Zero gradient |

The results and statistics from the water-particle mixing process are recorded at the half-exit part of the duct for *z* ≥ *L*/2, for a specific timestep of the simulation, where shear mixing mostly diminishes, and the nanoparticles mix with the heavy metals due to the presence of the magnetic field. The concentration of adsorbents determines the contact areas between the adsorbent and the adsorbate, and, therefore, this becomes the main purpose of mixing (Ain *et al.* 2020). Thus, the mean concentration (mg/mL) of iron oxide nanoparticles and heavy metals is found for the dimensionless height *y*/*H* (10 layers of the micromixer), as shown in Figure 2.

The visualization of the results is based on three parameters, namely, the effect of the frequency of the magnetic field, the velocity ratio between the streams and the radius ratio of the magnetic nanoparticles and heavy metals.

In Figure 3, for the case of *V*_{p}/*V*_{c} = 1 (Figure 3(a)), no mixing is observed under *f* = 01.Hz for radius ratios *R*_{particles}/*R*_{Heavy metals} = 1 and *R*_{particles}/*R*_{Heavy metals} = 10, since all the nanoparticles are located near the edges of the micromixer, while the heavy metals are at the centre of the duct. In the case of *V*_{p}/*V*_{c} = 5 (Figure 3(b)), the nanoparticles are more spread out and also exist in regions where heavy metals exist. When the ratio of stream velocities *V*_{p}/*V*_{c} = 10 and *V*_{p}/*V*_{c} = 20 is increased further, as shown in Figure 3(c) and 3(d), respectively, the nanoparticles locate themselves in almost all areas across the height of the duct, and, thus, we can reasonably expect that they can absorb the heavy metals from the contaminated water.

Similarly as above, under *f* = 1 Hz for the case of *V*_{p}/*V*_{c} = 1 (Figure 4(a)), no mixing is observed under all the selected radius ratios. In the other cases of ratios *V*_{p}/*V*_{c} = 5 (Figure 4(b)), *V*_{p}/*V*_{c} = 10 (Figure 4(c)) and *V*_{p}/*V*_{c} = 20 (Figure 4(d)), the nanoparticles are spread almost uniformly across the height of the duct for both radius ratios *R*_{particles}/*R*_{Heavy metals} = 1 and *R*_{particles}/*R*_{Heavy metals} = 10, and, hence, the nanoparticles and heavy metal particles are located at the same layers of the duct.

Under *f* = 3 Hz and for *V*_{p}/*V*_{c} = 1 (Figure 5(a)), no mixing is observed under all the selected radius ratios, as observed previously. As the velocity ratio increases (Figure 5(b)–5(d)), the distribution of the nanoparticles is almost uniform. In addition, the concentration of the nanoparticles in the middle of the duct where the heavy metals are located for ratios *V*_{p}/*V*_{c} = 10 and *V*_{p}/*V*_{c} = 20 is higher than that for the ratio *V*_{p}/*V*_{c} = 5.

Finally, under *f* = 5 Hz, when *V*_{p}/*V*_{c=}1 (Figure 6(a)), no mixing is observed under all the selected radius ratios, as observed in the previous cases. In the other cases of *V*_{p}/*V*_{c} = 5 (Figure 6(b)), *V*_{p}/*V*_{c} = 10 (Figure 6(c)) and *V*_{p}/*V*_{c} = 20 (Figure 6(d)), the nanoparticles are spread almost uniformly across the height of the duct. Thus, effective mixing is achieved.

A difficulty arises in discerning the role of frequency due to the scale of the above figures. Therefore, in order to evaluate the role of frequency in mixing efficiency, the percentage difference of concentration (*Δ*C%) is calculated. An interesting observation in these calculations is the area of the duct (two middle layers) where the heavy metals and nanoparticles coexist for velocity ratios *V*_{p}/*V*_{c} ≥ 5. The results of the calculations show that for radius ratios *R*_{particles}/*R*_{Heavy metals} = 1 and *R*_{particles}/*R*_{Heavy metals} = 10, frequency has a minor impact on mixing. As the radius ratio increases further to *R*_{particles}/*R*_{Heavy metals} = 100, the effect of frequency on the distribution of the nanoparticles becomes more obvious. The absolute value of *Δ*C% between 1 Hz and 3, 1 and 5 Hz under the selected velocity ratio where mixing is observed for the two middle layers of the duct is shown in Table 2. In the case *V*_{p}/*V*_{c} = 5, a maximum *Δ*C% is observed for both frequencies. Minor differences are found between *f* = 3 Hz and *f* = 5 Hz for each *V*_{p}/*V*_{c}. The combination of the micromixer length and the increase in the fluid velocity ratio results in a reduction of the effect of the magnetic field on the particles, which is reflected in Table 2, which shows that, as the velocity ratio increases, the *Δ*C% decreases.

V_{p}/V_{c} = 5. | V_{p}/V_{c} = 10. | V_{p}/V_{c} = 20. | |||
---|---|---|---|---|---|

ΔC = |C_{3 Hz} − C_{1 Hz}|%
. | ΔC = |C_{5 Hz} − C_{1 Hz}|%
. | ΔC = |C_{3 Hz} − C_{1 Hz}|%
. | ΔC = |C_{5 Hz} − C_{1 Hz}|%
. | ΔC = |C_{3 Hz} − C_{1 Hz}|%
. | ΔC = |C_{5 Hz} − C_{1 Hz}|%
. |

57.58% | 55.53% | 28.82% | 29.18% | 35.10% | 35.42% |

306.35% | 326.19% | 86.56% | 82.50% | 44.93% | 42.17% |

V_{p}/V_{c} = 5. | V_{p}/V_{c} = 10. | V_{p}/V_{c} = 20. | |||
---|---|---|---|---|---|

ΔC = |C_{3 Hz} − C_{1 Hz}|%
. | ΔC = |C_{5 Hz} − C_{1 Hz}|%
. | ΔC = |C_{3 Hz} − C_{1 Hz}|%
. | ΔC = |C_{5 Hz} − C_{1 Hz}|%
. | ΔC = |C_{3 Hz} − C_{1 Hz}|%
. | ΔC = |C_{5 Hz} − C_{1 Hz}|%
. |

57.58% | 55.53% | 28.82% | 29.18% | 35.10% | 35.42% |

306.35% | 326.19% | 86.56% | 82.50% | 44.93% | 42.17% |

To summarize the existing results, mixing is not successful for all cases with *V*_{p}/*V*_{c} = 1 under all selected frequencies and radius ratios. As the *V*_{p}/*V*_{c} increases, mixing is observed independently of the values of frequency and radius ratio. Moreover, minor differences are observed between *V*_{p}/*V*_{c} = 20 and *V*_{p}/*V*_{c} = 10, as shown in Figures 3–6. Additionally, the concentration of the particles increases for *V*_{p}/*V*_{c} = 20 and *V*_{p}/*V*_{c} = 10 compared with the case of *V*_{p}/*V*_{c} = 5 at the desired layers. Moreover, for the case of *R*_{particles}/*R*_{Heavy metals} = 1, the effect of the external magnetic field is insignificant and the mixing mostly depends on the velocity ratio. As the radius ratio increases further to *R*_{particles}/*R*_{Heavy metals} = 100, the concentration and the mixing effectiveness for each layer remain similar to the case of *R*_{particles}/*R*_{Heavy metals} = 10 under the same conditions (frequency and velocity ratio), but the effect of frequency is more obvious. According to our previous work, when the radius ratio was equal to 100, efficient mixing of nanoparticles and heavy metal ions were observed under different frequencies of the magnetic field and different velocity ratios (Karvelas *et al.* 2020). Moreover, from previous findings, it is found that between inlet angles and velocity ratio, it is the latter that affects mixing. As the velocity ratio between the inlet streams increases, the mixing of particles with the contaminated water also increases (Karvelas *et al.* 2018), which coincides with the results of the current research.

Hence, in order to describe the mixing effectiveness of the micromixer, three factors should be taken into account. These are the velocity ratio of the inlets, the radius ratio between nanoparticles and heavy metals and the frequency of the magnetic field. The velocity ratio has a major role to play in the mixing process as it appears to be independent of particle size. The radius ratio and the frequency are interconnected, because, as the radius ratio increases, the effect of the frequency is more intense, but both factors seem to be affected by the velocity ratio. For *R*_{ratio} < 10, the mixing efficiency depends on the velocity ratio, while for *R*_{ratio} ≥ 10, a combination of the three variable factors is necessary for mixing. Thus, the critical value combination for mixing from our simulations is found to be *R*_{particles}/*R*_{Heavy metals} = 10, *V*_{p}/*V*_{c} = 5 and *f* = 3 Hz.

## CONCLUSIONS

In conclusion, from an observation of the results of this study, it is found that as the velocity ratio increases, the mixing effectiveness also increases. The impact on mixing due to velocity ratio is more important between *V*_{p}/*V*_{c} = 1 and *V*_{p}/*V*_{c} = 5. At the middle layers where nanoparticles exist in regions where heavy metals coexist, a lower concentration is found for *V*_{p}/*V*_{c} = 5 compared with higher velocity ratios. Also, minor effects on mixing are observed when comparing *V*_{p}/*V*_{c} = 10 and *V*_{p}/*V*_{c} = 20. As the nanoparticles’ size increases, the effect of the external magnetic field is more intense on the nanoparticle distribution, which is one of the highlighted results from the simulations. This fact indicates that for achieving effective mixing, the radius ratio should be *R*_{ratio} ≥ 10. In addition, the concentration of the Fe_{3}O_{4} nanoparticles, which is a significant parameter of the adsorption mechanism, increases across the height of the duct due to the increase in the radius. Therefore, increasing the size of the nanoparticles amplifies both mixing and adsorption through the effect of the magnetic field and concentration, respectively. We must consider that the increase in size has an impact on the specific surface area and finally on the adsorption mechanism. Hence, there is a critical range of radius from which the advantages of surface area and magnetic field can be maximized.

Several parameters should be investigated, such as contact time and the mean distance between nanoparticles and heavy metals, and also initial concentrations. Furthermore, this simplified geometry, under various values of the external magnetic field, needs to be investigated in future work.

## ACKNOWLEDGEMENTS

The authors are grateful to the Greek Research & Technology Network (GRNET) for the computational time granted in the National HPC facility ARIS.

## AUTHOR CONTRIBUTIONS

All authors have read and agreed to the published version of the manuscript. Conceptualization was done by Evangelos Karvelas; methodology was prepared by Evangelos Karvelas; software was applied by Christos Liosis; validation was done by Christos Liosis and Ioannis Sarris; formal analysis was performed by Christos Liosis; investigation was carried out by Evangelos Karvelas; resources were supplied by Theodoros Karakasidis; data curation was done by Theodoros Karakasidis; writing and the original draft preparation were done by Christos Liosis; writing, review and editing were done byIoannis Sarris; visualization was done by Evangelos Karvelas; supervision was conducted by Theodoros Karakasidis; project administration was done by Theodoros Karakasidis.

## FUNDING

This research received no external funding.

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.