Simulation analysis of UF membrane filtration process based on magnetic field characteristics Open Access

particle acceleration (m/s²)

C, D

inertial loss, viscous resistance coefficient matrix

d

particle diameter (m)

body force (N)

gravitational acceleration (m/s²)

K

turbulent kinetic energy (J/kg)

N

number of phases

P

pressure (Pa)

mass-averaged velocity (m/s)

Membrane fouling will reduce the membrane performance and increase the filtration cost. Membrane pollution is generally caused by inorganic, colloidal, organic and microbial growth on the membrane surface. Pollution will lead to the decrease in permeation flux, increase in energy consumption and reduction of membrane life (Bartels et al. 2005). The main methods to control membrane fouling are the chemical method (Semiat et al. 2003) and physical method.

Chemical methods can use scale inhibitors to reduce silica scaling (Neofofistou & Demadis 2004; Semiat et al. 2001) and inorganic scaling (Chaussemier et al. 2015). However, it will induce additional organic fouling in seawater desalination (Sweity et al. 2014) and groundwater treatment (Duiven et al. 2010).

Physical methods increase the shear rate and shear stress on the membrane surface in order to slow down concentration polarization (Jutta et al. 1998; Takata et al. 1998; Bian et al. 2000). Besides traditional methods such as increasing the flow rate of feed liquid or reducing the cross-sectional area, new methods such as vibrating hollow fiber module (VHFM) (Low et al. 2005), rotating disk system (Dal-Cin et al. 1998) and vibration shear enhancement treatment (VSEP) (Culkin et al. 1992) can enhance the vibration of the membrane.

The above methods will increase energy consumption, so the physical method of magnetization treatment is introduced. Magnetization technology has the advantages of low investment, simple operation, innocuity and is pollution-free, and it has many functions such as anti-scaling, descaling, sterilization and corrosion inhibition. It is a promising anti-scaling and descaling technology. Pretreatment of Fe⁰ by magnetic field in advanced oxidation process can not only improve the removal rate of pollutants, but also greatly reduce reagent consumption and operation cost (Li et al. 2017; Pan et al. 2017). Pre-magnetizing Fe⁰ in Fenton process can also increase COD removal rate and reduce H₂O₂ consumption (Huang et al. 2018).

Firstly, the magnetic field will affect some physical and chemical properties and structures of liquid water. The magnetic field can improve the conductivity and pH of water samples, reduce the redox potential (Yin et al. 2011), reduce the surface tension and increase the viscosity (Xiao-Feng & Bo 2008). In addition, it can increase the additional volume of water and reduce the specific heat and boiling point (Esmaeilnezhad et al. 2017). This may be due to the influence of the magnetic field on the internal structure of water. After magnetic treatment, the internal energy of water molecules decreases and the activation energy increases, thus forming more hydrogen bonds and increasing the average size of water clusters (Wang et al. 2013b).

The magnetic field has an impact on the salt solution. Previous studies have found that the anti-scaling efficiency of permanent magnets on hard water scaling ability is about 45% (Mahmoud et al. 2016). Furthermore, it has been found by experiments that the sulfate scale after magnetic treatment will produce relatively small particles and more stable dispersion, and the kinematic viscosity of 0.5 M Ba(NO₃)₂, 0.5 M Sr(NO₃)₂ and 0.5 M Ca(NO₃)₂ solutions after magnetic treatment is higher than that of untreated solutions (Jiang et al. 2017). The results of nuclear magnetic resonance (NMR) showed that the number of hydrogen bonds between water molecules and hydrated ions increased. The magnetic field can increase the number of hydrogen bonds, thus inhibiting the formation of calcium carbonate and magnesium carbonate precipitates. In addition, under different magnetic field strengths, the ratio of calcite, aragonite and vaterite will change, and the ratio of aragonite will reach its peak under the best conditions (Silva et al. 2015). From a micro perspective, the magnetic field increases the number of water molecules participating in hydration and the radius of the dynamic hydration layer in salt solution (Gu et al. 2019).

Magnetization, as a pretreatment method, will also have a certain impact on the subsequent membrane process. It was found that magnetic powder combined with polydimethyldiallyl carbonate has good performance in reducing membrane fouling, improving dehydrogenase activity and promoting biomass growth (Wang et al. 2016). In the process of coagulation membrane filtration, magnetic removal is used to enhance flocculation and treat micro-polluted surface water, which can not only enhance the performance of removing various pollutants, but also help to reduce the decline of permeation flux and generate loose and porous filter cake layer (Wang et al. 2017). Magnetizing the solution with permanent magnets significantly increases the recovery of permeation flux and hydraulic permeability (Bretanha et al. 2021). However, few studies focused on the direct action of the magnetic field on the membrane filtration process.

CFD (Computational Fluid Dynamics) technology involves many disciplines such as computer science, physics, fluid mechanics, numerical calculation and visualization technology. When the knowledge of these disciplines is integrated, it can provide ways and methods to build fluid flow models. With the gradual deepening of membrane technology research, it is found that due to the limitation of physical model experimental conditions, some membrane module structural design problems can only be analyzed qualitatively or semi-quantitatively. Systematic and quantitative research that goes deep into the mechanism level is hindered. In addition, the mechanisms of mass and heat transfer and membrane fouling affect the efficiency and stability of membrane separation, but the research is also limited by experimental conditions. CFD technology can overcome these problems well, and the quantitative accuracy of the obtained results is high. It can provide a scientific basis for experimental design and component optimization, and visually simulate the internal flow state of components. Therefore, more and more researchers in membrane technology try to introduce CFD technology into the research of membrane technology.

Numerical simulation is used to explore the geometry influence of the membrane module on the distribution of volume flow rate, permeation flux and permeation rate in a space-filled disc membrane module. The results show that the volume flow rate and permeability change with different structures, which provides guidance for the optimization of membrane modules (Li et al. 2011). Wenyuan Ye et al. found through simulation that hydrodynamics near the membrane surface will also have a great influence on membrane fouling (Ye et al. 2018). Moreover, the numerical simulation of colloid fouling and enhanced concentration polarization of filter cake in the membrane module can predict the temporal and spatial changes of permeation flux and filter cake layer thickness in the filtration system (Uppu et al. 2019).

The mechanism of polymethyl methacrylate (PMMA) colloidal particles deposited on the surface of a corrugated membrane in suspension particles was investigated by simulation and particle deposition experiments. It was found that stagnant flow areas were formed in valleys, in which more particles were deposited. High shear stress is distributed near the apex region, where few particles are deposited (Jung et al. 2015). Xing Du et al. studied the migration of particles with different sizes in the range of 0.5 microns to 100 microns by using the shear stress which is generated by cross-flow velocity. This experiment was used to study the particle size separation during the formation of composite membrane fouling (Du et al. 2019). Different particle deposition rates also have an impact on the formation of filter cake in the membrane process, but they show a nonlinear relationship. The deposited dirt tends to form larger clusters at the lowest 12.5 g/m²/h and the highest initial deposition rate of 31.25 g/m²/h, but tends to be more dispersed at the intermediate initial deposition rate of 25 g/m²/h (Han et al. 2021).

Previous simulation studies seldom mention the effect of external magnetic field on the fluidity of water and fluid without magnetic particles. Therefore, it is necessary to refer to the simulation method of magneto hydro dynamics (MHD). It has been found that the flow resistance of magnetic fluid in square pipes increases by forming clusters, which leads to an increase in pressure drop and friction coefficient (Itahashi et al. 2019). Shuyan Wang et al. simulated the flow behavior of the solid phase in a liquid-solid fluidized bed magnetized along with a transverse uniform magnetic field in a pre-fluidized bed mode. The distribution of particles in the bed was studied by changing the magnetic field intensity. The distribution of particle velocity and volume fraction under different magnetic field intensity is analyzed (Wang et al. 2013a). However, magnetic particles are not added into the solution, which is different from magnetic fluid. COMSOL Multiphysics is a powerful multi-physical field coupling tool, which can simulate many physical processes in the fields of science and engineering. Because the experimental process involves the process of magnetic field, solution flow and membrane filtration, and COMSOL uses the finite element method to solve the fluid problem, the advantage of coupling with other physical fields, such as structure and electromagnetism, it will be very convenient, and it can achieve real coupling calculation. On the other hand, when the finite element is discrete, it is continuous in second order, and the accuracy of fluid calculation is also relatively high. Therefore, this paper uses COMSOL to conduct simulation experiments.

In this paper, COMSOL was used to couple with magnetic field and flow field. It explores the influence of magnetic field on fluid flow and inorganic particle deposition in the device when 0.1 g/L SiO₂ solution is filtered by a flat ultrafiltration (UF) membrane. Combined with the experiment, the change trend of membrane specific flux and water quality indexes (turbidity, conductivity, SiO₃^2- and Ca²⁺) was investigated under the magnetic field, and the accuracy of simulation results was verified by experiments. Through the research, it is found that the magnetic field can reduce the deposition of particles on the membrane surface and slow down the membrane pollution, thus reducing the decay rate of membrane flux.

COMSOL (Version 5.4) was used for modeling, simulating internal fluid flows, meshing, and post-processing.

Numerical simulation of magnetic field action on fluid flow in COMSOL involves the coupling of two physical phenomena (no-current permanent magnet and fluid flow), which can be achieved by solving the following governing equation.

In this paper, the movement of particles in the membrane reactor needs to be analyzed, so it can be regarded as solid-liquid two-phase flow simulation. The basic equations of the multiphase model assume that the incompressible fluid has the corresponding conservation of mass and momentum equations without considering the energy equation. In this study, the mixture model was chosen to describe the particle motion. In this method, the conservation of mass and momentum provide the governing equations for the interpenetrating liquid and solid phases. The equation is shown below.

And α_k is the volume fraction of k phase.

where d_p is the diameter of the particle (Guo et al. 2017).

It consists of two parts, Darcy viscous drag term and inertia loss term.

In which D and C are viscous drag and inertia loss coefficient matrices, respectively. This negative momentum source term leads to the pressure drop in the porous media unit.

In which 1/α_ij is the term of coefficient matrix d; is the thickness of porous media in three coordinate directions.

Additional magnetic volume force is used to simulate the force of the magnetic field on fluid and particles in it.

The source of the magnetic force applied to the fluid in the external magnetic field has the result that the molecular annular current I is applied by the external magnetic field B₀. Set a micro-element control body in the fluid, and its volume dV₀ = dxdydz. At the center of the cell control body, the magnetic induction intensity of the external magnetic field is B₀. B₀ is arbitrary in the coordinate system. It has three components Bx, By and Bz.

Because I is the current per unit height, for each side of the micro-element, the currents in three directions above it are i_xdx, i_ydy and i_zdz. And because the fluid is nonmagnetic, B here is B₀. On each side surface of the micro-element, the components of current length and magnetic induction intensity are vertical or parallel, and their vector product is either zero or algebraic product.

In addition, by the formula ×H=j.

Geometrical modeling with COMSOL: the calculation area includes the middle cylindrical membrane filtration device with a radius of 30 mm. The filtration device is divided into an upper membrane area with a height of 30 mm, a membrane with a height of 0.5 mm and a lower membrane area with a height of 15 mm. The calculation area also includes the water inlet pipe in the middle of X-axis negative direction, the return water pipe at the upper end and the outlet pipe at the lower end in the positive direction of X-axis, with pipe radii of 3 mm. Two permanent magnets, 60 × 45 × 34 mm in size, are placed on both sides of the membrane module. A detailed view of the geometry can be seen in Figure 1. The magnet is placed close to the membrane module, the device frame around the flow area is not shown in the figure, and the magnet is 10 mm away from the fluid area.

The feature numbers are given below. The Re number in the device is less than 2000, it is laminar flow, so the laminar flow module is selected. The boundary in the negative direction of X-axis is selected as the inlet, the velocity inlet is adopted, the velocity is 0.05 m/s, and the pressure outlet is adopted. Because the boundary is a rigid wall, a non-slip boundary is adopted, the direction of the magnetic field is y-positive, and the magnetization of 506 kA/m is set. The relative permeability of water is 0.9999707 (293.15 K).

In the simulation, 0.1 g/L SiO₂ solution is used, and the size of SiO₂ particles in COMSOL is assumed to be 30 nm because the size of nanometer SiO₂ used in the verification experiment is 20–40 nm. A polyvinylidene fluoride (PVDF) UF membrane is used in the experiment, and its transmittance is 0.4.

Through the design of experiments, the accuracy of simulation results is verified. Diatomite containing nano-SiO₂ (nano-SiO₂, 20–40 nm, Sigma) is dispersed in deionized water, which is prepared into stock solution of inorganic pollutants with a concentration of 0.1 g/L, and then placed in the refrigerator at 4 °C for later use. In order to ensure the uniform dispersion of inorganic pollutants during each use, it is necessary to perform oscillation and ultrasonic treatment first. At 20 °C and 0.1 MPa, the pure water flux of the flat UF membrane is 400 ± 50 L·m^-2·h^-1, the contact angle is 75°, and the average pore diameter of the UF membrane is 30 nm.

In this experiment (Figure 2), the temperature of the feed liquid in the system is controlled at 293.15 K by using a water bath thermostatic bath. The whole system runs in cross-flow mode. The specific operation mode is as follows: the raw water is pressurized by the water inlet pump and enters the membrane module for filtration, the water inlet pressure is constant, the circulating liquid finally flows back to the stock solution pool, and the system flow and water inlet pressure are controlled by valves in the return pipeline. The membrane filtration effluent enters the effluent pool, and the effluent pool is placed on an electronic balance, which is used to collect the change of membrane effluent and record it by a computer. All experiments were repeated three times, and membrane modules with good consistency were used in the experiments. The forward water pressure of the membrane is 0.1 MPa respectively, and the water inlet speed is controlled at 0.05 m/s.

At the initial stage of membrane filtration, the velocity field of fluid in the reactor is constantly changing. The velocity distribution of fluid in the middle vertical section with and without magnetic field is shown over time in Figure 3. At the beginning of filtration (Figure 3, 10 s), a high-speed region is formed in the central area due to the pressure of the water flow at the inlet. It can be seen that under the magnetic field, the fluid velocity in the main flow area is faster. With the passage of time, the velocity under both conditions gradually tends to be stable, while the overall flow velocity with the magnetic field is always higher than that in the control group (Figure 3, 120 s). The water viscosity decreases under the magnetic field (Xiao-Feng & Bo 2008), the flow resistance between water molecules decreases, so the fluid velocity increases.

The streamline distribution of water flow in the vertical cross-section is shown in Figure 4. From the initial filtration to the steady-state, the velocity of water flow with the magnetic field is higher than that in the control group, which is consistent with the phenomenon shown in Figure 3. At 10 s, eddy currents are formed on the upper and lower walls under both conditions (Figure 4, 10 s). It can be seen that the water flow near the membrane surface is faster and more regular under the magnetic field. As the filtration process reaches the stable stage (Figure 4, 120 s), multiple vortices appear near the membrane surface under the magnetic field. In order to investigate the influence of the magnetic field on the distribution of contaminated particles, it is necessary to further analyze the variation law of fluid velocity on the membrane surface.

In Figure 5, the red area on the right side is formed by the impact of the backflow on the membrane surface after the water flows through the right wall. At 10 s, the fluid velocity on the membrane surface is slightly higher under the magnetic field (Figure 5, 10 s). As the process continues, the fluid velocity under both conditions gradually tends to be stable. At 120 s, the difference in the distribution of the high-speed region is more significant under both conditions (Figure 5, 120 s). It shows that under the magnetic field, the overall velocity on the membrane surface is higher than that in the control group.

In order to reflect the flow velocity near the membrane surface accurately, three cross-sectional heights were selected equidistantly in the lower region of the reactor (Figure 6), and the average velocity on these planes was calculated. The results (Figure 7) show that under both conditions, the closer to the membrane surface, the lower the average velocity of water flow on the plane. It also shows that the average fluid velocity of each layer increases under the magnetic field, which confirms the previous analysis results. The increase of flow velocity will change the shear force of water on the polluted layer, and reduce the thickness of the filter cake layer to a certain extent. More inorganic pollution particles can be brought to the reflux port, which will affect the distribution of pollutant particles in the reactor and the accumulation effect on the membrane surface.

The volume fraction of pollutant particles in the middle vertical section under both conditions over time is shown in Figure 8. In the initial stage (Figure 8, 10 s), there is little difference in the diffusion trend of particles under both conditions. After that, the particles continue to diffuse along with the water flow and begin to accumulate on the membrane surface gradually. With the continuous filtration (Figure 8, 60–120 s), the volume fraction of particles in the reactor begins to show a higher trend without the magnetic field. After120 s (Figure 8, 120 s), under the magnetic field, the volume fraction of particles in the reactor and on the membrane surface is lower than without the magnetic field.

In order to consider the influence of the magnetic field on membrane fouling, it is necessary to further analyze the distribution characteristics of particle volume fraction on membrane surface under both conditions. At the initial stage (Figure 9, 10 s), the volume fraction of particles on the membrane surface is higher under the magnetic field, and the accumulation of particles first appears in the right region. With the continuous accumulation of particles on the membrane surface (Figure 9, 60–120 s), the volume fraction of particles increases rapidly and the accumulation range expands gradually under both conditions, which means that the membrane surface is further fouled. It can be seen from Figure 9 that the magnetic field reduces the volume fraction of particles on the membrane surface effectively. The pollution particles deposited on the membrane surface are more serious, and their distribution range is wider without the magnetic field.

Among the above three heights (Figure 6), the two heights closest to the membrane surface were selected (Figure 10), and the average volume fraction of the membrane surface was compared under both conditions. At Z= − 25 and membrane surface, the average volume fraction of particles is lower under the magnetic field. Combined with the analysis in Figure 7, the magnetic field increases the velocity of the fluid, resulting in a higher shear force on the membrane surface. It can be inferred that due to the increase of shear stress, the deposition process of fouling particles on the membrane surface is slowed down (Zuo & Wang 2013; Liu et al. 2020). In addition, Gu et al. (2019) found that the magnetic field enhances the radius of the dynamic hydration layer around particles in salt solutions. Therefore, fewer clusters in the same region will result in the decrease in the volume fraction of pollutant particles.

Under the magnetic field, the increase of fluid velocity in the reactor will carry more pollution particles to the outlet (Table 1), instead of depositing on the membrane surface. The simulation results show that the magnetic field acting on the membrane filtration process can slow down the membrane fouling.

In order to verify the simulation results, membrane filtration experiments were carried out under these two conditions. Diatomite was used to simulate inorganic pollutants in water, and the single-cycle filtration time was 80 minutes. Each group was repeated three times, and then the average value was taken. Membrane specific flux (J/J₀) is shown in Figure 11.

From the initial filtration to 35 minutes, the membrane specific flux increased gradually. This is due to the filter cake layer gradually formed on the membrane surface at the initial stage of filtration, which could form a certain barrier effect on pollutants, and the specific flux under the action of the magnetic field was higher than that of the control group. With the passage of time, due to further membrane pollution, the filter cake layer gradually became dense, which also hindered the passage of water, and the specific flux under both conditions gradually decreased. After 80 minutes of filtration, the specific flux of the control group decreased to 76%, and stabilized at 85% in the magnetic field. The experimental results show that the magnetic field acting on the membrane filtration process can increase the filtration flux and improve the membrane performance to a great extent (Carlesso et al. 2016).

Membrane fouling has always been the focus problem affecting flux and limiting membrane life. In this study, the UF membrane filtration process under the magnetic field was investigated by multi-physics coupling simulation, and the results were verified by experimental studies. The simulation results show that the magnetic field can increase the water flow velocity in the reactor and reduce the pollutant particles deposition on the membrane surface. It can be concluded that the magnetic field slows down the cake layer formation of the membrane surface to a certain extent, thus improving the anti-fouling performance of the membrane. The experimental results show that after 80 minutes filtration, the specific flux increases by 9% under the magnetic field. It can be envisioned that the magnetic field acting directly on membrane materials will be a promising green technology for water treatment, and the magnetic field utility needs to be further explored.

The authors declare no conflict of interest.

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