# Air Purification Performance Analysis of Magnetic Fluid Filter with AC Non-Thermal Plasma Discharge

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{x}), sulfur oxides, carbon monoxide and dioxide, and particulate matter (PM); NO

_{x}and PM emissions are key issues.

_{2.5}(PM with an aerodynamic equivalent diameter less than 2.5 μm), is a worldwide environmental concern. Global averages reported that, in 2012, 25% of urban ambient PM

_{2.5}came from traffic, 15% from industrial activities including power generation, 20% from domestic fuel burning, 22% from unspecified sources of human origin, and 18% from natural dust and sea salt [2]. In summary, the majority of PM originates from combustion; the sources include exhaust gas from diesel engines and combustion gas from boilers, that is, fossil-fuel-based energy conversion devices.

_{3}). For example, diesel engines offer many advantages such as high energy density of fuel, high efficiency, and relatively low carbon dioxide (CO

_{2}) emissions, along with lower volatile organic compound (VOC) emissions. These advantages make diesel engines favorable for many applications such as automobiles, ships, electric power generators, and construction machinery. Owing to their widespread use, there is considerable evidence for the contribution of diesel combustion towards PM.

_{2.5}was also proposed, and numerical analyses were carried out [12]. However, it is known that the collection efficiency of low-resistive PM is obstructed by re-entrainment in an ESP [13]. Therefore, ESPs are less effective if used directly to filter out the low-resistive diesel particulates and aerosols originating from combustion. Ideally, PM collection via electrostatic forces that can collect low-resistive PM must be employed; however, this remains challenging.

_{3}) during the NTP discharge, which serves to sterilize the air in an air purifier. A previous study confirmed the feasibility of this collection technique [14]. The collection efficiencies with and without NTP were investigated in the filter with six lumps of the magnetic fluid. For further development of the magnetic fluid filter with NTP discharge, it is necessary to understand the collection mechanism, characteristics of collection, and power consumption for different conditions of NTP discharge.

_{3}concentrations generated by the magnetic fluid filters with NTP discharge are investigated under different discharge conditions.

## 2. Physical Transport Phenomena and the Principle of PM Collection in a Magnetic Fluid Filter with NTP Discharge

#### 2.1. Physical Transport Phenomena Contribution to PM Collection

_{3}by-product generation.

_{p}< 2), Stokes’ law can be applied. The drag force (F

_{drag}) due to Stokes’s law is given by

_{p}is the PM diameter. Considering non-continuum effects when the PM becomes significantly smaller, the Cunningham correction factor (C

_{c}), which is a slip correction factor, is introduced into Stokes’ law, such that

_{c}is given by

^{−8}m at 298.15 K (25 °C) and 1 atm. α, β, and γ are theoretical or empirical correction parameters. Based on previous research, α = 1.257, β = 0.400, and γ = 1.100, as reported by Davies [18]; α = 1.142, β = 0.558, and γ = 0.999, as reported by Allen and Raabe [19]; and α = 1.165, β = 0.483, and γ = 0.997 for nanoparticles at 0.5 < Kn < 83, as reported by Kim [20]. For a gaseous ambient fluid, the PM velocities are as follows:

- (1)
- Migration velocity vg due to gravitational force (terminal settling velocity)

_{p}and the relaxation time of the fluid τ

_{f}are, respectively, expressed as

_{p}is the density of the PM, μ is the viscosity of the fluid, and ρ

_{f}is the density of the fluid. For a gas, since ρ

_{p}≫ ρ

_{f}, the velocity v

_{g}can be simplified to

- (2)
- Migration velocity v
_{c}due to centrifugal force

_{c}due to centrifugal force, or terminal velocity, is given by

_{c}is the centrifugal effect. For a gas, since ρ

_{p}≫ ρ

_{f}, the velocity v

_{c}can be simplified as

- (3)
- Migration velocity v
_{i}due to inertial force

_{i}due to inertial force is given by

_{s}are the distance and time taken, respectively, for the PM travelling at velocity u

_{0}to come to rest owing to Stokes fluid resistance.

- (4)
- Migration velocity v
_{B}due to Brownian diffusion

_{B}due to Brownian diffusion in the x-direction is expressed as

_{c}in the displacement definition provided by Einstein [21], displacement can be expressed as

_{B}is the coefficient of Brownian diffusion, k

_{B}is the Boltzmann constant (1.38 × 10

^{−23}J/K), and T is the absolute temperature.

- (5)
- Migration velocity v
_{e}due to electrostatic force

_{e}due to electrostatic force is

_{p}is the relative permittivity of the PM and ε

_{0}is the permittivity of a vacuum (8.85 × 10

^{−12}F/m). For an ideal conductive PM, when ε

_{p}→ ∞, the equation becomes

_{p}is the number of particles, e is the elementary charge (=1.60 × 10

^{−19}C), N

_{ion}is the ion concentration, and v

_{ion}is the mean thermal velocity of the ions [23]. Diffusion charging acts predominantly on smaller particles, with sizes of 0.2 μm or less.

#### 2.2. Principle of PM Collection in a Magnetic Fluid Filter with NTP Discharge

_{3}O

_{4}) is commonly used for the ferromagnetic particles, which are coated with surfactants. The hydrophilic end of the surfactant attaches to the surface of the ferromagnetic particle, and the hydrophobic end attaches to an oil-based solvent (such as kerosene). The surfactant prevents the aggregation of ferromagnetic particles. In a water-based magnetic fluid, a double layer of the surfactants is coated on the ferromagnetic particles.

_{c}= 86.6 × 10

^{−4}T [25].

_{3}production have been reported in the literature [26]. O

_{2}in the air contributes towards the formation of O

_{3}via the O molecule (O) by NTP discharge according to the following reactions [27]:

_{2}+ e → O + O + e,

_{2}→ O

_{3}.

_{2}O, in the form of moisture, a small quantity of O

_{3}can generate an OH radical (•OH) with higher reactivity and oxidizability than other reactive species of oxygen. The OH radical is generated via the self-decomposition of O

_{3}through reactions (19), (20) [28], (21), and (22) [29]:

_{3}+ OH

^{−}→ HO

_{2}

^{−}+ O

_{2},

_{3}+ HO

_{2}

^{−}→ O

_{3}

^{−}+ HO

_{2},

_{3}

^{−}+ H

^{+}→ HO

_{3},

_{3}→ •OH + O

_{2}.

_{3}injection [30,31], or oxidation via the OH radicals and O

_{3}generated during NTP discharge. The generated OH radicals and O

_{3}also contribute to proofing against mold and bacteria in air purification [27].

## 3. Experimental Setup and Method

_{3}concentration is shown in Figure 2b. Prior to the experiments for investigating and evaluating the performance of the filter, sampling of exhaust gas and clean air is carried out. Clean air is used for the dilution of the exhaust gas. To generate exhaust gas in a laboratory environment, diesel particulates from a diesel-engine power generator (KDE2.0E-60Hz, KIPOR, Wuxi, China) are used as low-resistive PM. The system combines a four-stroke direct injection diesel engine (KM170F) and a generator. The diesel engine is air-cooled using a single cylinder.

_{c}value. At the top of the magnetic fluid, in which the spike is formed, the magnetic flux density is 95 mT. A glass plate with a thickness of 2.0 mm, positioned beneath the upper electrode, is used as the dielectric.

_{exh}), the PM count after filtration only via the magnetic fluid (N

_{MF}), and the PM count after filtration via the magnetic fluid aided with NTP (N

_{MFNTP}) are used for calculating the PM collection efficiencies, which are defined as follows:

_{3}concentration generated, clean air is supplied to the filter (shown in Figure 2b) using a pump equipped with a membrane filter featuring a pore size of 0.20 μm. The volumetric flow rate of the source gas is set to 3.00 L/min using a regulation valve. The source gas flows into the magnetic fluid filter with NTP. The magnetic fluid filter and discharge conditions are the same as those used in the PM collection measurements. At the outlet of the magnetic fluid filter, the O

_{3}concentration is measured. A detector tube (No. 18M, Gastec Corporation, Kanagawa, Japan) is used to measure the O

_{3}concentration.

_{3}generation efficiency ζ

_{O3}is introduced to evaluate O

_{3}generation performance. ζ

_{O3}(in mg/Wh) is given by

_{in}= 3.00 L/min, t is the time (t = 60 min), C

_{O3}is the average measured O

_{3}concentration (ppm), M

_{O3}is the molar mass of O

_{3}(M

_{O3}= 48), V

_{mol}is the molar volume (22.4 L/mol for 0 °C = 273.15 K and 1 atm; 24.8 L/mol for 25 °C = 298.15 K and 1 atm), and P is the measured power consumption (W).

## 4. Results and Discussion

#### 4.1. PM Collection in a Magnetic Fluid Filter

_{MF}. Figure 5b shows the resulting PM collection efficiency in the magnetic fluid filter with NTP, η

_{MFNTP}. The graph indicates the relationship between the PM diameter in the measurement range d

_{p}and the PM collection efficiency η

_{MF}or η

_{MFNTP}for different values of n. The average values and the standard errors are indicated in the graph.

^{6}particles/L for diesel particulates with diameter d

_{p}≥ 0.3 μm, 2.16 × 10

^{6}particles/L for d

_{p}≥ 0.5 μm, 1.76 × 10

^{6}particles/L for d

_{p}≥ 1.0 μm, 1.26 × 10

^{6}particles/L for d

_{p}≥ 2.0 μm, 4.98 × 10

^{3}particles/L for d

_{p}≥ 5.0 μm, and 0 (not detected) for d

_{p}≥ 10.0 μm.

_{MF}= 34, 68, 96, 100, and 100% for diesel particulates with d

_{p}≥ 0.3, 0.5, 1.0, 2.0, and 5.0 μm, respectively. In this case, the inertial and gravitational forces and Brownian diffusion contribute towards the PM collection. The application of NTP improves the PM collection efficiencies with the aid of the electrostatic force. As a result, η

_{MFNTP}= 71, 90, 99, 100, and 100% for diesel particulates with d

_{p}≥ 0.3, 0.5, 1.0, 2.0, and 5.0 μm, respectively. PM with d

_{p}≥ 0.5 μm can be collected with η

_{MFNTP}≥ 90%, which is the collection efficiency generally required for air purifiers. As d

_{p}increases, η

_{MFNTP}also increases for all n. As n increases, η

_{MFNTP}also increases. In other words, η

_{MFNTP}increases proportionally with an increase in the surface area at which PM collection occurs. The resulting η

_{MFNTP}= 71% for diesel particulates with d

_{p}= 0.3 μm could be improved by increasing n. In particular, the results demonstrate that diesel particulates with d

_{p}= 0.3–1.0 μm can be controlled by n. In addition, it is considered that the electrostatic force contributes to the collection, as the collection efficiency of these particles is significantly improved by the NTP discharge.

_{p}= 0.5, 1.0, and 2.0 μm, respectively [32]. The magnetic fluid filter with NTP, thus, exhibits equivalent or superior performance to hybrid filters.

_{p}= 1000 kg/m

^{3}, μ = 1.84 × 10

^{−5}Pa·s in air at 298 K and 1 atm, g = 9.81 m/s

^{2}, t

_{s}=1.00 s, and T = 298 K. For C

_{c}, α = 1.257, β = 0.400, and γ = 1.100 for micro-size PM with d

_{p}≥ 1.00 μm and α = 1.165, β = 0.483, and γ = 0.997 for nano-size PM with d

_{p}< 1.00 μm. For v

_{e}, the values of the parameters are E = 50 kV/cm (10 kV for NTP discharge in the 2 mm gap between the spike of magnetic fluid and the electrode), N

_{ion}= 1.00 × 10

^{13}/m

^{3}, and v

_{irons}= 2.38 × 10

^{2}m/s for positive charging and 3.00 × 10

^{2}m/s for negative charging [33]. Figure 6a shows the relationship between the diameter of PM and the migration velocity for each transport mechanism. The migration velocity due to inertial forces is calculated as the gas flows into the magnetic fluid filter at a flow rate of 0.53 L/min. In this case, u

_{0}= 0.05 m/s. The measuring range of PM diameters is also indicated in the figure. The migration velocity due to electrostatic forces is the combination of the velocity due to field and diffusion charging, and the solid line shown approximates the two charging effects considered. For larger PM with d

_{p}≥ 0.50 μm, the migration velocities due to gravitational and inertial forces are sufficiently large for effective PM collection. For smaller PM with d

_{p}< 0.50 μm, the migration velocities due to Brownian diffusion are sufficiently large for effective PM collection. Electrostatic forces include field charging, which is dominant for large particles, and diffusion charging, which is dominant for small particles. The effective electrostatic force is indicated in the figure as a solid line.

^{−4}s, as indicated by the dashed line in the figure. When the effective traveling time is less than the dashed line, PM can be instantly adsorbed at the magnetic fluid interface by the NTP discharge. In other words, for PM with d

_{p}≥ 1.2 μm, there exists a high probability that collection via electrostatic forces will occur, which is consistent with the experimental results of the collection efficiency, η

_{MFNTP}. However, it is possible that the PM could escape from the discharge and not be collected, especially for a small n. Even if the traveling time is greater than that shown by the dashed line, as is the case for d

_{p}< 1.2 μm, η

_{MFNTP}can be improved if the probability that the PM comes in contact with the discharge is increased by increasing n. Therefore, the η

_{MFNTP}obtained in the experiment improves as n increases, even for d

_{p}< 1.2 μm. In this study, the discharge voltage is constant. However, Equation (13) suggests that v

_{e}is enhanced by the strong electric field with a high discharge voltage. In other words, a higher discharge or input voltage to the power supply could improve the PM collection via electrostatic force.

_{in}= 2.83 L/min, whereas Q

_{in}= 0.53 L/min in the PM collection experiment. Δp is measured using a differential pressure gauge (DPG-01U, Custom Corporation, Tokyo, Japan) at the inlet and outlet of the magnetic fluid filter, in which the stainless-steel pipe is installed. In this case, the flow velocity in the magnetic fluid filter is u = 0.26 m/s, whereas the flow velocity on the top of the lumps of magnetic fluid is typically u

_{max}= 0.90 m/s. The approximate line is indicated as a solid line. The magnetic fluid filter container is a sudden expansion and contraction structure. Therefore, even in the absence of magnetic fluid, there is a pressure drop Δp

_{0}= 44 Pa at n = 0. The pressure loss is expressed by following Equation (26), and Δp = 46 Pa at n = 6.

_{MF}is 1.8 Pa at n = 6 with u = 0.26 m/s and u

_{max}= 0.90 m/s. This pressure loss is caused by the flow path geometry due to the presence of magnetic fluid, and it could be improved by optimizing the arrangement of lumps of magnetic fluid. This Δp

_{MF}can be considered sufficiently low by taking into account the pressure loss of the recent electrostatic filters with low pressure loss, for example, 3.8 Pa at 1.1 m/s filtration velocity [3] and 4.9 Pa at 0.1 m/s [34]. Furthermore, this result exhibits a significant advantage as it shows a much smaller pressure loss compared to that of a generic HEPA filter.

#### 4.2. Power Consumption of NTP Discharge in a Magnetic Fluid Filter

_{MFNTP}, the hypothesis that an increase in spikes leads to improved collection efficiencies with energy conservation has been validated.

#### 4.3. O_{3} Generation of a Magnetic Fluid Filter

_{3}concentration C

_{O3}for an inlet air flow rate of Q

_{in}= 3.00 L/min. The ambient temperature and humidity are 17 °C = 290.15 K and 39%, respectively. The average values and standard errors are also shown. A quadratic polynomial approximation trend curve is plotted. The O

_{3}concentrations are 20, 47, 72, and 187 ppm at n = 1, 2, 4, and 6, respectively, and C

_{O3}increases with n. Figure 9b shows the relationship between the number of lumps of magnetic fluid n and the O

_{3}generation efficiency ζ

_{O3}. The resultant ζ

_{O3}and the approximate curve using a quadratic polynomial approximation are graphically represented. For 0 °C and 1 atm, the ζ

_{O3}values are 0.15, 0.43, 0.63, and 1.53 mg/Wh at n = 1, 2, 4, and 6, respectively. For 25 °C and 1 atm, the ζ

_{O3}values are 0.14, 0.39, 0.57, and 1.39 mg/Wh at n = 1, 2, 4, and 6, respectively. This shows that ζ

_{O3}increases as n increases. This result is concluded to be due to the small difference in P for n = 1–6, whereas C

_{O3}increases as n increases.

## 5. Conclusions

_{3}concentrations generated are also investigated for different discharge conditions.

- (1)
- The relationship between the minimum diameter of PM in the measurement range d
_{p}and the PM collection efficiency with NTP η_{MFNTP}for different numbers of lumps of magnetic fluid n are investigated. Under n = 6, η_{MFNTP}= 71, 90, 99, 100, and 100% for d_{p}≥ 0.3, 0.5, 1.0, 2.0, and 5.0 μm, respectively. These collection rates are sufficiently high for air purification. As d_{p}increases, η_{MFNTP}also increases at all values of n. As n increases, η_{MFNTP}increases. The PM collection mechanism is a function of the particle migration velocity. - (2)
- The power consumption of the magnetic fluid filter with NTP P and the generated O
_{3}concentration C_{O3}are investigated for different numbers of lumps of the magnetic fluid n and the O_{3}generation efficiency ζ_{O3}is calculated from these data. The results show that ζ_{O3}increases proportionally with n. For 25 °C and 1 atm, the ζ_{O3}values are 0.14, 0.39, 0.57, and 1.39 mg/Wh at n = 1, 2, 4, and 6, respectively. - (3)
- Performance efficiency is improved in both PM collection and O
_{3}generation with an increase in the number of lumps of magnetic fluid or with an increase in the number of spikes of the magnetic fluid with discharge. Namely, the hypothesis that an increase in spikes leads to improved collection efficiencies with energy conservation has been validated.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Schematic of the experimental setup and method used: (

**a**) for evaluating the PM collection efficiency of the filter; (

**b**) for measurement of O

_{3}concentration.

**Figure 3.**Magnetic fluid filter with NTP. (

**a**) Schematic with structure and dimensions. (

**b**) Photograph.

**Figure 4.**Schematic depicting the arrangement of lumps of magnetic fluid in the filter at n = 1, 2, 4, and 6.

**Figure 5.**Experimental results of PM collection efficiencies in the magnetic fluid filter: (

**a**) without NTP η

_{MF}; (

**b**) with NTP η

_{MFNTP}.

**Figure 6.**Calculation results based on the migration velocity equations. (

**a**) Relationship between PM diameter and migration velocities for different transport mechanisms. (

**b**) Time for PM to travel 2 mm due to electrostatic forces for different PM diameters.

**Figure 7.**Relationship between the number of lumps of magnetic fluid n and the pressure loss across the magnetic fluid filter Δp for an inlet air flow rate of Q

_{in}= 2.83 L/min.

**Figure 8.**Relationship between the number of lumps of magnetic fluid n and the power consumption associated with the discharge P.

**Figure 9.**O

_{3}generation in the magnetic fluid filter with NTP. (

**a**) Relationship between the number of lumps of magnetic fluid n and the generated O

_{3}concentration C

_{O3}with an inlet air flow rate of Q

_{in}= 3.00 L/min. (

**b**) Relationship between the number of lumps of magnetic fluid n and the O

_{3}generation efficiency ζ

_{O3}.

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**MDPI and ACS Style**

Kuwahara, T.; Asaka, Y.
Air Purification Performance Analysis of Magnetic Fluid Filter with AC Non-Thermal Plasma Discharge. *Energies* **2024**, *17*, 1865.
https://doi.org/10.3390/en17081865

**AMA Style**

Kuwahara T, Asaka Y.
Air Purification Performance Analysis of Magnetic Fluid Filter with AC Non-Thermal Plasma Discharge. *Energies*. 2024; 17(8):1865.
https://doi.org/10.3390/en17081865

**Chicago/Turabian Style**

Kuwahara, Takuya, and Yusuke Asaka.
2024. "Air Purification Performance Analysis of Magnetic Fluid Filter with AC Non-Thermal Plasma Discharge" *Energies* 17, no. 8: 1865.
https://doi.org/10.3390/en17081865