Effect of external electric field on particle impact charging process

Journal Pre-proof Effect of external electric field on particle impact charging process

Jiawei Hu, Cai Liang, Chun Han, Qun Zhou, Jiliang Ma, Daoyin Liu, Xiaoping Chen PII:

S0032-5910(19)30884-8

DOI:

https://doi.org/10.1016/j.powtec.2019.10.061

Reference:

PTEC 14828

To appear in:

Powder Technology

Received date:

7 June 2019

Revised date:

11 October 2019

Accepted date:

12 October 2019

Please cite this article as: J. Hu, C. Liang, C. Han, et al., Effect of external electric field on particle impact charging process, Powder Technology(2019), https://doi.org/10.1016/ j.powtec.2019.10.061

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© 2019 Published by Elsevier.

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Effect of external electric field on particle impact charging process Jiawei Hu&, Cai Liang&,*, Chun Han, Qun Zhou, Jiliang Ma, Daoyin Liu, Xiaoping Chen (Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China) &

These authors contributed equally to this study and should be considered as the co-first author.

Corresponding author: Cai Liang E-mail address: [email protected] (C. Liang).

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Tel: +86 025 83795652 (Office); Fax: +86 025 83795652 (Office)

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Abstract

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Electrostatic charging of granular materials in both nature and industry usually takes place in

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the presence of an external electric field. Thus, it is essential to fully understand the impact

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charging of a single particle in such situations. Here, we used a variation of Millikan's method to measure the transferred charges by particle-plate impacting under an external electric field. The

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finite element method was used to determine the electric field at the impact point. We found that

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impact charges show different polarities under different directions of the vertical component of the

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electric field; meanwhile, both positive and negative impact charges were present for cases within the shielding cage. A hypothesis based on the theory of electronic energy levels was proposed to explain the total contact potential difference under an external electric field and within the shielding cage. Keywords: Particle charging, Electrostatic charges, Electric field 1. Introduction Triboelectric charging of granular materials is common in both nature and industry, due to continuous particle-to-particle and particle-to-wall contacts [1–7]. For instance, in desert sandstorms and volcanic explosions, the collisions between particles will lead to electrostatic 1

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charging and even atmospheric discharges [1, 3]. Also, the presence of static charge can affect various powder handling processes, such as fluidization, mixing, conveying, and storage [4, 5, 8– 11]. Because static charges can have a substantial influence on these fields, understanding the mechanisms of contact electrification is of fundamental importance. Contact electrification is a complex phenomenon, which is susceptible to both the properties of

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materials and environmental conditions [1, 2]. Great efforts have been put forth to reveal the

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effects of these factors on electrostatic charging. Generally, electrostatic charges for different

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materials vary with different work functions [12,13], functional groups [14] or resistivity of

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contact surfaces [15,16]. Since contact electrification arises from surface interactions [17], the

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surface impurities[18], and surface morphology [19] are directly relevant to the tribo-charging process. Other researches have hinted that electrostatic charges resulting from particle-particle and

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particle-wall interactions were also relevant to particle sizes [20]. On the other hand, many

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peer-reviewed articles have reported particle charges as caused by environmental conditions and

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powder handling factors [4–7]. For instance, [21]–[23] found that the degree of electrification grew with increasing superficial gas velocity and operating pressure when particles were under fluidization. As gas velocity and pressure rises, the level of electrification increases, due to enhanced gas velocity and pressure enlarging the bubble rise speed, frequency, and volume fraction. However, [24] observed the triboelectric charge on an insulator surface rapidly dissipating with lowered atmospheric pressure. The relative humidity and temperature of an environment have also been found to cause charge dissipation [23, 25, 26]. In addition to these influence factors, accompanying electric fields have been observed in the cases of dust devils [27–29], thunderstorms [29], and fluidized beds[21, 25, 30]. Several 2

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researchers have reported the highest potential in a fluidized bed—as high as 15 kV [25]. In dust devils, electric fields can reach up to ~100 kV/m [29]. Electrostatic charges in a

granular system

can also create an electric field [2], which can impose on charged particles and the particle charging process [31]. Shinbrot [32] stated that the mutual effects of electric fields and particle charges suggest a nonlinear feedback mechanism. However, how external electric fields affect the

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charging process remains poorly understood. Some preliminary work was carried out in 1964,

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indicating that particles gained induced charges when contacting with the metal surface within an

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external electric field [33]. Hays and Donald [34] studied the effect of an applied electric field on

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mercury-polymer contact charging by applying a bias voltage between the mercury and grounded

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substrate. The surface charge density of the insulator was found to be approximately linear with the applied field. In 2014, Zhou et al. [35] conducted a similar metal-insulator contact

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electrification test, using atomic force microscopy (AFM) with a bias voltage between the Pt tip

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and the metal substrate. The results implied that the applied bias could modulate both the polarity

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and density of contact electric charge transfer. Mizutani et al. [15] conducted experiments in 2015 by repeatedly tribocharging particles. They controlled the mass flow rate and particle charge with an initial vibrating plate in an electric field and measured the differences between the charges after they traveled to a second vibrating plate by calculating the difference between particle charges at the lower and upper ends of the second plate.

They found that the charge transfer of particles

depends on the initial charge as well as the external electric field, their chemical and electrical properties, and the travel distance of the particles. A common feature in all of the studies cited here was that all the contact electrification tests were conducted by contacting the insulator with the metal, which was directly connected to the power supply. These cases may be not practical in 3

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both nature and industry because the particle charging occurs when particles are exposed to the electric field rather than physically contacted with electrodes. To underline the mechanism of identical materials charging under an electric field in desert sandstorms, Pähtz et al. proposed that the polarization of particles provided the electrons for exchange [28]. Zhang et al. claimed the electric field yielded hydronium and hydroxide ions on

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the wet particle surfaces, which caused two insulators to become charged after contact and

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separation [36]. However, a need still exists for studying contact electrification under an electric

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field experimentally.

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This paper outlines the effects of an external electric field on impact electrification using a

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variation of Millikan’s method [37], in which the charge of an oil drop can be deduced from the steady speed in its vertical electrical and gravitational field. The experimental system consists of

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an electric field generation device, a particle-plate collision section, and a particle trajectory

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tracking system. Two vertical parallel electrodes generated the uniform horizontal electric field

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between the electrodes and the inclined electric field under the electrodes. The target plate lay beneath the vertical electrodes, which was subject to the inclined electric field. Meanwhile, we used an i-SPEED 221camera (China iX Cameras, Shanghai) to record the trajectories of the single particle passing through the uniform electric field before and after colliding with the target. The initial and the final charge of the particle were related to their accelerations [38]. In this approach, we highlighted the roles of the direction and magnitude of the external electric field in the contact electrification by comparing the impact charging under the electric field and in a shielding cage.

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2. Materials and methods

2.1. Materials

In this paper, we used polyformaldehyde (POM) and stainless steel (SS) as the impact particles. 3

The diameter and density of POM particles are 1.6 mm and 1410 kg/m , while SS particles have a 3

diameter of 1.0 mm and a density of 7930 kg/m . The 4-cm wide × 5 cm long target plate was also

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made of POM and SS.

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To ensure the sample surfaces were uncontaminated, we soaked test grains in alcohol for 30 min

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and rinsed them with deionized water five times. Then, these grains were dried at 50 °C over 12 h

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in a Zenith DHG-9070A drying oven (Zenith Lab Inc, China).

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2.2. Experimental systems and procedure

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Fig. 1 presents a schematic diagram of the impact charging experimental system for particles

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against the plate under an electric field. To reduce the influences from the external atmosphere, the experiment was conducted in a Plexiglas box (35 cm tall × 30 cm wide × 30 cm long), which was protected by pure Nitrogen gas. The relative humidity and temperature in the box were controlled at 5±2% humidity and 15±1 temperature by a Vaisala HUMICAP® transmitter (Vais la Corp., Helsinki, Finland). The copper parallel electrode plates (20 cm tall × 15 cm wide × 3 mm thick) had a 5 cm separation, and were vertically mounted on a Teflon bracket to guarantee high isolation. An electric field was created by connecting the left copper plates to a DC high-voltage supply (0–50 kV, 0–1mA). In this work, we set the potential difference V between the parallel electrodes to be 10 kV to create an approximate uniform electric field intens ity (E = V/L = 0.2 MV/m) between 5

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them. The target plate lay 5cm below the electrode plates. The sample particle dropped from a valve and fell by gravity into the region between two parallel electrode plates. After colliding on the target plate, the particle rebounded and rose into the electric field again. Outside the box, an i-SPEED 221camera, with a maximum frame rate of 204,100 frames per second and a maximum

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resolution of 1600 × 1600 pixels, recorded the particle trajectories of both the free-falling and

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rising process.

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To ensure uniformity of the electric field for determining the charge on each particle, we

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recorded the particle trajectories within the region around the center of the copper plates, which is

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the red rectangle in Fig. 1. As a result, the high-speed camera focused on the central area (approx. 4 cm wide × 6 cm long) between the parallel plates in the test. In this work, the frame rate and

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resolution were set at 2000 frames per second and 720 × 848 pixels. A thin string hung in front of

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a white backdrop as the referenced vertical line. Both the camera image and the copper plates

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were adjusted to be parallel to the vertical reference. Since the target plate lay below the parallel electrodes, the electric field from the electrodes was bound to influence the impact charging on the target plate. Also, to reveal the effect of the external electric field on the contact electrification, we conducted the same tests by shielding the target plate with a copper cage. On the top of the cage, a small hole (10 mm diameter) allowed particles to enter and exit. The external electric field generated by the parallel electrodes was analyzed using the finite element method [39]. The simulation model was established according to the real-scale parameters of the setup, and the computational domains involved the Plexiglas box, electrodes, target, metal valve, and metal 6

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cage. Since no volume charges occurred in the different phases in this system, the governing equations for the electric field computational domain are given in the Laplace equation .(1) and Faraday's law as expressed in (2):

2U  0

(1)

E  U

(2)

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where U is the electric potential, and E is the electric field. For the boundary conditions, we set the potentials on the surface of the left electrode, the

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surface of the left electrode, and the infinity distance in the simulation as:

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U left _ surface  10000  U right _ surface  0 U  0  

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(3)

by:

n

  rs 

U s   s n

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U g

(4)

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 rg 

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Due to the surface charges on the solid surfaces, the Neumann boundary conditions are given

where Ug is the electric potential of the gas phase, i.e., Nitrogen gas in this work; Us is the electric potential of the solid phase; ε rg is the relative permittivity of the gas (for Nitrogen gas, it is 1); εrs is the relative permittivity of the solids (for Plexiglas, it is 5.2; for POM, it is 3.8, and for metal it is positive infinity); ρs is the surface charge density of the solids (for the inner surface of Plexiglas −10

box it is 7.0 × 10

2

−10

C/m . For the POM target, it is 7.8 × 10

2

C/m , and for the metal target, it is

3.4 × 10−10 C/m2 ). Considering the continuity of the potential on the interface between the two phases, the electric potential of the gas phase is equal to the electric potential of the solid phase; thus:

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(5)

The calculated electric fields of the setup for the POM target and SS target when under the external electric field (with or without the metal cage) are displayed in Fig. 2. Notably, the surface electric field above the metal target is perpendicular to the surface since there would be an electrostatic balance inside the metal under the applied electric field, while the electric field on the

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POM target surface is inclined.

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For the cases of targets without cages, the surfaces of the target plates were exposed to the

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inverted curved electric field, and the average electric field norm on the POM target surface and

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the SS target surface was 48.60 kV/m and 27.64 kV/m, respectively. Because of the metal

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shielding cage, few external electric fields can go through the cage; moreover, the average electric field norm on the POM target surface and the SS target surface were 0.023 kV/m and 0.013 kV/m

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when the targets were within the cage. Fig. 3 shows the component of the electric field on the

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target surface when it was directly exposed to the electric field with and without the shielding cage.

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When the POM target and SS target were under the parallel electrodes without the cage, the component of the electric field grew from a minimum value to a maximum value along with the target plate surface and turned to zero at the middle of the target plate. As a result, on the left side of the target surface, the electric field inclines downward, while on the right side of the target surface, the electric field inclines upward.

3 Data and analysis

As shown in Fig. 4, the high-speed camera filmed at least 40 frames for both the free-falling process and the rising process so that we can attain the exact position of the particle at every

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frame. With the position and the interval time ∆𝑡 of each frame, the velocity and acceleration of the particle can be solved using a finite difference method [39] formulated as: (6)

∆𝑡

(7)

and

represent the position, velocity and acceleration of the particle at ith time,

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where

∆𝑡

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respectively.

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When the particle with charge Q traveled in the uniform electric field region, only the electric

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force EQ and the drag force 𝐹𝑥𝐷 acted on it in the x-direction. Hence, the motion of the particle

𝑚

𝐸𝑄

𝑥

𝐹𝑥𝐷

𝑥

(8)

is the x component of the particle’s acceleration, which

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where m is the mass of the particle;

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can be characterized by Newton’s second law of motion [40] as:

where

(C𝐷 𝜌𝜋𝑟 2 ) 2 𝑥

(9)

𝑥

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𝐹𝑥𝐷

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can be derived from Eqs. (6) and (7). The drag force 𝐹𝑥𝐷 of the particle is given by:

is the x component of particle velocity; r is the radius of the spherical particle, and 𝜌 is

the mass density of the particle. CD is the drag coefficient between the particle and the air, which is defined as [41]: C𝐷

24 𝑅𝑒 𝑝 for 𝑅𝑒 𝑝 < 1,

C𝐷

24 1 + 6 𝑅𝑒 𝑝

2 3

𝑅𝑒 𝑝 for 1 < 𝑅𝑒 𝑝 < 400,

(10) (11)

where Rep is the particle Reynolds number; however, when the air is stagnant, Rep defined as: 𝑅𝑒 𝑝

2𝑟

𝜈

(12)

where 𝜈 is the kinematic viscosity. 9

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With the above equations, we can estimate Q value every time. Then, by averaging the series of Q, the amount of charge carried by the particle is determined. With the trajectories of the free-falling and rising process, the initial charge 𝑄 can be computed before the particle impacts the target and the final charge 𝑄𝑓 can be calculated after the particle rebound is computed accordingly. We defined the impact charge ∆Q as the difference between the final charge and the initial charge. 𝑄

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𝑄𝑓

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∆𝑄

(13)

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For example, in Fig. 4, the initial charge, the final charge, and the impact charge of a POM

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particle colliding against the POM target were 8.46 (pC), 5.89 (pC) and −2.57 (pC), respectively.

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Moreover, Fig. 5 shows that the high-speed camera can also film the impact event on the target surface with an unfocused condition. Hence, we gained access to the position of the impact point

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after the image processing by MATLAB. With simulation results, the magnitude and direction of

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the external electric field acting on the impact point were identified as values on the target surface

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[42]. In the case of POM particle-POM target impact in Fig. 4, the position of the impact point, and the magnitude of the x and y components of the electric field on the particle at the impact point were 35.62 mm, 47.63 kV/m, 7.20 kV/m, respectively.

4 Results

4.1. Impact charges under the external electric field

To assess the impact charge of particles under the electric field with a specific direction, like the inclined downward (or upward) electric field, we moved the dropping valve to the left (or right) side of the parallel electrodes so that most particles collide on the left (or right) side of the target 10

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surface. Fig. 6 provides the impact charging results of different particles and target plates under the external electric field. As seen in Fig. 6, when particles collide on the left of the target, the average impact charges of particles tend to be negative for both the POM target and SS target. Conversely, particles turn to gain positive charges after colliding with the target on the right side. The remarkable error bars reveal the poor reproducibility for contact electrification experiments,

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which could result from the gaseous discharge when separating the contacted surfaces [43, 44].

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Grosshans and Papalexandris [45] also found the impact charges presenting a disperse data

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because of the non-uniform charges on the particle before colliding with the target. Thus, we

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conducted more than 50 trials for each test to analyze statistical regularities.

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To make more sense of these trends, we compared the statistical distributions of impact charges for different particles and different targets under both inclined upward and downward

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electric fields in Fig. 7. Despite the large dispersity, most of the data are concentrated around the

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mean value, suggesting that all impact charges approximately follow a Gaussian distribution curve.

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From Fig. 7, we can see the results under the inclined downward electric fields are significantly discrepant compared with those under the inclined upward electric fields. Furthermore, with few exceptions, most trials tend to gain negative impact charges when contact charging occurs on the left side of the target, and most impact charges are positive if the impact point is located on the right side.

4.2. Impact charges with the shielding cage

By shielding the target plate with a copper cage, the external electric field on the target surface decreased by several orders of magnitude smaller than that which was under the electric

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field directly. As shown in Figs. 8 and 9, the contact charging behavior of particles within the shielding cage differed from those exposed in the external electric field. There is no remarkable trend showing that most particles gain the same polarity of charges. For instance, most data are scattered around zero, showing both considerable positive and negative values in dozens of trials. In the cases of

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POM sphere-POM target and POM sphere-SS target, both the absolute values of the average

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impact charges are smaller than 1 pC, which are basically smaller than their counterpoints without

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the shielding cage. The vague results in the shielding cage imply that there will a more

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complicated mechanism determining the charge transfer compared to the cases under the strong

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electric field.

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4.3. Impact charges against the initial charges

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In addition, since the pre-charge on the particle is reported to affect the contact electrification

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process [6, 44], it is essential to obtain the “initial charge” of the particle. With this in mind, particles are shaking within glass and Teflon vessels to achieve charges with different magnitudes and polarities in this work.

As a result, the impact charges of particles under the external electric fields are displayed against their initial charges, as shown in Fig. 10 and Fig. 11. The impact charges of particles are scattered disorderly against the initial charge, suggesting no apparent relationship between the impact charges and the initial charges. Moreover, most of the impact charges are found to be positive or negative, as described in section 4.1, regardless of their initial charges. However, in Fig. 12, the impact charges by collision charging within the shielding cage show a general dependence

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on the initial charges of the particles.

5 Discussion

5.1. Polarization and neutralization under an electric field

There are many possible explanations for the difference in charging behaviors under different

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electric fields. The results in section 4.1 suggest that the direction of the external electric field can

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play a crucial role in the charging process, which agrees with the contact electrification hypothesis

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under the electric field proposed by Pähtz et al. [28]. As shown in Fig. 13(a), the target plate and

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the sample particle will be polarized by the tilted downward directed field before they come into

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contact. Such polarization will cause a positive charge buildup in the lower parts of the particle and the target (displayed in red), while their upper parts will be negatively charged (displayed in

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blue). When the bottom of the particle collides with the top surface of the target, part of positive

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charges on the target surface will neutralize with the negatively charged part of the particle ( Fig.

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13(b)). During the collision, charge transfer occurs such that the particle gains net negative charges; thus, the target obtains net positive charges after they separate (Fig.13(c)). Then, according to the hypothesis of polarization and neutralization, the particle should gain negative charges by impact charging. Notably, the “polarization” effect for the metal target in this paper is induction, which is much stronger than polarization. Therefore, the particle gains negative charges after the contact-separation process under the inclined downward electric field. Consequently, when the electric field was upward, the impact charge of the particle becomes positive after colliding with the target. As mentioned above, the effect of ‘neutralization’ appears to result in a charge transfer under 13

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the external electric field. The amount of transferred charge depends on the polarized charges or induced charges on the contacting domains of the particle and the target and the neutralization efficiency according to [46]. However, there is no apparent driving force in this charging model, and it is difficult to quantitatively describe the factor effects on the contact electrification. 5.2 Driving forces for impact charging within the shielding cage

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Several different potential differences affected the charge transfer in the condenser model,

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and the total contact potential difference for contact electrification process can be expressed as [6,

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42, 44]:

(14)

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V  Vc  Ve  Vb  Vex

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where V c is the contact potential difference caused by the different surface work functions between two bodies; V b is the potential difference arising from the surroundings; V e is the potential

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difference caused by the initial charge on the contact surface of the particle; V ex is the potential

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difference from the external electric field.

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Since the charge on the target was three orders of magnitude smaller than that of the particle, and the external electric field on the particle was approximately zero, the main factors for the impact charging within the shielding cage w ere the potential differences from the different surface work functions between the contact objects and the initial charge on the particle. The charges on the surface were reported to affect the Fermi energy level of the solid [35, 47], and the positive charge density on the solid surface would result in the energy of the electrons below the former Fermi level [47], where dc is the critical gap between the contact surfaces .

To reveal how the above driving forces influence the charge transfer process, Fig. 14 schematically illustrates the electronic energy level of the contact surfaces for the impact charging 14

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cases within the shielding cage. For the SS target in Figs.14(a) and (b), the initial charges on the contact surface of the particle (𝜌0𝑝) induce equal charges of opposite polarity on the target surface, and for the POM target in Figs.14(c) and (d), the initial charges on the contact surface of the particle would induce some polarized charges on the target surface which were smaller than those 𝑝

of the SS target surface. Both the initial charges on the contact surface of the particle (𝜌0 ) and the

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induced charges on the target surface (𝜌𝑝𝑡 ) would change the energy level of the particle surface as

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well as the target surface. Assuming the contact surface charges of the particle had the same

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polarity as the initial charges on the particle, defining the positive charges on the contact surface

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of the particle led to a negative change in the energy level [47]. Thus, the positive total contact potential difference meant the particle gained positive charges. The total contact’s potential

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difference for the initial charge of POM 𝑄0𝑝 < 0 is given as:

V  (  E p ( 0p )  E t (  tp ))/e

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(15)

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where Δ𝐸 𝑃and Δ𝐸 𝑡represents the absolute values of surface energy level changes for the particle

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and target;  is the difference between the work functions of the particle and the target, which is (   ) in this work. p

t

Then, for the initial charge of POM 𝑄0𝑝 > 0 , the total contact potential difference for the contact surfaces is expressed as:

V  (  E p ( 0p )  E t (  tp ))/e

(16) 𝑝

Since both the Δ𝐸 𝑃 and Δ𝐸 𝑡 resulted from the initial charge of the particle 𝑄0 , we can consider (E  E ) / e as a function of 𝑄0𝑝 . Thus, by combining the Eqs. (15) and Eqs. (16), p

t

the total contact potential difference for the contact surfaces can be summarized as:

V  Vc  Ve (Q0p )

(17) 15

Journal Pre-proof where the contact potential difference Vc   / e . For the SS target, Vc  (   ) / e , and t

p

for the POM target, Vc  0 . In [12], the induced potential difference V e arising from the initial charge on the contact surface 𝑝

of the particle was deemed as k e𝑄0 . Therefore, the transferred charge ΔQ in the condenser model can be expressed as

Q=kC (Vc  keQ0p )

f

(18)

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Eqs. (12) illustrates a linear trend between the impact charge and the initial charge of the

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particle for cases within the shielding cage. Although the results of impact charging within the

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shielding cage presented in Fig.12 are scattered, they reveal a roughly linear trend, which

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demonstrates the dominating effect of the particle’s initial charge on the impact charging process.

5.3. Driving forces for impact charging with the external electric field

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Fig. 15 shows the results of impact charges for both POM sphere-POM target and POM

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sphere-SS target against the vertical and horizontal component of the electric field. In Fig.15(a),

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most data of impact charges are located in the first and third quadrant, which demonstrates the positive (negative) y component of the electric field leading to the positive (negative) impact charge. The external electric field revises the total contact potential difference between the particle and the target surface, which led to the distinct behaviors of charge transfer on the different sides of the targets. Nevertheless, in Fig.15(b), because of all the POM sphere-SS target cases, the x component of the electric field was zero and most of the impact charges of the POM sphere-POM target were concentrated in a small x component range of the electric field (40 kV/m-50 kV/m). The x component of the electric field seems to make little difference in the upright contact electrification. 16

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The external electric field was reported to shift the energy of electron states of contacted surfaces based on the surface state theory [34], which also altered the driving forces for charge transfer. According to solid-state physics, when an external electric field is exposed on metal, the free electrons in the metal will move on to the metal’s surface to create an inverted built-in electric field with a value equal to the external electric field. When the external electric field is exposed on

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the isolator, polarized charges appear on the isolator surface in the form of electric dipoles. Thus,

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when POM spheres impact the SS target and the POM target, the induced charges on the contact

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surface of the particle (𝜌𝐸𝑝) and the target (𝜌𝐸𝑡 ) are a result of the external electric field changing

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the Fermi energy levels of both the particle and the target, as shown in Figs.16–19.

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Concerning the cases of particles with initial charges, it is reasonable to assume the charges will redistribute following the strong external electric field. For example, if the particle and target

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are under the inclined upward electric field and the initial charge of POM 𝑄0𝑝 > 0 , the initial

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positive charges on the particle contact surface will move inside the particle surface leaving the

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negative polarized charges on the contact surface of the particle, as shown in Fig. 16(b) and Fig. 𝑝

18(b). Accordingly, when the initial charge of POM 𝑄0 < 0

in Fig. 16(c) and Fig. 18(c) appear

on the contact surface of the particle there are both negative initial charges (𝜌0𝑝) and polarized charges (𝜌𝐸𝑝). Therefore, with the effect of the strong downward electric field, the contact surface of the particle is always negatively charged, regardless of how the particle surface is initially charged. Also, because of the polarized charges and the initial charges on the contact surface of the particle, other induced charges (𝜌𝑝𝑡 ) will be caused by the charges on the contact surface of the particle. As a result, Fig.16(d) and Fig.18(d) display the electronic energy level for contacted objects under the inclined upward electric field, suggesting a total contact potential difference for 17

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cases with an inclined upward electric field, which can be given by:

V  (  E p ( Ep  0p )  E t (  Et   tp ))/e

(19)

For both the SS target and the POM target, when the external electric field is downward as shown in Fig.17(d) and Fig.19(d), the total contact potential difference for contact surfaces can be expressed as:

V  (  E p ( Ep  0p )  E t ( Et   tp ))/e

(20)

As described above, the magnitude of (E  E ) / e is a result of both the external electric

f

t

oo

p

pr

field and the initial charges on the particle, but the positive or negative of Δ𝐸 𝑃and Δ𝐸 𝑡 are

e-

determined by the direction of the external electric field. Therefore, the external electric field

Pr

dominates the contact potential difference by creating induced charges and redistributing the initial charges on the contacted surface.

al

For the POM sphere–POM target cases (   0 ), Fig.18 and Fig.19 clearly show that the

rn

external electric field significantly enlarged the contact potential difference for the contact

Jo u

surfaces, which caused the electrons to transfer from the particle to the target under the inclined upward electric field, while the electrons transferred from the target to the particle under the inclined downward electric field. For the POM sphere-SS target cases, the potential difference

(E p  E t ) / e were due to the strong external electric field; thus, the initial charges on the particle might the be larger than the contact potential difference  / e . This indicates that the trend of the charge transfer for the POM sphere–SS target cases were similar as the POM spherePOM target cases, i.e., the particle was positively charged when the external electric field was inclined upward, and the particle was negatively charged when the external electric field was inclined downward. 18

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When conducting the metal-insulator contact electrification test, Zhou et al. also found that the dielectric target gained negative charges when the contact electrification was under a vertical upward electric field because of the change in its Fermi energy level [35]. 6. Conclusions We developed a new approach for measuring the transferred charge of a single particle collision

f

under an external electric field. By calculating the initial and final charge of the particle from the

oo

particle movement, we were able to acquire the impact charge due to the particle-plate collision.

pr

Also, the electric fields on the target surfaces were determined by the finite element method. In

e-

cases of targets without cages, the electric field inclined downward on the left side of the target

Pr

surface, but on the right side of the target surface, the electric field inclined upward. Also, the average electric field norm on the POM target surface and the SS target surface were 48.60 kV/m

al

and 27.64 kV/m, respectively. The average electric field norm on the POM target surface and SS

rn

target surface were 0.023 kV/m and 0.013 kV/m, respectively, when targets were within the cage.

Jo u

The effects of the direction and magnitude of the external electric field on the contact electrification were investigated by controlling the position of the impact point and shielding the target plate with a metal cage. We found that when particles collided under the inclined downward electric field, the average impact charges of particles tended to be negative for both the POM and SS targets, while particles tend to gain positive charges after colliding under the inclined upward electric field. Results under an external electric field were consistent with the polarization and neutralization hypothesis of contact electrification, and the impact charges showed no apparent relationship with the initial particle charges. Furthermore, results show that it is the vertical component of the electric field that affects upright impact charging rather than the horizontal 19

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component of the electric field. In addition, considerable positive and negative impact charges were evident for cases within the shielding cage, and the impact charges by collis ion charging within the shielding cage showed a general dependence on the initial charges of the particles. Based on the theory of the electronic energy level, the contact potential difference caused by initial charges on the particle affected the impact charges as well as the contact potential

f

differences from the different work functions of the surface when impact charging tests were

oo

conducted with a shielding cage. When an external electric field was present, it dominated the

pr

total contact potential difference by creating induced charges and redistributing the initial charges

e-

on the contact surfaces. Overall, some relevant mechanisms were shown to master the triboelectric

Pr

charging process, and different factors dominated contact electrification in different cases.

Nomenclature

2

acceleration of the particle, m/s

k

electrification efficiency, dimensionless

ke

parameter in Eq. (14), V /C

m

mass, kg

r

radius of the spherical particle, m

s

position of the particle, m

u

velocity of the particle, m/s

Jo u

rn

al

a

C

capacitance between the contact bodies, F

CD

drag coefficient, dimensionless

E

electric field strength, V/m

E

electric field, V/m 20

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𝑄0𝑝

initial charge on the particle, C

Qi

initial charge on the particle, C

Qf

final charge on the particle, C

Rep

particle Reynolds number, dimensionless

U

electric potential, V

Ug

electric potential of the gas phase, V

oo

f

F xD

electric potential of the solid phase,V

Vb

potential difference arising from the surroundings, V

Vc

potential difference caused by surface work function, V

Ve

induced potential difference, V

V ex

potential difference arising from external electric fields, V

Greek letters

al

Pr

e-

pr

Us

relative permittivity of the gas, dimensionless

ε rs

relative permittivity of the solid, dimensionless

𝜈

kinematic viscosity, s/m2

ρ

density of the particle, kg/m3

Jo u

rn

ε rg

ρs

surface charge density of the solids, C/m 2

𝜌0𝑝

initial surface charge density of the particle, C/m2

𝑝

𝜌𝐸

induced surface charge density of the particle due to the electric field, C/m

𝜌𝐸𝑡

induced surface charge density of the target due to the electric field, C/m2

𝜌𝑝𝑡

induced surface charge density of the target due to the charges on the particle, C/m

η

2

2

neutralization efficiency, dimensionless 21

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work function of object, eV

∆𝑡

interval time of each frame, s

Δφ

difference of work function of objects, eV

Δ𝐸 𝑃

surface energy level changes for the particle, eV

Δ𝐸 𝑡 surface energy level changes for the target, eV transferred charge of the particle, C

ΔV

total contact potential difference, V

oo

f

ΔQ

pr

Acknowledgments

e-

This work was funded by the National Natural Science Foundation of China (Grant No.

Pr

51976039), Fundamental Research Funds for the Central Universities and the Scientific Research

Jo u

References

rn

al

Foundation of Graduate School of Southeast University (YBPY1905).

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[28] T. Päht z, H.J. Herrmann, T. Sh inbrot, Why do particle clouds generate electric charges?, Nat. Phys. 6 (2010) 364–368. doi:10.1038/nphys1631. [29] N.O. Renno, V.J. Abreu, J. Koch, P.H. Smith, O.K. Hartogensis, H.A.R. De Bruin , D. Burose, G.T. Delory, W.M. Farrell, C.J. Watts, MATADOR 2002: A pilot field experiment on convective plumes and dust devils, J. Geophys. Res. Planets. 109 (2004) 443–459.

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fluidized bed and its mechanism analysis, Powder Technol. 325 (2018) 545–556.

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under different conditions of particle charge and external electric field, Powder Technol. 301 (2016) 153–159. doi:10.1016/ j.powtec.2016.06.008.

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[33] A.Y.H. Cho, Contact charging of micron-sized particles in intense electric fields, J. Appl. Phys. 35 (1964) 2561–2564. doi:10.1063/ 1.1713799. [34] D.A. Hays, D.K. Donald, Effect of an electric field on the contact electrification of polymers by mercury, in: Conf. Electr. Insul. Dielectr. Phenom. - Annu. Rep. 1971, 1971: pp. 74–82. doi:10.1109/ CEIDP.1971.7725148. [35] Y.S. Zhou, S. Wang, Y. Yang, G. Zhu, S. Niu, Z.H. Lin, Y. Liu, Z.L. Wang, Manipulating nanoscale contact electrificat ion by an applied electric field, Nano Lett. 14 (2014) 1567–1572. doi:10.1021/nl404819w. [36] Y. Zhang, T. Pähtz, Y. Liu, X. Wang, R. Zhang, Y. Shen, R. Ji, B. Cai, Electric field 26

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and humidity trigger contact electrification, Phys. Rev. X. 5 (2015) 1–9. doi:10.1103/PhysRevX.5.011002. [37] R.A. Millikan, On the Elementary Electrical Charge and the Avogadro Constant, Phys. Rev. 2 (1913) 793–796. [38] S.R. Waitukaitis, H.M. Jaeger, In situ granular charge measurement by free-fall

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videography, Rev. Sci. Instrum. 84 (2013). doi:10.1063/ 1.4789496.

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[39] H. Labair, S. Touhami, A. Tilmatine, S. Hadjeri, K. Medles, L. Dascalescu, Study of

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charged particles trajectories in free-fall electrostatic separators, J. Electrostat. 88 (2017) 10– 14.

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[40] P.T. Sardari, H. Rahimzadeh, G. Ahmadi, D. Giddings, Nano-particles Deposition in the Presence of Electric Field, J. Aerosol Sci. 126 (2018) 169–179.

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[41] W.C. Hinds, Aerosol Technology: Properties, Behavior, and Measurement of Airborne

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Particles, J. Aerosol Sci. 14 (1999) 175. doi:10.1016/0021-8502(83)90049-6. [42] J. Hu, X. Zeng, C. Han, C. Liang, Q. Zhou, J. Ma, D. Liu, X. Chen, Measurement of single particle impact charging under an external electric field, Rev. Sci. Instrum. 90 (2019). doi:10.1063/1.5085080. [43] T. Matsuyama, H. Yamamoto, Charge relaxation process dominates contact charging of a particle in atmospheric conditions, J. Phys. D. Appl. Phys. 28 (1995) 2418–2423. doi:10.1088/0022-3727/28/12/005. [44] J. Hu, Q. Zhou, C. Liang, X. Chen, D. Liu, C. Zhao, Experimental investigation on electrostatic characteristics of a single grain in the sliding process, Powder Technol. 334 (2018) 27

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[47] J. Lowell, A.C. Rose-Innes, Contact electrification, Adv. Phys. 296 (1980) 947–1023.

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rn

al

Pr

e-

pr

doi:10.1080/00018738000101466.

28

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Jo u

rn

al

Pr

e-

pr

oo

f

The authors claim no conflicts of interest.

29

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f

Fig. 1. A schematic diagram of particle-plate impact charging instrument.

oo

1.High-speed camera, 2. Perspex box, 3. Humidity and temperature sensor, 4. Ball valve, 5.

pr

Pressure gauge, 6. Electrode plates, 7. Teflon bracket, 8. Shield cage,9. Humidity and temperature

Jo u

rn

al

Pr

e-

sensor, 10. N2 inlet, 11. High-voltage source.

Fig. 2. Calculated electric field (a) when the POM target was under the parallel electrodes, (b) when the POM target was shielded by the metal cage, (c) when the SS target was 30

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under the parallel electrodes, and (d) when the SS target was shielded by the metal cage. POM target under electrodes without cage SS target under electrodes without cage SS target under electrodes with cage SS target under electrodes with cage

100

es.Ey (kV/m)

50

0

-50

-100

0

10

20

30

40

50

f

x(mm)

oo

Fig.3. The vertical component of the electric field along with the target plate surface. 120

Qf =5.98pC

Qi =8.46pC

y (mm)

Free-falling

25

Pr

60

40

Rising

e-

80

pr

100

30

35 x (mm)

40

45

rn

al

Fig. 4. Typical results of particles’ charges of the free-falling process and the rising process: A POM particle colliding against the POM target with an initial charge of 8.46 (pC) and a final

Jo u

charge of 5.89 (pC).

Fig. 5. An image of the particle collision on the target plate.

31

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Impact charge (pC)

Under electrodes without cage-right

Under electrodes without cage-left

8

4

1.056

0.875

POM sphere -POM target

POM sphere -SS target

0

-4 -2.832

-2.578

POM sphere -POM target

POM sphere -SS target

-8

Fig. 6. Results of impact charging test under the inclined downward electric field and the

(b)

(a) 30

30

POM sphere-SS target under electrodes without cage-left under electrodes without cage-right

25 20

e-

Count

20

Count

35

pr

25

POM sphere-POM target under electrodes without cage-left under electrodes without cage-right

oo

f

inclined upward electric field.

15 10

15

0 -12

Pr

10

5

5

-10

-8

-6

-4

-2

0

2

4

6

8

0 -12 -10 -8

-6

-4

Impact charge(pC)

-2

0

2

4

6

8

10 12

Impact charge(pC)

rn

al

Fig. 7. Distributions of impact charges under the inclined upward and downward electric field for

2

Impact charge (pC)

Jo u

(a) POM sphere-POM target and (b) POM sphere-SS target. Under electrodes with cage 0.145

0

-2

-0.919

-4 POM sphere -POM target

POM sphere -SS target

Fig. 8. Results of impact charging test in the shielding cage. (b) 15

(a) 25 POM sphere-POM target under electrodes with cage

POM sphere-SS target under electrodes with cage

20

Count

Count

10 15

10 5 5

0 -4

-2

0

2

Impact charge(pC)

4

6

0 -8

-6

-4

-2

0

2

4

6

8

Impact charge(pC)

32

Journal Pre-proof Fig. 9. Distributions of impact charges with the shielding cage for (a) POM sphere-POM target and (b) POM sphere-SS target. (a) 9

6

POM sphere-SS target under electrodes without cage-left

6

3

Impact charge (pC)

Impact charge (pC)

(b) 9

POM sphere-POM target under electrodes without cage-left

0 -3 -6 -9

3 0 -3 -6 -9

-12 -16

-8

0

8

-12 -16

16

-8

Initial charge (pC)

0

8

16

Initial charge (pC)

oo

f

Fig. 10. Results of impact charge under the inclined downward electric field vs. the initial charge for (a) POM sphere-POM target and (b) POM sphere-SS target. POM sphere-POM target under electrodes without cage-right

POM sphere-SS target under electrodes without cage-right

6

e-

6

Impact charge (pC)

9

3 0 -3 -6 -16

-8

0

Pr

Impact charge (pC)

9

(b)12

pr

(a)12

8

3 0

-3

16

-6 -10

-5

0

5

10

Initial charge (pC)

al

Initial charge (pC)

rn

Fig. 11. Results of impact charge under the inclined upward electric field vs. the initial charge for

Jo u

(a) POM sphere-POM target and (b) POM sphere-SS target. (b) 9

POM sphere-POM target under electrodes with cage

POM sphere-SS target under electrodes with cage

6 Impact charge (pC)

Impact charge (pC)

(a) 6

3

0

3 0 -3 -6

-3 -8

-4

0

4

8

12

Initial charge (pC)

-9 -8

-4

0

4

8

12

Initial charge (pC)

Fig. 12. Results of impact charges within the shielding cage vs. the initial charge for (a) a POM sphere-POM target and (b) POM sphere-SS target.

33

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Fig. 13. Illustration of the charging mechanism of particle collision with the target plate in the

Jo u

rn

al

Pr

e-

pr

oo

f

inclined downward electric field proposed by Pähtz et al.[28].

Fig. 14. Schematic diagram of electronic energy level for contacted objects within the shielding cage: (a) POM sphere-SS target, 𝑄0𝑝 < 0, (b) POM sphere-SS target, 𝑄0𝑝 > 0, (c) POM sphere-POM target, 𝑄0𝑝 < 0, and (d) POM sphere-POM target, 𝑄0𝑝 > 0.

(a)

Impact charge (pC)

Impact charge (pC)

(b) 10

POM sphere-POM target POM sphere-SS target

10

5

0

-5

POM sphere-POM target POM sphere-SS target

5

0

-5

-10

-10 -40

-30

-20

-10 0 10 es.Ey (kV/m)

20

30

40

-10

0

10

20 30 es.Ex (kV/m)

40

50

60

34

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Fig. 15. Results of impact charges against the vertical and horizonal component of the electric

pr

oo

f

field.

𝑝

𝑝

0; (b) POM sphere-SS target, 𝑄0 < 0; (c) POM

Pr

electric field: (a) POM sphere-SS target, 𝑄0

e-

Fig.16. Schematic diagram of the induced charges on contacted objects under the inclined upward

Jo u

rn

inclined upward electric field.

al

sphere-SS target, 𝑄0𝑝 > 0, and (d) the electronic energy level for contacted objects under the

Fig.17. Schematic diagram of induced charges on contacted objects under the inclined dow nward 𝑝

electric field: (a) POM sphere-SS target, 𝑄0

𝑝

0; (b) POM sphere-SS target, 𝑄0 < 0; (c) POM

sphere-SS target, 𝑄0𝑝 > 0. and (d) the electronic energy level for contacted objects under the 35

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pr

oo

f

inclined downward electric field.

e-

Fig. 18. Schematic diagram of the induced charges on contacted objects under the inclined upward 𝑝

𝑝

0; (b) POM sphere–POM target, 𝑄0 < 0; (c)

Pr

electric field: (a) POM sphere–POM target, 𝑄0

POM sphere–POM target, 𝑄0𝑝 > 0, and (d) the electronic energy level for contacted objects under

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the inclined upward electric field.

Fig. 19. Schematic diagram of the induced charges on contacted objects under the inclined downward electric field:(a) POM sphere–POM target, 𝑄0𝑝 target, 𝑄0𝑝

< 0; (c) POM sphere–POM

target, 𝑄0𝑝

0 ; (b) POM sphere–POM

> 0, and (d) the electronic energy level for

contacted objects under the inclined downward electric field. 36

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Graphical abstracts

38

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Highlights A variation of Millikan's method to measure impact charges was developed. The electric field on impact point was calculated with finite element method. Effects of electric field on contact electrification were studied.



A hypothesis involved electronic energy level for contact charging was proposed.

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39

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