Particle Collection of Electret Media under Different Filtration Pressures

Received: November 20, 2022
Revised: January 1, 2023
Accepted: January 3, 2023

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Cite this article:

Liu, Z., Chen, D.R., Niu, Q., Mensah, D.A., Ji, Z. (2023). Particle Collection of Electret Media under Different Filtration Pressures. Aerosol Air Qual. Res. 23, 220405. https://doi.org/10.4209/aaqr.220405

HIGHLIGHTS

• Filtration pressure effect on the electret media filtration performance was observed.
• The adverse pressure effect was obvious at a positive filtration pressure.
• A revised model including the pressure effect on electret filter performance was proposed.

Keywords: Electret media, Charged fibrous media, Filtration pressure, Aerosol filtration, Particle penetration

1 INTRODUCTION

Because of additional electrostatic forces, filtration media made of electrically charged fibers, i.e., electret media, achieve higher filtration efficiencies while maintaining the same pressure drop than mechanical media (with their microstructures unchanged). The above advantages make electret media excellent candidates for removing particles in gases while reducing the energy consumption of filtration systems. Because of high particle filtration efficiency, electret media have been selected to apply in respirators, surgical masks, cleanroom filter panels, and air cleaning equipment in HVAC (Heating, Ventilation and Air Conditioning) systems.

Existing materials for charged media include resin-wool fibers, electret fibers, and electrospun polymer fibers. Resin-wool fibers (Feltham, 1979) has existed for several decades. It contains highly charged resin particles attached to wool fibers with charges in the opposite sign. Resin-wool fibers are typically ~17 µm in diameter and can carry the highest surface charge density although not in the most efficient configuration. Fibers in electret media, which are comparable in size to wool fibers, were produced by shredding a sheet of polymers that has been electrically charged by the corona discharging (Turnhout et al., 1976). Nowadays, electret media are mostly made of melt-blown polypropylene fibers and electrically charged by hydrospray. The chemical compositions of electrospun fibers could be various. They are polymer materials (produced from polymer solutions) and polypropylene (produced from its melt). In addition, the studies on composite charged media to achieve high-efficiency filtration have also been reported by Wang et al. (2020) and Tang et al. (2018). Charging filtration media are manufactured by several processes, including the corona charging, triboelectric charging, induction charging, and hydro charging. Note that the particle collection efficiency of charged media would be further improved when particles are also electrically charged. The particle charging, however, requires the use of specific equipment, which is not widely applied due to the hardware cost, reliability, and space limit.

Charged media (as opposed to electrostatic precipitators in which dust particles are electrically charged and collected via the established electrical field) improve the collection efficiency of dust particles by utilizing the electrostatic forces established between dust particles and medium fibers. Because the electrostatic forces are additional to the existing mechanical mechanisms (i.e., particle diffusion, interception and impaction), the particle collection efficiency of charged media are improved while the resistance of filters remains unchanged, resulting in improved figures of merit (FOM) when compared to that of mechanical media. FOM is expressed as

where η is the particle collection efficiency, and Δp is the pressure drop. The electrostatic effect for removing particles in electret media can be attributed to charged fibers and dust particles. In most cases, charged fibers is more critical than charged particles. It is because (1) more electrical charges can be placed on fibers compared to that on particles; (2) the image force on particles can be induced when dust particles come close to highly charged fibers, providing an attractive force between particles and fibers; (3) the capital and operational costs of charging particles and maintenance of additional equipment can be saved.

Various factors affect the filtration efficiency of electret media, for examples, aerosol flowrates, fiber diameters, and the charge levels of filter fibers and particles. Chazelet et al. (2011) experimentally found that the charge states of particles and fibers have a significant impact on the particle penetration of charged filters. While the objective for the work done by Shi et al. (2013) was to find relevant methods for updating filter testing standards, it found that the air velocity has its effect on the filtration efficiency of charged media when examining the effect of the particle charge state on the filtration efficiency of charged media and glass-fiber filters. Imani et al. (2019) studied the performance of two electrostatic aerosol samplers and confirmed the importance of measuring the velocity field when evaluating the collection efficiency of electrostatic samplers. Alonso et al. (2007) have shown that the effect of image force on the performance of charged media was not negligible even for small particles with a unit charge. Rodrigues et al. (2017) studied the effect of the particle charge level on the collection efficiency of clean electret media. They particularly investigated the electrostatic force, i.e., image force, between charged particles and uncharged media, and proposed a total collection efficiency model for electret media should take into the consideration of dipole image force. Givehchi et al. (2015) studied the effect of electrostatic waves on nanoparticle filtration and concluded that the electrostatic effect has a relatively strong correlation with the particle penetration of filter media for particles in the size range of 20–100 nm.

As the advance in the production of charged fibers, research have been studied the filtration performance of charged media (Fjeld and Owens, 1988; Murtomaa et al., 2005; Baumgartner and Löffler, 1986). Filtration models for charged media (Brown, 1981; Brown et al., 1988) have also been developed. Sanchez et al. (2013) concluded three basic electrostatic filtration mechanisms in charged media: the electrostatic induction force, in which charged fibers polarize nearby uncharged particles; the image force, in which charged particles polarize nearby uncharged fibers; and the Coulombic force, in which particles and fibers are charged. Podgorski and Bacazy (2008) investigated the performance of charged media by the Brownian dynamics simulation. The flow convection, particle diffusion, particle inertia, and electrostatic forces were considered in the simulation. The collection efficiency of a single, bipolar-charged/uncharged fiber for uncharged and charged particles in the sub-micrometer size range was calculated. It is found the increase of fiber charge density resulted in the significant improvement in the single-fiber collection efficiency and the reduction of the most penetrating particle size (MPPS). An interpolation formula related to fiber charge density and particle size was also proposed in the same study. According to the work of Kanaoka et al. (1987), the particle Brownian diffusion, and Coulombic and induction forces are useful for collecting fine particles in the electrode tube filtering process. By considering individual collection mechanisms described above, the collection efficiency of a single and charged fiber was proportional to the Peclet number, and inductive and Coulombic force parameters to the powers of –2/3, 2/5, and 3/4, respectively.

d_f/D (U is the filtration velocity, d_f is the fiber diameter and D is the diffusion coefficient of particles); K_In is the inductive force parameter of particles; and K_C is the Coulombic force parameter. The definition of K_In and K_C can be found in the Section 2.4. The effect due to the interaction between the inductive and Coulombic forces was considered by the last term of Eq. (2).

The effective charge status of fibers in charged media was often determined by the measurement of particle penetration through charged media and the fitting of existing single-fiber models. Romay et al. (1998) estimated the effective fiber charge density in electret media from a simplified Coulombic capture model. Assuming negligible compound effect among different particle capture mechanisms, the single fiber efficiencies due to the Coulombic and dielectrophoretic capture mechanisms were obtained in the work. The power-law expression was used to fit the obtained single fiber efficiencies as the function of the parameters derived from the single fiber models.

Although the collection mechanisms of charged media are well known, the existing models of charged media were developed using the size-fractionated particle filtration efficiency measured under the ambient pressure (i.e., 1.0 atm) and temperature (i.e., 20–25°C). However, industrial applications often require removing particles in the environments at the pressure and/or temperature different from the ambient. Examples of industrial filtration applications at pressures different from the ambient include the purification of compressed natural gas (e.g., up to 35 MPa at the gas injection process of natural gas storages), the air/gas quality control in space exploration (e.g., down to 0.6 kPa on the Mar’s sur-face), and the purification of semiconductor process gases (e.g., less than 13 kPa at the atomic layer deposition processes). Thus, the examination of existing models for charged media is required for the filtration efficiency prediction at the operational pressures different from the ambient.

The objective of this study is therefore to experimentally investigate the filtration efficiency of charged media under different operational pressures. The collected data was then applied to examine the existing models and to develop an update to existing models making them applicable for the prediction of particle penetration of charged media at the operational pressure different from the ambient.

 
2 MATERIALS AND METHODS

 
2.1 Charged Filtration Media and Experimental Conditions

Two electret filtration media were selected for this study, i.e., E1 (3M) and E2 (MERV13). Fig. 1 shows the SEM images and fiber diameter distributions of fibers in selected media. For the reference, the basic properties of two charged media and test conditions are summarized in Table 1. The fiber diameters were measured by the imaging method. The weight of filter medium samples (a disc with a diameter of 47 mm) was weighed by an electronic balance, and the thickness of media samples was measured with a digital caliper. Multiple samples randomly obtained from filter media were measured and the average was reported. Samples of filter media were cut into round slices with the diameter of 47 mm and placed in a filter holder (Inline 47 mm SS, Pall Corp., USA).

Fig. 1. The SEM images and measured fiber size distributions of test media E1 and E2.

Our experiments were conducted at the filtration pressure of 0.33, 0.5, 1, 2 and 3 atm. The selected pressures were limited by the particle instruments used in our setup. The face velocities for testing electret media were set at 0.1 m s^–1, corresponding to the volumetric flowrates of 5.76 min^–1 at a test filtration pressure, respectively (calculated based on the filtration area of test filter samples).

 
2.2 Experimental Setup

Two experimental setups (shown in Fig. 2), i.e., one is for testing the electret media under a positive pressure and the other is for testing the media under a negative pressure (related to the ambient pressure) were used to measure the particle penetration of selected media under different operational pressures. In each setup, a Differential Mobility Analyzer (DMA, TSI Model 3081/3085) operated by the DMA platform (TSI model 3080) was applied to classify test particles in a narrow electrical mobility distribution from polydisperse particles produced by different aerosol generation systems. A Condensation Particle Counter (CPC, TSI Model 3772/3775) was used to monitor the number concentration of DMA-classified particles prior to the introduction into the testing environment. By the design, DMAs and CPCs can be operated at a positive pressure condition. For the testing at negative pressures, orifice plates were installed after the DMA classification to reduce the operational pressure of charged media to the selected level. The CPC (TSI model 3772) was used at the downstream of filter holders to measure the number of particles penetrating test media.

Fig. 2. Schematic diagrams of experimental setups for measuring the particle penetration of charged media under a positive- and negative- pressure condition: (a) for the positive pressure up to 3 atm; (b) for the negative pressure down to 0.2 atm.

Two filter holders were used in the setups. One holder was for housing test filter media and the other is without test media (as a dummy holder). The upstream concentration of test particles was measured when the line with the dummy filter holder was open and the other line with filter media was closed. The downstream particle concentration was measured when the line with the test media holder was open and the line with the dummy holder was closed. The switch of two lines was controlled by two on/off valves in two lines.

Two aerosol generation systems were utilized to produce polydisperse particles for the DMA classification: one was for test particles in electrical mobility sizes ranging from 20 to 50 nm and the other one is for test particles in the electrical mobility size range of 75–600 nm. A custom-made Collison atomizer with NaCl solutions of 0.1–1% by volume was applied to produce polydisperse droplets. The resultant polydisperse NaCl particles were then obtained by passing the droplets through a diffusion dryer with silicone gel as the desiccant. Test particles in the electrical mobility sizes of 50–400 nm were classified by a DMA from the resultant NaCl particles. The evaporation and condensation method was applied to produce polydisperse NaCl particles with the modes of particle size distributions ranging from 20 to 50 nm.

A high-temperature tube furnace was used to evaporate the NaCl powder loaded in a ceramic boat which was placed in the middle location of the furnace tube. The furnace temperature was set at 680°C. By passing a clean carrier flow through the furnace tube, a NaCl-vapor-rich flow at high temperature exited the furnace tube and its temperature was cooled down by the natural convection. Polydisperse NaCl particles were formed during the cooling-down of the vapor stream. A DMA was then applied to obtain test particles in electrical mobility sizes of 20–50 nm. To minimize the multi-charged fraction of DMA-classified particles, test particles were selected from the right-hand side of the mode of polydisperse NaCl particle size distributions.

For singly charged particles, no further charge control was applied after the DMA classification. The charge status of DMA-classified particles was reduced to the Fuchs’ bipolar charge distribution by passing them through a Po-210 neutralizer when Fuchs’-bipolar-charged particles are required. Neutral particles were obtained by first reducing the charges on particles to the Fuchs’ bipolar charge distribution and then directing them through an electrostatic precipitator to remove the charged fractions of particles.

2.3 Method to Discharge Electret Media (Media Discharge Treatment)

Isopropyl Alcohol (IPA, commonly known as either isopropanol or 2-propanol) was used for the discharging of electret media, and for balancing the electrostatic surface charges on filter fibers. We placed a glass dish filled with liquid IPA in a large plastic container, and then cover the dish with a stainless-steel mesh, on which charged filter media was laid. Notice that the liquid IPA was not in contact with the filter media. The plastic container was finally buckled by a plastic lid with small holes for venting. The media remained in the container for more than 24 hours (according to the ISO standard 16890-4-2016). The above process was performed in a chemical fume hood.

 
2.4 Existing Model for Electret Media

Methods have been proposed to measure the charge density of fibers in charged media, e.g., the measurement of bipolar ions necessary to remove the electrical charges in charged media. For example, Romay et al. (1999) proposed a method for the measurement of charge density that employed the neutralization of electrical charges by bipolar ions generated from alpha-ray irradiation. However, none has been very convincing except the use of a hard X-ray method (Zenkevich et al., 2013), which is not easily accessible. Other approaches to estimate the charge density on fibers in charged media is by the fitting the measured size-fractionated collection efficiency of particles at different charge states by existing models.

For the prediction of the particle collection efficiency for electret media having dipolar charges on fibers, single fiber theories were popularly adopted. Brown (1981) and Brown et al. (1988) derived the equations for the single-fiber collection efficiencies attributed to the induced and Coulombic forces. The formula for single fiber efficiencies due to the induced and the coulombic effects were given by Lathrache and Fissan (1987) with the Kuwabara flow field assumption:

where η_In is the single-fiber collection efficiency by the induced force; η_C is the single-fiber collection efficiency by the Coulombic force; the Ku is the Kuwabara hydrodynamic factor; K_In is the induced force parameter; and K_c is the Coulombic force parameter (defined in the following):

in which the α is the packing density of media; C_c is the Cunningham slip correction; ε₀ is the dielectric constant of vacuum (8.85 × 10⁻¹² F·m^–1); ε_f is the dielectric constant of fiber material; ε_p is the dielectric constants of the particle; µ is the fluid viscosity; d_f is the fiber diameter; d_p is the particle diameter; u is the filtration velocity; n_p is the number of charges on a test particle; e is the elementary charge, i.e. 1.6 × 10^–19 C; and Q_f is the charge density on a fiber (C m^–2). The Cunningham slip correction factor, C_c , which corrects for reduced the drag force on particles in gas flow, is calculated as (Allen and Raabe, 1985).

Under the consideration of slip flow boundary condition (at negative pressures), the Kuwabara hydrodynamic factor shall also be a function of Knudsen number. Assuming the tangential velocity component is assumed proportional to the local tangential stress component, the Kuwabara (Pich, 1966) hydrodynamic parameter in the slip flow regime can be expressed as

where the constant 0.998 is the gas-material momentum accommodation coefficient (Willeke, 1976; Epstein, 1924). The gas molecules are assumed undergoing pure diffuse reflection. The flow Knudsen number based on the fiber diameter is a dimensionless number defined as is defined as

where the mean free path of carry gas (Maxwell, 1879), λ, can be calculated as

where λ_r is the reference gas mean free path at 293 K and ambient pressure (1 atm); P and T are the pressure and absolute temperature of the gas, respectively, and S_u is the gas Sutherland constant. We can obtain the Ku factor at a specific pressure by Eqs. (4–10).

The overall single-fiber efficiency (i.e., η) for a charged medium can then be calculated by the single-fiber efficiencies resulted by the mechanical and electrostatic mechanisms as shown in the following (Baumgartner et al., 1986; Chang et al., 2015; Chen et al., 2014).

where η_D, η_R, η_DR, η_I, η_In, and η_c, are the single-fiber efficiencies due to the diffusion, interception, interception of diffusing particles, impaction, dielectrophoretic, and Coulombic capture mechanisms, respectively. In the cases testing with neutral particles, the measured single-fiber efficiency is the combination of both mechanical and dielectrophoretic efficiencies. In the cases testing with charged particles, the measured single-fiber efficiency is the combination of mechanical, dielectrophoretic and Coulombic efficiencies. The penetration of particles through electret media, Pen, can be calculated as

where Pen is the percentage of particles penetrated through electret media, L is the thickness of filter media, d_f is the fiber diameter of filter media, and α is the packing density of the media.

Otani et al. (1993) assumed the additivity for the single-fiber collection efficiencies of charged media, i.e., η = η_M + η_In and η_C = η_In + η_C, and obtained the , , and  values from the measured penetration of uncharged particles through an uncharged medium, P_M, the penetration of uncharged particles through a charged medium, P_In, and the penetration of singly-charged particles through a charged medium, P_C:

where L is the filter thickness;  is the experimental single-fiber collection efficiency of uncharged particles through an uncharged medium;  is the experimental single-fiber collection efficiency of uncharged particles through a charged medium; and  is the experimental single-fiber collection efficiency of singly-charged particles through a charged medium. The charge density on fibers in charged media can then be deduced from the above data.

Based on the existing single fiber models, it can be found that the single fiber efficiencies due to the inducted and Columbic forces follow the following functional relationship with the consideration of the filtration pressure effect because it is related to the flow field：

where A and B are dimensionless parameters relating to the flow field around a charged fiber. Experimental data obtained in this study can be used to determine the fitting coefficients, i.e., A, B, via Eqs. (17–18).

 
2.5 Calculation of Particle Penetration through Electret Media for Fuchs’ Bipolar-charged Particles

The caluclation of the penetration of eletret media when testing with Fuchs’ bipolar-charged particles shall consider the charge distribution of test particles. The distribution of bipolar charge distrbution for particles in submicrometer-szied rang can be obatined using the birth-and death equatoion with the Fuchs model (Fuchs, 1963). Wiedensohler (1988) furher provide an approximation allowing simple calculation of the bipolar charge distribution for aerosols in the submicrometer size range, which was applied in this work for calculating the penetration of electret media for Fuchs’ bipolar-charged particles..

 
3 RESULTS AND DISCUSSION

 
3.1 Experimental Observation

The particle penetration of charged and uncharged media (i.e., E1/E2; E1D/E2D, respectively) using test particles in the Fuch’s bipolar charge distribution and single charge statuses were measured at the filtration pressures of 0.33, 0.5, 1, 2, and 3 atm. The particle collection efficiency of test media was then calculated from the measured penetration data. Fig. 3 shows the particle penetration of test media (E1 and E2) for Fuchs’-bipolar-charged particles at the face velocity of 10 cm s^–1.

Fig. 3. Particle penetration of test filter media for Fuchs’-bipolar-charged particles (Solid symbols: E1 and E2; Open symbols: E1D and E2D).

It is found that the particle penetration of test media for singly charged particles is generally lower than that for Fuch’s-bipolar-charged particles under the same pressure. The particle penetration through test media increased as the operational pressure increased. For E1 and E2 media (i.e., charged media) at a given pressure, the particle penetration through test media increased, reached a maximal value, and then decreased as the particle size increased. It is because the particle diffusion and electrostatic force has greater effects on particles in small sizes (due to their high diffusivity and electrical mobilities). For particles in large sizes, the collection of test media was improved because of the mechanical filtration mechanisms (i.e., interception, particle inertia) and dielectrophoresis. Notice that the most penetrating particle size (MPPS) is a function of the particle charge state. For single-charged particles, the MPPSs of test media were ~0.3 µm, while it was close to 0.1 µm for Fuch’s-bipolar--charged particles. It is because the Coulombic effect on the particle collection increased as the decrease of particle size (attributed to high electrical mobility of small particles), while the dielectrophoresis effect increased as the increase of particle size.

Fig. 4 show the measured particle penetration of test media (charged and uncharged) under three different particle-fiber charge conditions, i.e., charged particles and uncharged fibers (for the image force); uncharged particles and charged fibers (for the polarization force); and charged particles and charged fibers (for the Coulombic force). Under the a given pressure, the particle penetration of test media under the condition of the Coulombic force was the lowest among three charge combination conditions. More, the MPPS of the charged media, E1, was at ~100 nm for neutral particles, at ~200 nm for singly charged particles. The MPPS of discharged media, E2, was ~30 nm for neutral particles and ~300 nm for singly-charged particles. Under the contribution of the electrostatic forces, the MPPS of two test media has thus significantly altered. After the media discharge, the MPPSs of E1D and E2D media for singly charged and neutral particles were close to each other (i.e., ~300 nm), consistent with the findings reported by other research groups (Sanchez et al., 2013; Kanaoka et al., 1987; Romay et al., 1998), More, under a given pressure, the particle penetration of E2 media was in general higher than that of E1 media. As the filtration pressure increased, the penetration of both test media increased. It is found that the improvement on the filtration efficiency was attributed to the charge density on fibers (i.e., the charge density for E2 media is higher than that E1 media. Under a high pressure, the filtration efficiency of test media was reduced (compared to that at the normal pressure).

Fig. 4. Measured penetration of E1 and E2 media for singly charged and neutral particles at different filtration pressures (E1 and E2: charged media; E1D and E2D: discharged media; solid symbols: for neutral particles; open symbol: for singly charged particles).

The particle penetration of electret media for neutral particles was used to estimate the charge density on fibers. By the best fitting with Eq. (3) and Eqs. (12–15), the effective charge density on individual fibers of test electret media can be obtained. The charge density on fibers of test electret media was thus determined as ~5.50 E-5 C m^–2 (for E1 media) and 9.05 E-5 C m^–2 (for E2 media) (Walsh and Stenhouse, 1998; Kim et al., 2005; Chang et al., 2016).

3.2 Comparison with Existing Filtration Models

3.2.1 for the inducted force (i.e., K_In and η_In)

Given the effective charge density on fibers of both electret media E1 and E2 (i.e., 5.50 E-5 C m^–2 for E1 media 9.05 E-5 C m^–2 for E2 media), the η_In (i.e., the single fiber efficiency due to the inducted force) can be deducted in the following procedure. The single fiber efficiency due to the mechanical mechanisms, η_M, can be obtained from the measured penetration for discharged media when challenged by neutral particles (Eq. (14)). The single fiber efficiency due to both inducted force and mechanical mechanisms. i.e., η_MIn, can be deducted from the measured penetration for charged media when tested by neutral particles (Eq. (15)). Assuming the additivity for η_MIn (i.e., η_MIn = η_M + η_In), η_In can be obtained. Note that an existing relationship of η_In as the function of K_In, reported in previous research, is shown in Eq. (3). The above relation can be expressed as Eq. (17), taking into the consideration of filtration pressure effect.

Fig. 5 shows the comparison of the single fiber efficiency, η_In, of test electret media obtained from the measured penetration data and calculated by the Eq. (3) (as the function of particle size). Note that the figure as the function of K_In can be found in Fig. S1. It is found that, in the cases at the filtration pressure of 1.0 and 0.5 atm, the calculated data are in reasonable agreement with the experimentally derived ones. However, an obvious deviation between the calculated and measured single-fiber efficiencies, η_In, was found in the cases at the filtration pressures of 0.33 and 3 atm. The above observation shall be attributed to the pressure effect on the flow field around medium fibers.

Fig. 5. Comparison of single fiber efficiency, η_In, obtained from the measured data and calculated by Eq. (3) (Symbols: measured; Lines: calculated).

To get a better fitting, the values of A coefficient were obtained by finding the best fitting of Eq. (17) to the measured η_In. Fig. 6 shows the fitted A coefficients as a function of fiber Kn# for both test electret media. For the reference, the numerical values of fitted A can be found in Table S1. As the filtration pressure increased (i.e., the fiber Kn # decreased), the A coefficient in Eq. (19) decreased. More, the pressure effect on the A coefficient at high pressure (> 1 atm) was more obvious than that on low pressure (< 1 atm). Based on the curve characteristics, we proposed to fit the A coefficient of Eq. (17) by Eq. (19). The dimensionless parameters, i.e., a, b, c, d, e, and f can be found in Table 2. Fig. S2 shows the comparison of the calculated particle penetration through test electret media for neutral particles with the measured penetration data to confirm the fitting quality of the resultant formula for η_In. Fig. S2 shows that the matching of calculated and measured data at 1.0 atm filtration pressure is generally reasonable although it is not perfect. The difference between the measured and calculated data is closely related to the selection of expressions of single fiber efficiency (i.e., Eqs. (17) and (18)), which a variety of expressions have been proposed in precious works. We selected the ones widely used.

Fig. 6. The fitted A coefficient as a function of fiber Kn # (for η_In). (Solid symbols: A parameter; Line: fitted by Eq. (19)).

3.2.2 For the Coulombic force (i.e., K_C and η_C)

Following the similar procedure as described in Section 3.2.1, the η_C (i.e., single fiber efficiency due to the Coulombic force) can be calculated by Eq. (16) (with the measured penetration data for charged media tested by singly charged particles). Recall that an existing relationship of η_c as the function of K_C, reported in previous research, is shown in Eq. (3). The general relation between η_C and K_C can be expressed in Eq. (18) with the consideration of the filtration effect on the particle penetration.

Fig. 7 shows the comparison of the measured single fiber efficiency due to the Coulombic force, η_C, of test electret media and the calculated by Eq. (4) (as a function of particle size). For the reference, the same figure plotted as the function of K_C can be found in Fig. S3. It is found that the agreement between the measured and calculated data at the pressures at 1.0 and 0.5 atm is in general better than those in the cases at the filtration pressure at 3 and 0.33 atm.

Fig. 7. Comparison of single fiber efficiency, η_C, obtained from the measured data and calculated by Eq. (4) (symbols: measured; lines: calculated).

To get a better fit to the measured data, the B coefficient was obtained by fitting Eq. (18) to the measured η_C. The fitted B coefficients for two electret media as the function of fiber Kn # is shown in Fig. 8. The numerical values of the B coefficients at different filtration pressures can be found in Table S2.

Fig. 8. The B coefficient in Eq. (18) as a function of fiber Kn # for η_C. (Symbols: B parameters; Lines: fitted by Eq. (20)).

It is found that the value of the B coefficient in Eq. (18) increased as the filtration pressure increased (except for the case at the pressure of 3 atm, which should be considered as an outlier).

Eq. (20), which is the same functionals as Eq. (19)) was also selected to fit the values of the B coefficient (shown in Fig. 8).

where a, b, c, d, e and f are dimensionless parameters. Again, the selection of the functional is simply based on the data characteristics. Using the fitted B coefficients with Eqs. (3) and (18), the measured particle penetration through test electret media for singly charged particles can be represented (shown in Fig. S4).

 
3.2.3 Comparison of the modified model with the measured particle penetration thorugh electret media for Fuchs’-bipolar-charged particles

The measured penentration of test eletret media for Fuchs’-bipolar-charged particles at the 1 atm filtration pressure was lastly used for the comparison them with those calculated by the existing and developed models. Fig. 9 shows the above comparison. In addition to the penetration data collected in this work, the measured penetration data reported in the work of Chang et al. (2016) were also included. Note that the data given in the work of Chang et al. (2016) were measured at the face velocity of 5 cm s^–1.

Fig. 9. Comparison of particle penetration of electret media for Fuchs’-bipolar-charged particles at the 1 atm filtration pressure (Symbols: measured; Solid lines: calculated using the Lathrache and Fissan’s model (1987); Dashed curve: calculated by the modified model).

It is found that the improvement on the prediction of particle penetration by the modified model over the existing model was observed in the cases with electret media tested by Chang et al. (2016) at the face velocity of 5 cm s^–1. In the case with E1 media, the data calculated by the existing and modified models are in good agreement with the measured ones for particles in the sizes less than 50 nm. Although the deviation between the calculated and measured data were observed for particles in the sizes larger than 50 nm, and the modified models better followed the general trend of the measured data than the existing one. In the case with E2 media, the calculated data were in general followed the measured data although the deviation between the measured penetration was shown. Several factors may result in the above-observed deviation for E1 and E2 media. One likely reason might be attributed to the uniformity of microstructures of test electret media, particularly for E2 media. It is because E2 media were recovered from commercial HVAC panels and its uniformity was not perfect by the visual examination. Other reasons are due to the facts that (1) the single fiber efficiency model may not work well if the diffusivity and resident time of the particles is not sufficiently great to distribute the incoming particles uniformly in concentration within an inter-layer spacing of the media (Brown, 1993). Note that E2 media has thinner thickness and higher packaging density than E1 media; (2) the estimation of fiber charge density of test electret media is not independent from the existing model although its approach is commonly used in literatures; and (3) the single-fiber efficiency due to the mechanical mechanisms (i.e., particle diffusion, interception, and impaction) may work well for all filter media.

 
4 CONCLUSION 

The effect of operational pressure on the particle filtration of electret media was investigated in this study. Two electret media were tested at the face velocity of 10 cm s^-1 under the filtration pressures of 0.33, 0.5, 1.0 and 3.0 atm. Particles in a narrow electrical mobility size range were classified by a DMA and the charge status of DMA-classified particles was conditioned to obtain neutral, singly charged or Fuchs’-bipolar-charged particles for this testing. It is found that the particle filtration efficiency of electret media decreased as the operational pressure increased. More, the maximal penetrating particle sizes (MPPS) for neutral and singly charged particles was measured at ~100 and 200 nm for media E1, respectively. For media E2, the MPPS was ~30 and ~300 nm for neutral and singly charged particles, respectively. The above observation is because of the enhanced electrostatic effect for small particles, resulting in the smaller MPPSs.

Using the particle penetration data measured under the different combinations of charge status on filter media (i.e., charged and discharged media) and test particles (i.e., neutral, singly charged and Fuchs’-bipolar-charged), the single fiber efficiency due to the induced and Coulombic forces, η_In and η_C as the function of particle size were obtained at different filtration pressures. It is found that both η_In and η_C of both test electret media were a function of filtration pressure (i.e., a function of fiber Kn #) in addition to the known parameters (i.e., α, Ku, K_In and K_C) already included in existing single-fiber models. A modification to the existing model was proposed to better describe the measured penetration data. However, only two electret media were tested in this study. To generalize the proposed modification, more electret media having different charge density and microstructures should be tested.

 
ACKNOWLEDGEMENT

This research was supported by the National Natural Science Foundation of China (No. 51904315), and the China Scholarship Council (No. 201906445004).