# Effect of particle electrostatic charge level on collection efficiency of an electric metal mesh filter

Mohamed Akram Sayoud, Noureddine Zouzou

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Mohamed Akram Sayoud, Noureddine Zouzou. Effect of particle electrostatic charge level on collection efficiency of an electric metal mesh filter. Journal of Electrostatics, 2025, 138, pp.104159. 10.1016/j.elstat.2025.104159. hal-05241305

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Submitted on 19 Nov 2025

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# Effect of particle electrostatic charge level on collection efficiency of an electric metal mesh filter

M.A. Sayoud* and N. Zouzou

Institut Pprime, CNRS, Université de Poitiers, ISAE-ENSMA, F-86962, Futuroscope, France

## ARTICLE INFO

### Keywords:

- Particle electric charge level
- Electric metal mesh filter
- Electrostatic forces
- Collection efficiency

## ABSTRACT

The effectiveness of filter media technique for air purification is no longer a matter of debate. However, the challenge now is to determine ways of optimizing particle-fiber interactions in order to achieve the optimal balance between particles collection efficiency and pressure drop across the filter. In this paper, we are particularly interested in interactions of an electrical nature, governed essentially by Coulomb, dielectrophoretic (DEP) and image forces. At first, we developed a special experimental protocol that enabled us to focus mainly on these interactions. Then, by controlling particle charge levels, we were able to dissociate the contribution of each force on collection efficiency and to explore parameters influencing them, such as particle and wire diameters, mesh size, inter-grid distance and electric field intensity within an Electric Metal Mesh Filter (EMMF). The results revealed that the contribution of Coulomb force to collection efficiency is the most important, particularly in the case of strong field and high charge level. The efficiency by DEP force increases with field intensity, particle diameter and decreasing fiber diameter, whereas the effect of inter-grid distance and mesh size were limited. As for image force, its impact on collection efficiency increases with particle charge, although it remains marginal.

## 1. Introduction

Air pollution, a long-standing issue, remains today a major concern for both human health and ecosystem balance. In terms of impact on humans, pollution can cause or contribute to increased mortality and serious illnesses [1]. Health effects range from minor upper respiratory irritation to chronic respiratory and cardiovascular diseases, lung cancer, acute respiratory infections in children, and chronic bronchitis in adults [1–3]. It can also worsen pre-existing heart, lung conditions or asthmatic attacks [1]. Pollutants may originate from natural sources such as volcanoes and wildfires, but the primary and most harmful sources are anthropogenic activities [4]. These generate the most dangerous particulate matter, especially particles with an aerodynamic diameter of less than 2.5 µm, mainly produced during the combustion of fossil fuels used for energy production and transportation [4,5].

In order to deal with these growing risks posed by air pollution, a number of purification techniques have been the subject of extensive research over the last few decades. Air purification using filter media is one of the techniques having received wide validation from the scientific community [6]. These media are made of porous structures formed by

fibers. Depending on the application, these fibers can be made from materials such as polymers, glass, or metals, and are commonly used in respirators, coal dust filters, and indoor air purifiers [7,8]. Filter media are generally divided into two main types: woven and non-woven media. The most widely used is non-woven media, primarily due to their low cost and design flexibility [9]. These media are characterized by random fiber arrangements with varying diameters, which enhances their ability to capture particles of different sizes [7]. However, for the purposes of our electrical study, precise control over both the electric field and the fiber charge was required. Such control is difficult to achieve with non-woven media due to their structural irregularities and the risk of fiber charge instability [10]. Therefore, we chose to use woven media, in the form of metallic grids, whose uniform and conductive structure allowed us to polarize the fibers and create a steady and well-defined electric field within the filter [10].

The performance of an air filter is primarily evaluated based on two key factors. The first one is the pressure drop, mainly influenced by filter geometry such as media's fiber diameter, thickness, void fraction, and number of layers [11–13]. In terms of collection efficiency, it depends on several capture mechanisms divided into two main categories. The first

<footnote>This article is part of a special issue entitled: ELECTROSTATICS 2025 published in Journal of Electrostatics.</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: mohamed.akram.sayoud@univ-poitiers.fr (M.A. Sayoud).</footnote>
concerns mechanical mechanisms, strongly influenced by particle size and filtration velocity [7]. This category includes three main mechanisms: inertial impaction, interception and diffusion [14]. The second category, which is the main focus of this study, involves mechanisms of an electrical type, mainly represented by electrostatic interactions of particles with fibers, or with the external electric field [15]. They are recognized for their effectiveness in the MPPS (Most Penetrating Particle Size) zone, usually located between 0.15 and 0.5 µm, where mechanical mechanisms are generally less efficient [11,15]. Moreover, they offer the advantage of improving collection efficiency without affecting the pressure drop across the filter [16].

The role of electrostatic forces in enhancing air filtration performance is no longer in doubt among researchers. In the literature, several works have discussed the effect of these forces on collection efficiency, especially for fibrous filters [16–19]. However, no fundamental study has been carried out to explore the role of each force in filtration process, or parameters that can reinforce them in order to maximize their contributions to collection efficiency. The present study takes this approach. This work proposes a detailed analysis of electrical mechanisms, based on the control of a key parameter: particle electric charge level, considered as one of the most crucial for these mechanisms. Controlling this parameter enables us to examine in depth the various electrostatic forces, Coulomb, DEP and the image force, to dissociate their respective contributions, and thus to study them separately in order to better understand the factors that govern them. The ultimate aim is to identify the optimum combination of conditions for designing a high-performance air filter, achieving both high collection efficiency and low pressure drop.

In section 2 of this paper, we present the principal electrostatic forces, their equations and the parameters capable of amplifying them. The following two sections will be dedicated to a detailed description of our experimental setup and elaborated protocols used in our investigation. Finally, the results will be presented and discussed in section 5.

## 2. Electrostatic forces

In order to evaluate the contribution of electric forces to particles collection efficiency, it is essential to analyze the main parameters governing their behavior. This approach aims to identify the optimal combination of conditions that maximize the impact of each force. These forces depend mainly on particles' electric charge levels, electric field intensity and gradient, as well as particle size and its proximity to the fiber surface [20]. In air purification, three principal electrostatic forces can act on particles.

**Dielectrophoretic (DEP) force:** It arises when a neutral particle is exposed to a non-uniform electric field. Under the action of this field, the particle becomes polarized, producing an induced dipole moment, the interaction between this latter and the electric field gradient generates a net force $\vec{F}_{DEP}$, given by equation (1) [21]:

$$ \vec{F}_{DEP} = 2\pi r_p^3 \varepsilon_0 \varepsilon_{rm} \left( \frac{\varepsilon_{rp} - \varepsilon_{rm}}{\varepsilon_{rp} + 2\varepsilon_{rm}} \right) \nabla |\vec{E}|^2 \quad (1) $$

where, $\vec{E}$ is the electric field. $r_p$ is the particle's radius. $\varepsilon_{rp}$ and $\varepsilon_{rm}$ are the relative permittivities of the particle and the medium, respectively.

Depending on the sign of the Clausius-Mossotti factor ($\frac{\varepsilon_{rp}-\varepsilon_{rm}}{\varepsilon_{rp}+2\varepsilon_{rm}}$), the DEP force acts differently on a particle. If this factor is positive, particles are attracted to regions of higher electric field intensity. If it is negative, particles are repelled from those regions [22]. According to equation (1), dielectrophoretic force can be amplified by adjusting the electric field intensity, gradient of the electric field squared, the permittivity of the particle or medium, or the particle size.

**Coulomb force:** In the field of filtration, Coulombic interactions act on a charged particle interacting with either an electrically charged fiber

or an external electric field [11]. It is described by the following equation [23]:

$$ \vec{F}_C = q_p \vec{E} \quad (2) $$

where, $q_p$ is the electric charge of the particle.

In our case, Coulomb force can be controlled by adjusting either the electric field intensity or the particle charge level.

**Image force:** This force appears when a charged particle approaches a conductive fiber. The particle's electric field induces an electrostatic attraction, producing a net force that drives it toward the fiber [23]. The image force acting on the particle can be expressed by the following equation [24,25].

$$ \vec{F}_{img} = - \frac{q_p^2}{16\pi\varepsilon_0(\delta + r_p)^2} \vec{n} \quad (3) $$

where, $\delta$ is the distance between the surfaces of the particle and the conductive fiber. $\vec{n}$ is the normal vector, perpendicular to the surface and directed towards the particle. This force becomes significant when a highly charged particle approaches the fiber [26].

After identifying the parameters that can amplify electrostatic forces, the next two sections will provide a detailed presentation of the experimental setup used in this investigation and the protocols developed specifically to explore the impact of these parameters on forces and, consequently, on collection efficiency.

## 3. Setup overview

The experimental setup is illustrated schematically in Fig. 1. It is composed of particle generation, charging, and collection units, as well as two measurement cells dedicated to evaluating particles' electric charge levels and collection efficiency.

### 3.1. Particle generation, charging and collection

The first step of the experimental procedure is aerosol generation. This is carried out using a particle generator (Palas, AGK-2000), with a 10 % NaCl solution to obtain polydisperse aerosols. A drying system (Palas, TR-2000) was installed at the generator outlet, at a pressure of 4 bar, ensuring dried particles release. The second step, and the most crucial for this work, is to control the charge level of the particles. For this purpose, a bipolar discharge system (Palas, CD-2000) was used. It consists of a dry compressed air inlet, an aerosol inlet and outlet, two ionization chambers for positive and negative charging, and a mixing chamber where particles interact with ion-enriched air. Thanks to its independently switchable power supplies, the unit can be configured either to charge particles positively or negatively by supplying the corresponding ionization chamber, or to neutralize them by turning on both power supplies. In order to obtain a higher charge level, another charger was used. This charger is actually a particle sensor (Pegasor, PPS-M), based on the principle of highly charging the particles using a positive corona discharge unit, and then measuring their total charge. Based on this measurement, it is possible to deduce the total number of particles passing through the filter. Since it collects only a minority of the charged particles, we were able to using it as a charger. The principle of this charger is the same as the first one, with the difference that it has only one ionization chamber (positive). It is therefore designed only to charge particles positively, and cannot be used to neutralize them. It's worth nothing that both chargers operate via the diffusion charging mechanism.

Particles are collected using an Electric Metal Mesh Filter (EMMF), which has a cylindrical geometry with an internal diameter of 20 mm, respectively, and a width of 220 mm. The EMMF is composed of a set of three electrically isolated metallic grids, with adjustable inter-grid distance $d_g$ between 5 and 20 mm, arranged such that the high-voltage grid
<figure><img src="image_2.png" /><figcaption>Fig. 1. Schematic illustration of the experimental setup.</figcaption></figure>

is surrounded by two grounded grids (see Fig. 2). This configuration ensures a well-defined and steady electric field distribution inside the filter. High-voltage dc source (Keithley, model 248, ±5 kV) was employed to supply the middle grid with negative polarity. It should be noted that the equivalent of “fiber” in the case of a metal grid is “wire”.

Four types of stainless-steel grids were selected for this investigation. Their specifications are presented in Table 1; a microscopic image of the D-type grid is shown in Fig. 3. Since the main objective is to analyze in depth the role of electrostatic interactions in filtration process, the effect of mechanical mechanisms was minimized by choosing wire diameters and pore size at least 25 times larger than particles diameters. It should be noted that all the grids have a plain weave, except for the type A grid, which has a twill weave.

## 3.2. Collection efficiency measurement

The efficiency measurement principle consists of generating the particles, directing them through the filter, and then calculating particle concentrations upstream and downstream the EMMF by means of an

<figure><img src="image_3.png" /><figcaption>Fig. 2. Schematic illustration of the EMMF.</figcaption></figure>

<table><caption>Table 1
Grids' specifications.</caption><thead><tr><td>Grids</td><td>wire diameter (μm)</td><td>Pore size (μm)</td><td>Void (%)</td></tr></thead><tbody><tr><td>A</td><td>25</td><td>26</td><td>25</td></tr><tr><td>B</td><td>50</td><td>75</td><td>36</td></tr><tr><td>C</td><td>100</td><td>150</td><td>36</td></tr><tr><td>D</td><td>100</td><td>250</td><td>51</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Fig. 3. Microscopic image of the D-type grid.</figcaption></figure>

optical aerosol spectrometer (Palas, Welas 1100) sensitive to particles sized from 0.2 to 10 µm. Given that the aerosol spectrometer has only one inlet, it was necessary to create a circuit reproducing the flow upstream the filter. To this purpose, a bypass filter was set up with no grids inside [10,27]. The overall collection efficiency η is calculated using the following equation [28]:

$$ \eta = 1 - \frac{C_{\text{DOWN}}}{C_{\text{UP}}} = 1 - P \qquad (4) $$
Where $C_{UP}$ and $C_{DOWN}$ are the total particle concentration upstream and downstream the filter, respectively, and P is the overall penetration.

Fig. 4 presents the particle size distribution. Results indicate that this latter is centered in the MPPS zone, with a median diameter of 0.274 µm. It is important to note that the use of a highly concentrated NaCl solution (10 %) in the aerosol generator generally leads to the formation of large particles. However, in our case, the application of a relatively high pressure (4 bars) in the generator as well as in the drying system, resulted in reduced size (<2 µm) and efficient particles drying. Ultrafine particle concentrations could not be measured due to the detection limit of the aerosol spectrometer, which is not sensitive to particles smaller than 0.2 µm.

### 3.3. Particle electric charge level measurement

An electrical low-pressure impactor (Dekati, ELPI+) was used during this phase to perform real-time measurements of electrical charge for particles ranging from 0.1 to 2 µm. As its name indicates, the ELPI+ is a cascade impactor that classifies particles into 14 size classes based on their aerodynamic diameter. This classification relies on particle inertia: larger particles are collected in the upper stages, while smaller ones are deposited in the lower stages [9,28]. This instrument was used to measure the different charge levels provided by the particle chargers. These levels, as functions of particle diameter, are shown in Fig. 5. The Pegasor charger was used to obtain charge level 3. For the levels 2 and 0, the Palas charger was employed. The particles' initial charge corresponds to level 1.

In this study, level 3 is considered as the maximum charge level $q_{pmax}$ that can be obtained in our experimental conditions. If we focus on the range of particles with the highest concentration, we can deduce that level 2 is between 42 and 48 % of the maximum level. Level 1 is around 12 %, while the level zero is associated to an attempt of neutralization ($q_p < 3\% q_{pmax}$). It is worth mentioning that precise control of neutralization for polydisperse particles is particularly complicated. In our case, we succeeded in reducing the initial charge, which was already low, but even at this level, which is considered “neutral”, some particles retain a certain residual charge. However, for the purposes of analysis and separation of the effects of the different electrostatic forces, this residual charge is considered negligible ($q_p \approx 0$).

## 4. Experimental protocols

In order to dissociate the effects associated with mechanical and electrical mechanisms on collection efficiency, and to evaluate the specific impact of each electrostatic force, two experimental protocols were implemented.

<figure><img src="image_5.png" /><figcaption>Fig. 4. Typical NaCl particle size distribution for a flow rate of 0.4 L/min.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5. Particles' electric charge levels.</figcaption></figure>

### 4.1. Protocol 1

It is based on equation (4) and evaluates the combined contributions of all the mechanisms. Under the assumption that the various collection mechanisms operate independently from each other [12], the overall penetration $P_{p1}$ measured via this protocol can be expressed as follows:

$$P_{p1} = \frac{C_{DOWN}}{C_{UP}} = P_{mec} \cdot P_{elec} = 1 - \eta_{p1} \quad (5)$$

with,

$$P_{elec} = P_{DEP} \cdot P_{Coulomb} \cdot P_{Image} \quad (6)$$

If the high voltage grid is connected to ground, the external electric field becomes zero $E = 0$, and equation (5) reduces to equation (7). This latter gives the contribution of the image force and mechanical mechanisms.

$$P_{p1_{V-0}} = \frac{C_{DOWN_{V-0}}}{C_{UP}} = P_{mec} \cdot P_{Image} = 1 - \eta_{p1_{V-0}} \quad (7)$$

Therefore, equation (5) can be written as follows:

$$P_{p1} = \frac{C_{DOWN}}{C_{UP}} = \frac{C_{DOWN_{V-0}}}{C_{UP}} \cdot P_{DEP} \cdot P_{Coulomb} \quad (8)$$

In neutral charge conditions ($q_p \approx 0$), the image force becomes negligible ($\overrightarrow{F_{Image}} \approx 0$). Thus, the mechanical penetration can be given by the following equation:

$$P_{mec} = P_{p1_{V-0,qp=0}} = 1 - \eta_{mec} \quad (9)$$

However, when the particle charge is no longer negligible ($q_p \neq 0$), the penetration due to the image force can be described by Equation (10):

$$P_{Image} = \frac{P_{p1_{V-0,qp=0}}}{P_{mec}} = \frac{P_{p1_{V-0,qp=0}}}{P_{p1_{V-0,qp=0}}} = 1 - \eta_{Image} \quad (10)$$

### 4.2. Protocol 2

Regarding the second protocol, it can be derived from equation (8). Substituting the measurement of upstream particle concentration by the measurement of downstream particle concentration in the absence of voltage provides equation (11), which gives the impact of DEP and Coulomb forces to the collection efficiency.

$$P_{p2} = \frac{C_{DOWN_{V-0}}}{C_{DOWN_{V-0}}} = P_{DEP} \cdot P_{Coulomb} = 1 - \eta_{p2} \quad (11)$$

If the charge level imposed corresponds to neutralization ($q_p \approx 0$), the Coulomb force can be neglected ($\overrightarrow{F_C} \approx 0$). Therefore, only the contribution of the DEP force is taken into account and equation (11) becomes
as follows:

$$P_{DEP} = P_{p2dp=0} = 1 - \eta_{DEP} \qquad (12)$$

If the other particle charge levels are considered, where ($q_p \neq 0$), the penetration due to the coulombic interactions can be expressed by Equation (13):

$$P_{Coulomb} = \frac{P_{p2dp=0}}{P_{DEP}} = \frac{P_{p2dp=0}}{P_{p2dp=0}} = 1 - \eta_{Coulomb} \qquad (13)$$

## 5. Results and discussion

In the upcoming subsections, the influence of the parameters previously mentioned in section 2 on electrostatic forces, and their contribution to collection efficiency, are presented and discussed separately. At the end, a global comparison between the contributions of each electrostatic force and mechanical mechanisms to the collection efficiency will be presented. In order to conduct these experiments, a flow rate of 0.4 L/min was set.

### 5.1. Image force and mechanical mechanisms contributions

The first electrostatic force examined in this study is image force. Its effect on the penetration is estimated from equation (10). Before that, the combined contribution of this force and the mechanical mechanisms was determined using equation (7). This contribution is illustrated in Fig. 6 by the black columns. The charge level corresponding to the first column is considered neutral, meaning that its value only reflects the effect of mechanical mechanisms (see Eq. (9)).

This figure shows that the image force, significant only in the near proximity of the wires, increases with the charge level of the particles, improving collection efficiency. The reason for this is that a highly charged particle generates a more intense electric field around itself, leading to strengthening this force. The collection efficiency from both mechanical mechanisms and image force mechanism remains low (less than 12 %). Therefore, other mechanisms are necessary to enhance the overall efficiency of the filter.

### 5.2. Dielectrophoretic (DEP) force contribution

As previously explained, the permittivities of the medium and the particles are among the parameters affecting dielectrophoretic strength. However, in our case, these properties cannot be adjusted, as they remain constant during the whole experiment. On the other hand, the electric field gradient is a factor that can be used to amplify this force [21]. In the case of a dc field, this gradient is only significant in the vicinity of the wires; outside this area, notably away from the porous surface of the grids, it becomes negligible. In filtration, control of the

<figure><img src="image_7.png" /><figcaption>Fig. 6. Effect of particle charge level on collection efficiency by image force and mechanical mechanisms. Experimental conditions: Grid A; $d_g = 5$ mm.</figcaption></figure>

field gradient can be achieved by manipulating the applied voltage on the middle grid, modifying wire diameter and mesh size, or by adjusting the distance between the grids. Equation (12) was used for the DEP force tests.

The influence of the mesh size and the applied voltage on the collection efficiency for two sets of grids (C and D) having the same wire diameter (100 µm) is illustrated in Fig. 7(a). As expected, the collection efficiency increases with the applied voltage, due to dielectrophoretic force enhancement. However, in our conditions, the mesh size has an insignificant effect on the efficiency, which remains practically constant despite a difference of 100 µm between the openings of the two sets of grids. Therefore, we can neglect the effect of the mesh size on the collection efficiency by DEP force.

Fig. 7(b) shows the evolution of the collection efficiency versus the applied voltage for three different wire diameters. Similar to mesh size, this parameter has a negligible influence under low electric field conditions. However, from a voltage of 3 kV, a difference begins to appear between grids A, B and C on collection efficiency. As wire diameter decreases, the difference in efficiencies increases. This difference becomes more significant as the applied voltage increases. The effect of wire diameter on the electric field gradient is explained by the idea that an electrode with a smaller radius of curvature generates a stronger electric field gradient in its vicinity [20].

The next parameter that can influence the efficiency by DEP force is the distance between the grids. To better identify its effect, a second high-voltage power supply (Spellman, model SL 30N10X3039, -30 kV; -0.33 mA) was installed. Fig. 8(a) illustrates the evolution of collection efficiency as a function of applied voltage for two different inter-grid distances. At constant applied voltage, increasing the inter-grid distance leads to a decrease in collection efficiency. To achieve close efficiency levels between the two configurations, it is necessary to increase the voltage applied to the central grid significantly. This is clearly reflected in the figure: to achieve an efficiency of about 67 %-70 %, a voltage of 7 kV is applied for an inter-grid distance of 5 mm, while a voltage of 28 kV is required for a distance of 20 mm. In order to enable a proper comparison between the different configurations, an average electric field $E_a = \frac{V}{d_g}$ was maintained constant for the two inter-grid distances during the experiment. This can be observed in Fig. 8(b), which shows the evolution of the efficiency as a function of the average field intensity. Keeping the average electric field constant means that, as the distance between the grids increases, the voltage applied to the central grid must be higher. For a significant average field, the collection efficiency increases with the inter-grid distance. This enhancement is mainly due to the increase in applied voltage, which produces a higher field gradient close to the wires.

The last parameter that can enhance dielectrophoretic force is particle diameter. Fig. 9 presents the fractional efficiency by DEP force (charge level 0, Grid A and $d_g = 5$ mm). It is clear that an increase in particle size significantly improves the collection efficiency. This is because the larger the particle, the stronger the dipole induced in it [12].

In the context of practical air filtration, certain parameters such as the permittivities of the medium and particles, or their size, are considered external, and therefore uncontrollable. The principal control factor is the electric field gradient, which can be manipulated through the filter design and the field intensity. The results revealed that mesh size has a negligible effect on the collection efficiency by DEP force. It is therefore recommended to select grids with large openings in order to reduce pressure drop. As far as the distance between the grids is concerned, its influence on the efficiency, for a constant average field, proves to be limited, as the trade-off between collection effectiveness and power supply is not advantageous. Thus, it is better to set the inter-grid distance as small as possible, in order to amplify the average field with the lowest applied voltage, and therefore the minimum power dissipation. What remains is a reduction in wire diameter, a promising parameter for intensifying the electric field near the wires and thus
<figure><img src="image_8.png" /><figcaption>Fig. 7. Effects of applied voltage on electrical collection efficiency by DEP force for different (a) mesh sizes and (b) wire diameters. Experimental conditions: Charge level 0; $d_g = 5$ mm.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 8. Effect of the distance between grids as a function of (a) applied voltage and (b) average electric field on collection efficiency by DEP force. Experimental conditions: Charge level 0; Grid A.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 9. Effect of particle diameter on collection efficiency by DEP force for three different applied voltages.</figcaption></figure>

improving collection efficiency. However, this reduction must not affect the robustness of the filter media.

### 5.3. Coulomb force contribution

Equation (13) was used for these tests. Three different charge levels were chosen, as well as several values of applied voltage, in order to precisely estimate the influence of these two parameters on Coulombic interactions, and therefore on collection efficiency.

Fig. 10 provides the impact of particle charge level and applied voltage on collection efficiency. Higher the particle charge, greater the efficiency by Coulomb force. The same applies to the applied voltage: a higher voltage generates a stronger electric field, which reinforces the Coulomb force and thus improves collection. For the level 3 of particle charge and an applied voltage of -4.9 kV, the Coulomb force contribution to collection efficiency exceeds 96 %.

### 5.4. Comparison between mechanisms

Under practical conditions, all capture mechanisms, whether
<figure><img src="image_11.png" /><figcaption>**Fig. 10.** Effect of particle charge level and applied voltage on collection efficiency by Coulomb force. Experimental conditions: Grid A; $d_g$ = 5 mm.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 11.** Comparison between mechanisms and forces' contributions on the collection efficiency. Experimental conditions: Grid A; $d_g$ = 5 mm; $V_a$ = -4.9 kV.</figcaption></figure>

mechanical or electrical, act simultaneously [7]. However, depending on the operating parameters, some may have more impact than others. Fig. 11 shows the relative contribution of each electrostatic force, as well as mechanical mechanisms, to particle collection efficiency, as a function of three different charge levels for an applied voltage of -4.9 kV. The black columns present the overall collection efficiency, calculated using equation (5).

For a relatively strong average electric field $E_a \approx 1 \text{ kV} \cdot \text{mm}^{-1}$, the figure illustrates that above a certain charge level (in our conditions, $q_p > 40\% q_{p,max}$), the Coulomb force becomes predominant. This is illustrated in the black column corresponding to charge level 3, where the efficiency due to Coulombic interactions is very close to the overall efficiency of all combined mechanisms ($\eta_{p1} \approx 98\%$). Compared to other forces or mechanisms, Coulomb force acts over a wider range: it is capable of attracting particles from relatively far distances from the wires [12], this range depends on both the intensity of the electric field and the charge level of the particles. However, when the particles are slightly charged, the influence of the dielectrophoretic force can exceed that of Coulomb's, since it is exerted on all particles, regardless their charge [12]. Concerning the contribution of mechanical mechanisms, their effect remains negligible compared to other forces. This result was expected, since extreme conditions were set up to limit their influence, thus bringing us closer to the hypotheses of mechanism independence. As for the image force, it can be considered as an adhesion force, as it is only significant for particles travelling at a very close distance from the wires, and its effect becomes more significant when the particles are highly charged. To further enhance this force, it would be necessary to use grids with very fine openings, close to the diameter of the particles.

However, such a configuration would lead to a significant pressure drop.

To the authors' knowledge, the experimental methodology adopted in this study is the first to allow in-depth investigation of the role of electrical mechanisms in the filtration process, in particular the specific contribution of each force to collection efficiency, as well as the parameters influencing these contributions. The results obtained have enabled a better understanding of the interactions between particles and fibers, opening the way to electret filter design optimization. However, the main limitation of this work lies in the absence of control of humidity inside the filter, a factor considered to be the main enemy of electrostatic interactions, particularly in the case of charged fibrous media [29]. In the present investigation, several hypotheses were used, particularly that of the independence of the collection mechanisms, along with the neglect of the impact of particle accumulation on the wires, which can modify the electric field locally. In perspective, it would be relevant to study the modes of particles accumulation under the influence of the electric field, to analyze their trajectories, and to assess the impact of these deposits on the field distribution and, consequently, on electrostatic interactions.

## 6. Conclusion

In this paper, we examined the effects of particle and wire diameters, mesh size, distance between the grids and electric field intensity on electrostatic forces, and therefor on the collection efficiency, by controlling the electric charge level of particles. The main results are as follows.

(1) The contribution of Coulomb force on collection efficiency is the most dominant when a strong electric field and high particle charge level are present.

(2) The dielectrophoretic force (DEP) acts on all particles, no matter their charge. It becomes most important compared to other forces when the particles are low-charged. Its effect on particle collection efficiency is strongly dependent on the electric field gradient in the vicinity of the wires, a parameter that can be enhanced by reducing the diameter of the wires or/and by increasing the applied voltage.

(3) Mesh size and inter-grid distance are two parameters whose impact on improving collection efficiency by DEP force remains limited. It is therefore recommended to use closely-spaced grids with large openings, to further reduce pressure drop and minimize electric power loss.

(4) The image force can be assimilated to an adhesion force. It is only effective near the wires, and becomes more important when the particles are highly charged.

(5) For applications where particle charge can be controlled, the air filter should be designed to enhance the Coulomb force, by increasing the particle charge level. On the other hand, when this charge cannot be controlled, the use of fine-diameter wires is recommended to enhance the electric field gradient in their vicinity, thus amplifying the DEP force. In both cases, it is essential to maintain a strong electric field inside the filter by increasing the applied voltage, and that's to ensure optimum collection efficiency.

## CRediT authorship contribution statement

**M.A. Sayoud:** Writing – review & editing, Writing – original draft, Visualization, Validation, Project administration, Methodology, Investigation, Formal analysis, Conceptualization. **N. Zouzou:** Writing – review & editing, Validation, Supervision, Project administration, Methodology, Investigation, Conceptualization.
Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.

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