Mixing of Fe₃O₄ nanoparticles under electromagnetic and shear conditions for wastewater treatment applications

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 Fe₃O₄ 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 Fe₃O₄ 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 Fe₃O₄ 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 Fe₃O₄ 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.

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 Fe₃O₄ 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/m³ (Teja & Koh 2009), Poisson's ratio equal to 0.31 and Young's modulus 200 × 10⁹ 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/m³, v = 0.323 and 123 × 10⁹ 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 Fe₃O₄ 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 Fe₃O₄ 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.

A series of simulations are performed for Fe₃O₄ 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.

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 (ΔC%) 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 ΔC% 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 ΔC% 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 ΔC% decreases.

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.

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 Fe₃O₄ 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.

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

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.

This research received no external funding.

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