Electrostatic charging and precipitation of nanoparticles in technical nitrogen: Highly efficient diffusion charging by hot free electrons

Journal of Aerosol Science 141 (2020) 105495

Contents lists available at ScienceDirect

Journal of Aerosol Science journal homepage: http://www.elsevier.com/locate/jaerosci

Electrostatic charging and precipitation of nanoparticles in technical nitrogen: Highly efficient diffusion charging by hot free electrons Patrick Bürger, Ulrich Riebel * Lehrstuhl Mechanische Verfahrenstechnik (MVT), Brandenburgische Technische Universit€ at Cottbus-Senftenberg (BTU), 03013, Cottbus, Germany

A R T I C L E I N F O

A B S T R A C T

Keywords: Corona discharge Electrostatic precipitation Free electrons Electron temperature Ion mobility Diffusion charging

Electrostatic charging and deposition of a liquid nano-aerosol was studied in dry air and in technical (3.6 % O2) nitrogen. The experiments have shown that electronic charging of aerosols can be important in technical scale electrostatic precipitators (ESPs). Already at operation volt­ ages just slightly above the corona onset voltage, the contribution of the free electrons to the overall current is estimated to be around 50 %. Due to the high temperature of free electrons, diffusion charging by free electrons allows to reach exceptionally high particle charge and extremely high precipitation efficiency. A strongly simplified theoretical model was developed, which gives a good prediction of particle charge based on averaged values of particle diameter, current density, electric field strength, electron temperature and residence time. The ion mobilities were determined by fitting the current-voltage characteristics with a modified Townsend (Monrolin et al. 2018) equation and are significantly higher than the values typically used to describe diffusion charging in air. This may be ascribed to the very dry gas phase and the short average lifespan of the ions under ESP conditions, which is in the order of 1 ms. From the practical point of view, electronic charging might be relevant in a number of tech­ nical applications, including high temperature ESPs, ESP applications in dry and oxygen-free gases and pulsed corona systems.

1. Introduction In the field of gas cleaning by electrostatic precipitation (ESP), some results with exceptionally good performance are ascribed to particle charging by free electrons. Typical situations where a contribution of free electrons to particle charging is being suspected include, among others. � Particle charging and precipitation in ESPs with very small diameter (tube type) or electrode spacing (duct type) � Particle charging and precipitation with very high corona voltages not far below spark-over voltage, or in pulsed coronas. In many more applications, including negative corona discharges in non-electronegative gases, corona discharges at elevated

* Corresponding author. E-mail address: [email protected] (U. Riebel). https://doi.org/10.1016/j.jaerosci.2019.105495 Received 9 July 2019; Received in revised form 8 November 2019; Accepted 29 November 2019 Available online 3 December 2019 0021-8502/© 2019 Elsevier Ltd. All rights reserved.

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

temperatures, pulsed corona discharges (Fitch Drummond 1987) and barrier discharges (Zouzou Moreau 2011), we may suspect that the conditions for electronic charging are given. However, there is very little experience and very little systematic research on this question so far. Here we have observed particle charging by free electrons in a model situation using technical nitrogen as a gas atmosphere. We discuss the “symptoms” which allow identification of electronic charging experimentally, and we present a very straightforward calculation scheme suited for simple situations. 2. State of knowledge In the literature on atmospheric corona discharges and electrostatic precipitators (ESPs), it is generally assumed that the charge transport in the gas outside the active corona zone is achieved by the drift of positive or negative gas ions, depending on the polarity of the corona. Just as well, the kinetics of particle charging in ESPs is described with ions as charge carriers. On the other hand, it is well known that stable corona discharges of negative polarity can exist only in gases with a sufficient degree of electronegativity or in gas mixtures containing a sufficient fraction of electronegative gases (Raizer 1991; White 1963). In air at ambient and near-ambient temperatures, positive and negative gas ions are found as so-called cluster ions, whereby other, mainly polar molecules react with or condense on the naked ion, forming significantly larger and less mobile clusters. With ions or cluster ions as charge carriers, the current transport through the passive zone leads to the build-up of a significant space charge density in the passive zone. The potential drop caused by the space charge in the passive corona zone equals the voltage difference between the corona onset voltage and the operation voltage and stabilizes the corona current. The consideration of the ion space charge directly leads to the derivation of the typical current-voltage characteristic of coronas which is also known as Townsend equation. For wire-tube coronas, a simplified version of the Townsend equation, is written as: i ¼ Zi

8 π ε0 � � UðU R2T ln RRWT

(1)

U0 Þ

Here i is the current per length of corona wire, Zi the ion mobility, RW and RT are the radii of the corona wire and the tube, U is the voltage of operation, and U0 is the corona onset voltage. Eq. (1) is valid for the range of low currents only (Riehle in Parker 1997; Robinson 1971; White 1963), or more precisely, for the condition that the field from the ionic space charge is negligible compared to the static field from the corona wire, hence ðU U0 Þ << U. The full version of the Townsend equation requires some steps of iteration when the current has to be determined for a given voltage of operation. Recently, Monrolin et al. (2018) provided an improved analytical solution for the current-voltage characteristic of wire-tube coronas: 82 9 � 132 � 0 > > > > � � 1þUU = 2 < 0 2 π Zi ε0 U0 RW 6 B C7 2 i¼ þ W 2 e 1 (2) A 5 41 @ � �2 1 > > RT > > : ; RT 2 ln RT RW

W-1 is Lambert’s W-1 function. The Monrolin-Praud-Plourabou� e (MPP) equation was introduced for positive coronas, but is equally applicable for negative coronas as long as free electrons do not contribute significantly to the current. When electronegative gas components are missing, the free electrons produced in the active zone of the corona can cross the passive zone without binding to gas molecules. The mobility of free electrons is by a factor of about 200–400 higher compared to the mobility of gas ions (Hinds, 1999; Raizer 1991, p. 11), see also Table 4. Due to the high electron mobility, even high currents do not build up a considerable space charge. The high current leads to local heating of the gas, and the corona discharge develops into an arc discharge. As a consequence, stable corona discharges of negative polarity do not exist in highly pure non-electronegative gases like nitrogen, hydrogen, methane, noble gases etc.. The literature also contains a number of hints on the role of free electrons in corona discharges, for the charging of fine aerosol particles and for ESP operation. Penney and Lynch (1957) study particle charging in a tubular charger of small dimensions and find that particle charge is significantly higher with negative corona polarity. White (1963) discusses deviations from the standard current-voltage characteristic as given by the Townsend equation occurring with high current densities. White interprets this as the effect of free electrons contributing to the current and proposes an empirical correction for the current-voltage characteristic. Crynack and Penney (1974) study a two-stage process, with particle charging by a small wire-duct charger and deposition by a plate-plate-precipitator with different gas atmospheres. The difference of particle deposition between positive and negative charger polarity is used as an indicator for electronic charging. Leal Ferreira, Oliveira, and Giacometti (1986) compare current-voltage characteristics for positive and negative point-to-plane coronas in ambient air. Their finding is that an electronic component of the corona current can be found for point-to-plate dis­ tances of less than 6 cm in combination with high voltage differences. Investigations on corona discharges at higher temperatures are reported by several authors. McDonald, Anderson, Mosley, and Sparks (1980) investigate particle charge from a larger duct-wire charger as a function of particle diameter and temperature (up to 343 � C). The authors demonstrate that electronic charging should be considered for temperatures above 140 � C even in technical scale 2

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

installations. Weber, Hübner et al. (1981), Parker (Parker 1997, p. 508), Villot, Gonthier et al. (2010) present experimental results showing that the operation range of negative coronas (defined as the voltage difference between corona onset and spark-over voltage) reduces with increasing temperature and is nearly zero for temperatures above 400 � C. The effect of a higher temperature can be compensated by a higher gas pressure, but only within a limited temperature range, reaching up to about 700 � C. It is generally agreed that high temperatures reduce the affinity of electrons to electronegative gas molecules. Parker (Parker 1997, p. 501) states that the presence of extremely electronegative gases like HF stabilizes ESP operation with negative corona at temperatures of up to 800 � C. Own measurements (Riebel, Lübbert and Lebedynskyy, 2012) and results from Hara, Suehiro, Sumiyoshitani, and Akazaki (1988), including a wider range of temperatures and positive corona polarity, indicate that positive corona discharges at atmospheric pressure are feasible in a temperature range of up to 800 � C at least. Villot, Gonthier et al. (2013) present a simulation scheme for the charge transport in wire-tube coronas modelling both active and passive zone. The model for the formation of negative gas ions from free electrons includes the effects from the electrostatic field, different gas components and temperature. Measurements by Marquard, Meyer, and Kasper (2007) show particle charging and deposition of nanoparticles in a wire-tube ESP with small dimensions (diameters 0.025 m, 0.04 m) operated with positive and negative voltage. The efficiency of negative charging in relation to positive charging corresponds to the ratio of ion mobilities in the range of low and intermediate operation voltages. In the range of high operation voltages and high N⋅t-products, the efficiency of negative charging increases significantly over that of positive charging. This is interpreted as an effect of free electrons. Aliat, Tsai, Hung, and Wu (2008) show that an adapted simulation of the Marquard results can match the experimental points by including the contribution of free electrons. 3. Theoretical considerations Different from the typical situation when charging aerosols in air, we expect an additional contribution to particle charging from free electrons when the electronegativity of the gas or gas mixture is low, or when the temperature is high. Free electrons are produced in the active zone of the corona. In case of a negative corona, the electrons are driven away from the corona wire by the electric field forces. In collisions between gas molecules and free electrons, the formation of negative gas ions occurs by an attachment of the electrons to electronegative gas molecules. This is described by an attachment coefficient β which is a function of the gas or gas composition, the field strength and the temperature (Chen & Davidson, 2003; Raizer 1991). Simulations by Aliat et al. (2008), Aliat, Hung, Tsai, and Wu (2009) and by Villot, Gonthier et al. (2013) show that the range of electrons in air is quite short at typical ESP operation conditions (field E ¼ 2–5 kV/cm, temperature T < 500 K, 1 bar ab), amounting to a few millimeters only. In technical size ESPs with precipitation tube diameters or plate-plate-spacings above 0.1 m the range of electrons covers only a very small fraction of the flow cross section. This explains why electronic charging does not have much effect in technical size ESPs operated in air at atmospheric pressure and temperatures below 300 � C. However, with elevated temperatures or a change of the gas, the range of free electrons can be increased to several centimetres at least. This is the case as well in the present work. In air or nitrogen at ambient conditions (1 bar, 298 K), electrons have a mean free path of about 0.40 μm (Raizer 1991, p. 11), which is much more than the mean free path of gas molecules (0.066 μm) or of positive and negative gas ions (0.016 μm and 0.019 μm, resp.) (Wiedensohler, Lütkemeier et al., 1986). The high value of the electron mean free path λe allows the free electrons to accumulate a considerable amount of kinetic energy ΔWkin between two collisions when an electric field E is present: (3)

ΔWkin ¼ λe e E

Moreover, collisions between electrons and gas molecules are nearly elastic as long as the kinetic energy of the free electrons stays below a value of about 10 eV (Raizer 1991). Because of the huge mass difference between electrons and gas molecules, collisions lead to a change of the electron flight direction, but the transfer of kinetic energy in the collisions is very low. Therefore, the mean kinetic energy of free electrons in an electric field is somewhat higher compared to the value given by Eq. (3), while the angular distribution of electron velocities is uniform in a rough approximation. More detailed analyses including discussions of the distribution of electron energy are found in the literature. Results from Gallimberti (1988), Chen and Davidson (2003) are compiled in Fig. 1. In the range of moderate field strengths up to about 110 Td (corresponding to 30 kV/cm at 1 bar/300 K), the average kinetic energy of free electrons may be approximated by (4)

W kin ffi 3 λe e E

Further, following the equivalence Wkin ¼ 3=2 � k � T, we may define an electron temperature Te . As the collisional energy transfer between electrons and gas molecules is very inefficient, electron temperature can be distinct from gas temperature. This resembles the situation of a cold or non-thermal plasma (NTP), even though the passive zone of a corona discharge does not fulfil all conditions for the plasma state. The resulting relationship between electric field and electron temperature is: Te ¼

2 λe e E k

(5)

In a further step, we discuss the effect of free electrons on particle charging kinetics. Our discussion will be based on the traditional distinction between the mechanisms of diffusion charging and field charging. The authors are aware that more sophisticated ap­ proaches with a better prediction quality exist. However, here we prefer to discuss the impact of free electrons based on equations with a simple mathematical structure. Regarding diffusion charging, the energy needed to overcome the repulsion from the charges already being on the particle is 3

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

Fig. 1. Mean kinetic energy of free electrons and electron temperature as a function of the electric field E (in kV/cm). Part of the data is adapted from Gallimberti (1988) and Chen and Davidson (2003).

provided from the thermal energy of the charge carriers. In case of ions, gas molecules and gas ions are in thermal equilibrium due to frequent collisions with a high rate of energy transfer. Hence the thermal energies of ions and gas molecules are the same. However, in case of charging by free electrons, we have to consider the non-equilibrium kinetic energy of the electrons, or the electron temperature. For a qualitative discussion, we compare the kinetics of diffusion charging by gas ions and by free electrons, resp.. For simplicity, we use the kinetic formula given by White (White 1951, 1963) which implicitly is valid for the free molecular regime (λi ; λe >> dp ) only (Gentry & Brock, 1967; Marquard, 2006). The rate of particle charging by gas ions is given as � � dn dqp ci CN;i 1 n e2 ¼ ¼ π dp2 exp (6) dt e dt 2 π ε0 dp k T 4 Here, n is the number of elementary charges, qp is the particle charge, dp the particle diameter, ci is the average thermal velocity of the gas ions, CN;i is the ion number concentration, and ðci ⋅ CN;i Þ=4 is the flux of particles hitting a surface. The first part of this equation gives the number of molecules that would hit the surface of the particle in case that no energy barrier from electrostatic repulsion exists. The exponential term describes the depletion of ion concentration near the particle surface due to the repulsive force of the charges sitting on the particle already. By integration, White’s formula for the time dependent particle charge qp hti is found: � � dp k T 1 π e2 ln 1 þ (7) qp hti ¼ 2 π ε0 dp ci CN;i t e 8 π ε0 k T The above equations can be adapted to describe charging by free electrons, when we replace (i) the ion concentration by the electron concentration, (ii) the gas temperature T by the electron temperature Te , and the ion thermal velocity by the free electron velocity ce corresponding to the electron temperature: sffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 k Te 6 λe e E ce ¼ ¼ (8) me me Here me is the mass of the electron, me ¼ 9.1⋅10-31 kg ¼ 5.48⋅10-4 amu. While it is generally assumed that all ions reaching the particle surface deliver their charge to the particle, this is not the case for charging by electrons. Following Romay and Pui (1992) or Aliat et al. (2008) we introduce an empirical accommodation coefficient γ e representing that electrons attach to the particle with a probability lower than 1. For the rate of particle charging by freely diffusing electrons we obtain: � � dn dqp π dp2 1 n e2 ¼ (9) ¼ ce CN;e γ e exp dt e dt 2 π ε0 dp k Te 4

4

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

As the mean free path of electrons is much larger than that of ions, this equation should be valid for particles of up to about 500 nm in air at STP in case of electronic charging. For further calculations, it may be convenient to express the concentration of free electrons with CN;e hri ¼

je e Ehri Zel;e

(10)

where Zel;e is the electrical mobility of the free electrons and je is the area-related current density (A/m2) of electrons. Considering the mechanism of field charging, the kinetics is determined by the current density only (Pauthenier & Moreau-Hanot, 1932): " � � #2 π dp2 dn 1 ne εp 1 � � ¼ CN;i Zi E 1 þ 2 (11) dt 4 π ε0 dp2 εp þ 2 ε 1 E 1 þ 2 εpp þ 2 and there is a well-defined saturation charge qsat : � � dp2 εp 1 qsat ¼ 4 π ε0 1 þ 2 E εp þ 2 4

(12)

εp is the relative dielectric permeability of the particle material. Hence, at the first view there is no influence from the nature of the charge carriers onto the mechanism of field charging. In a more detailed model (which shall not be discussed here), we would also have to include that the kinetic energy of the free electrons allows to overcome a repulsive potential at the particle surface. For the description of the particle charging rate reached by a combination of diffusion charging and field charging, the Lawless model (Lawless, 1996) generally is a good approach (Lübbert and Riebel 2011a, 2011b; Marquard et al., 2007). However, when charge carriers with different mobility contribute to charging, this would lead to different, non-compatible definitions of dimensionless time and hence the application of the Lawless model is problematic. Therefore, we are going to use the following approach: With Eqs. (6), (9) and (11), the contributions from the three mechanisms to the charging rate are calculated separately for the actual value of the particle charge and for a short time step, and are added afterwards to serve as the basis for the next time step. This allows calculating both the charging rates from the different mechanisms as a function of the particle charge, and the particle charge as a function of time. This procedure is justified as follows: Eqs. (6), (9) and (11) separately describe the charging rates from diffusion charging by ions, diffusion charging by free electrons and field charging by ions. Diffusion charging by free electrons does not have any interference with charging by negative ions, because the conversion of free electrons into negative ions is comparatively slow. Hence, the charging rate by free electrons is additive to the charging rate by ions. As for ionic charging, the Lawless approach (Lawless, 1996) is based on assuming a superposition of diffusion charging (active on the entire particle surface) with field charging (active only in a part of the surface). Field charging decreases and finally disappears during the charging process. Lawless concludes that the simple addition of the field and diffusion charging rates provides an upper bond for the particle charge, which nevertheless may serve as a useful estimate of real particle charge. 4. Experimental setup The main motivation for the experiments presented here was to demonstrate that electronic charging may have an important role in industrial size ESPs under certain circumstances. Such circumstances can be, for example, the ESP operation at elevated temperatures and/or in non-electronegative gases. Typical examples for the latter might be the aerosol removal from biomethane, from hydrogen or from pyrolysis gases. Unfortunately, most of these conditions are difficult to handle in the lab. Therefore, we created a similar situation by observing ESP operation in a stream of technical nitrogen. Central part of the experimental set-up is a wire-tube ESP with a tube diameter of 0.1 m and an active length of 0.5 m. The corona electrode is made from a twisted pair of stainless-steel wires, with a diameter of 3∙10-4 m for the single wire. The twisted wire electrode is used in order to enhance the electrohydrodynamic mixing of the aerosol flow. In this way, the precipitation behaviour follows the Deutsch theory more closely even in case of low Re numbers and positive corona. The active part of the precipitation tube is insulated electrically from the adjacent tubing, hence the current from the precipitation tube can be measured separately and without bias from currents through the cable insulations. The current is measured with a res­ olution of 0.1 μA (1 μA for currents above 150 μA). The gas and the aerosol are introduced into a T-piece at the upper end of the precipitation tube, about 0.5 m above the beginning of the active precipitation zone. For the reference measurements in air, dry filtered compressed air (around 9 bars absolute pressure, dew point 26.9 � C at ambient pressure) was expanded to ambient pressure in order to avoid variations of relative humidity. For the measurements in nitrogen, the same compressed air was passed through a membrane module (DWT GmbH, Mod. RG101707) producing technical grade nitrogen. The volume flow of gas (limited by the maximum supply of technical nitrogen and including the volume flow going through the aerosol generator) was adjusted to 5.0 m3/h (1.39 ltr/s) at lab temperature (20 � C) using a calibrated gas meter and was kept the same 5

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

in all the experiments reported here. The resulting flow velocity was 0.177 m/s, resulting in Re ¼ 1155 (for air) and a residence time of 2.83 s in the active part of the ESP tube. The aerosol is produced from paraffin oil (boiling point range 350–500 � C) in a Laskin type nebulizer operated with the technical nitrogen at 4 bar absolute pressure. The volume flow of aerosol at STP is around 0.48 m3/h (0.13 ltr/s). The aerosol is directly mixed into the main stream consisting of expanded compressed air or of technical nitrogen. For the reference experiments without aerosol, the Laskin nebulizer is operated without liquid in order to avoid any influence on the composition or volume flow of the gas phase. Samples of technical nitrogen (extracted from the outlet of the membrane module) and of air were analyzed by gas chromatography (model HP 6890 Agilent Technol.; column Carboxen 1000, WLD) to determine the volume fraction of oxygen. Additionally, the dew point was measured using a dew point device (EþE Electronic, model EE35). The background concentration of aerosol in the ESP with the different gas atmospheres was measured by SMPS as described below. With 55 to 76 particle counts per cm3, the background aerosol is negligible. The composition of the gas samples is documented in Table 1. Right after leaving the active zone of the ESP, the clean gas passes through another T-piece (ensures a good mixing of the gas); the clean gas samples are extracted about 0.5 m after the end of the active zone. The raw gas samples are extracted in the same place, however with high voltage switched off. Directly at the sampling port, the aerosol samples (0.018 m3/h) are passed through a radioactive FCE (Faraday cup electrometer) as described by Lübbert (2011). In this device, the aerosol is neutralized by passing through an 241Am aerosol neutralizer. The neutralization reduces particle losses especially in case of highly charged aerosols. The neutralization current is measured, which allows to determine the space charge density of the aerosol. In combination with the number concentration from the SMPS measurements, the average charge per particle can be determined. The residence time between leaving the active zone of the ESP and entering the radioactive FCE is 3.43 s. Electrostatic dispersion (Kasper, 1981) leads to particles losses during sampling. Assuming that all particles have uniform diameter, charge and mobility, the particle loss is compensated by calculation. For the particle penetration results presented in this work, the losses amount to 9 % relative at maximum. For the overall separation efficiency, the sampling losses lead to a reduction of 1 % absolute at maximum. The separation efficiency curves are not corrected, because the mobility is diameter dependent. Aerosol measurements were executed using an SMPS system (Grimm model 5.416) in combination with an X-ray aerosol neutralizer (TSI model 3088) adapted to the Grimm system (Fig. 2). The DMA sample flow was 0.018 m3/h, the aerosol samples were not diluted. The DMA was operated with positive polarity, so that negative aerosol particles only would reach the particle counter. Fig. 3 shows cumulative number distributions of the aerosol in air and in technical nitrogen, resp.. The aerosol concentration and size distribution was quite stable throughout the measurements. The number concentration is close to 6∙106 cm-3 and the number median diameter is around d50;0 ¼ 220 nm. The length median diameter � � (Q1 d50;1 ¼ 0:5) which is required for some of the calculations, was determined as d50;1 ¼ 279 nm. The effect of the gas phase on the bipolar charging of the aerosol was a special point of attention. Experiments by Wiedensohler, Lütkemeier et al. (1986) had shown that bipolar charge distributions measured in nitrogen are much more asymmetrical than in air. Compared to air, negative charging should be more efficient (and positive charging should be less efficient) in nitrogen by about a factor of three, and hence one might expect considerably higher particle counts in the nitrogen atmosphere. However, the differences are below the limit of detection in the present case. The discrepancy is most probably explained by the fact that our results are obtained with a high aerosol concentration, while the Wiedensohler results were most probably obtained with a very low aerosol concentration. An explicit concentration value is not given in the publication, but the aerosol was a monodisperse aerosol produced by classification in a DMA. In case of a high aerosol concentration, non-symmetric charging would lead to the build-up of strong space charge fields. Hence the space charge of the aerosol will retain ions of opposite polarity so that aerosol neutrality is enforced. 5. Experimental results 5.1. Current-voltage-characteristics First, the current-voltage-characteristics were measured for both polarities in both (aerosol-free) gas atmospheres. The corona onset voltage U0 was determined as the lowest voltage giving a detectable current reading (0.1 μA or more). Table 2 shows that U0 slightly varies with the polarity and the gas composition. With the experimental values of U0 , the MPP equation is fitted to the measurements using the ion mobility Zi as fitting parameter. Further, with the onset electric field expression developed by the same authors, an “equivalent diameter” for the twisted-wire electrode is determined from the positive corona onset voltage in air. This diameter is 0.41 mm and will be used in all theoretical calculations. Fig. 4 shows current-voltage-characteristics measured in air and in techn. nitrogen both without and with aerosol. All curves start with the corona onset voltage (defined with a current of 0.1 μA) and end at 500 μA which was the current limitation. First we discuss the measurements for the aerosol free case. What we see is that the measurement points and the fitted MPP Table 1 Gas phase composition data. Oxygen Dew point Water

[Vol %] [� C] [g/m3]

6

Air

Nitrogen (techn.)

20.95 26.9 0.502

3.60 57.1 0.0201

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

Fig. 2. Adaptation of TSI 3088 X-ray aerosol neutralizer to Grimm 5.416 SMPS system.

Fig. 3. Cumulative, non-normalized size distributions of the aerosol. In all cases, the aerosol is produced by a Laskin nebulizer operated with techn. nitrogen (4 bar abs), while the main volume flow is air or techn. nitrogen, respectively. The number median diameter d50,0 is at 220 nm. Table 2 Variation of corona onset voltage (0.1 μA) as a function of gas atmosphere and aerosol condition. Gas atmosphere Air Nitrogen (techn.)

Positive corona aerosol-free with aerosol aerosol-free with aerosol

10.3 kV 10.5 kV 10.8 kV 11.1 kV

Negative corona 11.1 kV 11.2 kV 11.5 kV 11.5 kV

equation (the mobility values are given in the figure) are in pretty good agreement both for air and for technical nitrogen. For air, we see the typical result that the current is about 25 % higher for the negative corona in comparison to the positive corona. This difference is explained by the higher mobility of negative ions. The ion mobilities determined for air by fitting correspond to the values given in the literature for “very dry” air (Robinson 1971, Table III)]. In technical nitrogen, positive ion mobility is about 10 % higher compared to positive ion mobility in air. This difference can be explained by the different composition (lower humidity, in the first place) of the gas phase. For technical nitrogen, the nominal mobility of the negative charge carriers is more than twice as high compared to air or to positive gas ions in nitrogen. A possible explanation is as follows: The technical nitrogen certainly contains enough oxygen to form negative gas ions. The mobility of these ions should be similar to the mobility of the negative ions in dry air. These negative ions build up a space charge field which stabilizes the corona discharge. In case that free electrons are present in addition to the gas ions, an additional current will be produced. However, the contribution of the free electrons to the space charge is negligibly low. In the present case we 7

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

see that for a given voltage difference ΔU ¼ U U0 (equivalent to a certain level of overall space charge density) we find more than twice the current compared to the negative corona in air. This allows us to conclude that the fraction of current transported by free electrons can exceed 50 %. Remarkably, the quality of the fit is comparably good with both gases and both polarities. This allows us to conclude that in practice the MPP equation is applicable to both corona polarities. Looking more closely, it appears that the experimental current values are slightly above the fitted MPP curves in case of higher currents or operation voltages. This might indicate that the ion mobility itself is increasing with a higher voltage or a shorter time of passage between the electrodes. Concerning the experiments with aerosol, the liquid paraffin aerosol has the advantage that it forms a thin smooth film which flows down on the tube wall. The effect of this liquid film on the current-voltage characteristic is below the detection limit. A cleaning of the electrodes was not necessary. Fig. 4 also shows the influence of the aerosol on the current-voltage-characteristics (CVC) both in air and in technical nitrogen. In most cases, we find that the current uptake in the presence of aerosol (hollow symbols) is slightly lower compared to the current uptake in the aerosol-fee gas. Hence, the aerosol concentration is high enough to produce some degree of corona quenching. That is, the apparent corona onset voltages and the current-voltage curves are slightly shifted towards higher voltages. Only in case of the

Fig. 4. Current-Voltage characteristics measured in air (above) and in technical nitrogen (below) with both polarities in absence of aerosol (full symbols) and in presence of aerosol (hollow symbols). The curves are theoretical fits (based on full symbols) using the Monrolin-Praud-Plourabou�e equation with the experimentally determined onset voltage and the charge carrier mobility Zi as fitting parameter. 8

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

combination of the nitrogen atmosphere with negative corona, we find a distinctive deviation from the simple shift, which shall be discussed later. 5.2. Separation efficiency All aerosol size distributions used for the calculation of separation efficiency or particle penetration are averages from six mea­ surements (three up-scans and three down-scans). The standard deviations (in terms of number concentration) were 0.7 % for the raw gas measurements in air and 2.5 % for the raw gas measurements in nitrogen. The clean gas measurements have an averaged standard deviation of 4.1 % (in air) and 10 % (in nitrogen). Assuming that raw gas and clean gas measurement deviations are independent, the resulting standard deviation for particle penetration or separation efficiency, resp., is estimated to be around 4.2 % in air and 10.3 % in nitrogen. The separation efficiency for the electrostatic precipitation of the aerosol was measured with three different operating voltages: 12.0 kV; 12.5 kV and 13.0 kV. It might seem strange that only such a narrow range of voltages was investigated. Our reasons were as follows: (i) The voltage should be clearly above the corona onset voltage U0 , because the reproducibility of U0 is quite poor. Robinson (Robinson 1971) states

Fig. 5. Separation efficiency as a function of particle diameter for different operating voltages and both polarities. Together with the voltage, the current uptake is given. Results with air (above) and technical nitrogen (below). 9

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

that U0 values are poorly reproducible in many gases other than air. (ii) The clean gas should still contain a sufficient quantity of particles to allow reliable measurements of number concentration, particle size distribution and particle charge. As the precipitation efficiency with the negative corona in technical nitrogen was extremely high, comparative measurements were feasible only in this very narrow range of operating voltages. Fig. 5 shows separation efficiency curves with air and technical nitrogen. In addition, the particle number penetration rates for all combinations are summarized in Fig. 6, which were corrected for space charge precipitation loss as described above. The original measurement results for aerosol number concentration and space charge density are shown in Table 3. In air, we see the typical behaviour with a shallow minimum of the separation efficiency in the size range between 100 nm and 300 nm, which is associated with the famous minimum in the electrical mobility curve (Hinds, 1999). In the particle size range below 30 μm the separation efficiency shows an irregular behaviour with strong statistical variations. Mainly two reasons contribute to this: (i) the raw gas concentration is very low in this size range, compare Fig. 3 (ii) Traces of organic vapours (e.g. paraffin). are oxidized or oligomerized by radicals from the corona discharge, which finally leads to the condensation of new particles. Similar processes are observed in the atmosphere under solar UV irradiation (Hallquist, Wenger et al., 2009). As the kinetics of particle formation is quite slow, a fraction of the particles may be formed in the clean gas after leaving the ESP (Mnich and Riebel 2008). In absolute numbers, the concentrations of newly formed particles are very low. But the effect on the separation effi­ ciency curve is strong, because the original aerosol contains only few particles in the same size range. In technical nitrogen, the behaviour with the positive corona is quite comparable to the behaviour with the positive and negative coronas in air. Differences like the ones between positive corona in air (at 12.0 kV/19.8 μA) and positive corona in technical nitrogen (at 12.0 kV/13.2 μA) probably can be ascribed to slight variations of U0 , of the voltage setting and readout (resolution 0.1 kV) or of the raw gas concentration. In the combination of technical nitrogen with the negative corona, the lowest voltage setting ( 12.0 kV/3 μA) does already lead to a good separation efficiency in relation to the extremely low current uptake of 3 μA only. Remarkably, we do not see a separation minimum in this case. We may explain this with Eq. (9), indicating that the charging velocity dn=dt is proportional to d2p in the initial stages while the charge on the particles is still low (low means, the energy of electrostatic repulsion is low compared to the thermal energy of the electrons). The second lowest voltage setting ( 12.5 kV/21 μA) shows a low particle penetration (around 0.1 %) in technical nitrogen while the comparable setting for negative corona in air ( 12.5 kV/32 μA) has a much higher particle penetration (6.4 %) in spite of the higher current uptake. The highest voltage setting ( 13.0 kV/70 μA) with negative corona in technical nitrogen features an extremely low particle penetration of 2.8∙10-5 with a total particle count of only 180 cm-3 in the clean gas. As Fig. 7 shows, the size distribution still cor­ responds to the original raw gas distribution. However here as well, the clean gas concentration of fine particles below 100 nm appears to be augmented by a small number of newly formed particles. 5.3. Particle charge Fig. 8 shows the average number of charges per particle for the clean gas aerosol. For each parameter combination, three values are presented: (i) nFCE : The experimental values nFCE are determined from the space charge density by FCE measurements divided by the number concentration from SMPS measurements in the clean gas. (ii) nPP : The experimental values nPP are derived on the basis of the Deutsch equation, using the particle number penetration CN = CN0 (shown in Fig. 6), and the length median particle diameter (d50;1 ¼ 279 nm) as an input:

Table 3 Original data of aerosol number concentration, aerosol space charge density and average charge per particle measured in the raw gas and the clean gas by radioactive FCE and SMPS. Type of Aerosol

CN [1/cm3]

ρel [pA∙s/cm3]

nFCE [-]

Raw gas (mean) Air

5.93∙106 6.19∙105 6.24∙105 4.15∙105 3.74∙105 3.83∙105 3.43∙105 7.74∙105 1.44∙106 4.24∙105 6.28∙103 2.64∙105 1.69∙102

0.22 2.02 1.78 1.43 1.29 1.37 1.25 2.27 1.93 1.47 0.05 0.93 0.002

0.23 20.4 17.8 21.5 21.5 22.4 22.8 18.3 8.3 21.6 49.7 22.0 73.9

Air Air Nitrogen (techn.) Nitrogen (techn.) Nitrogen (techn.)

þ12.0 kV 12.0 kV þ12.5 kV 12.5 kV þ13.0 kV 13.0 kV þ12.0 kV 12.0 kV þ12.5 kV 12.5 kV þ13.0 kV 13.0 kV

10

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

Fig. 6. Particle penetration in air and technical nitrogen (number-based, with correction for space charge precipitation loss) corresponding to the separation efficiency curves shown in Fig. 5.

Fig. 7. Cumulative number distribution (CND) of raw gas aerosol and clean gas aerosol in comparison for precipitation in technical nitrogen with negative corona at 13.0 kV. The number median diameters (d50,0) are 214 nm for raw gas #2 and 149 nm for the clean gas, resp..

nPP ¼

wel 3 π η d50;1 Emean Cu e

(13)

Here Cu is the Cunningham factor and wel is the migration velocity of the electrically charged particles in the averaged electrostatic field Emean : wel ¼

lnðCN =CN0 Þ V_ APE

(14)

Here, V_ is the volume flow of gas and APE the active area of the precipitation electrode. (iii)

P

P nth : Further, theoretical values nth are shown, which are derived on the basis of ionic diffusion charging, electronic diffusion charging and field charging, again using the length median particle diameter (d50;1 ¼ 279 nm) as an input. The details of this procedure will be explained in the discussion.

What we can see is that. � Generally, the different particle charge values are quite close together. � Generally, the nFCE values are slightly higher than the other values. 11

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

Fig. 8. Number of elementary charges per particle in air and technical nitrogen for both polarities. nFCE is determined from Faraday cup elec­ trometer measurements. nPP is determined from the corrected efficiency of particle precipitation via the Deutsch equation. Σnth is a theoretical prediction, whereby the contributions from the different charging mechanisms (ionic diffusion ch., field ch., electronic diffusion charging) are shown.

� For the case of negative corona in technical nitrogen, the charge values are much higher for 12.5 kV and 13.0 kV, but not for 12.0 kV. The increase of particle charge with increasing voltage is much more pronounced than in the other cases. A more detailed discussion of these findings will be given below. 6. Interpretation and discussion In the following section, a more profound analysis of different aspects of the experimental findings will be undertaken. 6.1. Ion mobilities In the first place, we have found much higher ion mobilities from the current-voltage characteristics in the ESP (see Fig. 4) compared to the values which are commonly in use for describing unipolar or bipolar diffusion charging of aerosols (Reischl et al., 1996; Wiedensohler, Lütkemeier et al., 1986). Hence, ion mass and thermal speed of ions will differ from the commonly used values as Table 4 Overview of charge carrier mobilities, masses and thermal velocities. The fat values are used for the theoretical calculations. Ion mobilities designated with “CVC” are the experimental values extracted from the current-voltage characteristics in Fig. 4. Ion masses are readings from Fig. 9. The Adachi (1985) and Mohnen (1977) values are cited from Reischl (1996). The bracketed values are lacking an experimental basis. Charge Carrier

El. Mobility Zi [10-4 m2/(V∙s)]

Mass [amu]

Electron (Raizer 1991, p. 11, p. 11) Pos. Ion/Air (Adachi 1985; Mohnen 1977) Pos. Ion/Air/CVC Pos. Ion/N2 (techn.)/CVC Neg. Ion/Air (Adachi 1985; Mohnen 1977) Neg. Ion/Air/CVC Neg. Ion/N2 (techn.)

592 1.40 1.80 2.01 1.90 2.54 (2.54)

5.48∙10-4 130 115 85 100 55 (55)

12

Therm. Velocity ci@ 293 K, [m/s]

252 293 365 (365)

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

well. In order to find appropriate values for our calculations, we have correlated ion mass and ion mobility values available from €, Karch, & Necid, various sources in literature (Fews, Holden, Keitch, & Henshaw, 2005; Huertas & Fontan, 1975; Reischl, M€ akela 1996), which is shown in Fig. 9. Table 4 shows the ion mobilities from the current-voltage characteristics (CVCs) together with the ion masses read from Fig. 9. For the negative corona in technical nitrogen, a charge carrier mobility of 5.82∙10-4 m2/(V∙s) was found with the MPP fit. However, Fig. 9 shows that such a mobility value is not at all plausible: Even “naked” O2 ions got a molecular weight of 32 amu and an electrical mobility below 3.0∙10-4 m2/(V∙s) should be expected. In default of better data, we assume that the mobility of neg. ions in technical nitrogen is equal to the mobility of neg. ions in air (2.54∙10-4 m2/(V∙s)). Possibly the real mobility is higher by about 10%, as the humidity in techn. nitrogen is lower than in air. The data from Table 4 shall be used in the further calculations. 6.2. Corona quenching in techn. Nitrogen with negative corona Second, looking for the particle separation curves and the particle penetration results, it seems contradictory that negative charging in technical nitrogen produces outstandingly high values of particle charge at 12.5 kV and 13.0 kV, but a low value only at 12.0 kV. To discuss this, we look at the details of the current-voltage curves measured in nitrogen which are shown in Fig. 10. We find that 12.0 kV is very close to the corona onset voltage of the negative corona in technical nitrogen ( 11.5 kV), and that the current uptake in the presence of aerosol is very low (0.4 μA) compared to the value without aerosol (39 μA). The suppression of corona current in presence of high aerosol concentrations is known as corona quenching. As the ratio of currents with aerosol and without aerosol is below 0.05, the regime of operation at -12 kV is strongly quenched (Lübbert and Riebel 2011a, 2011b). In the strongly quenched regime, the space charge of the negative ions and/or electrons is negligible compared to the space charge of the aerosol particles, and hence the particle space charge density ρel;p is limited by the difference between operation voltage and onset voltage:

ρel;p ¼

4 ε0 ΔU R2T R2W

(15)

Eq. (15) includes the assumptions that (i) the ionic space charge is negligible compared to particle space charge (which is verified by the low value of current uptake) and that (ii) the particle space charge is distributed uniformly within the aerosol volume or, that the mixing of flow by EHD flows is much faster compared to the drift velocity of the charged aerosol in the electrostatic field. With a ΔU of 500 V and a raw gas particle concentration of 5.93∙106/cm3 (see Table 3, line 1) we find that the particle space charge density is limited to 7.09 pA/cm3. When the space charge density is divided by the number concentration, we find 7.5 elementary charges per particle. This corresponds quite well with the result from the FCE measurement (8.3 charges/particle). A further, necessary condition to get corona quenching is that the aerosol charging kinetics (for single particles or low particle concentration) must allow to reach or to surpass the limiting space charge density from Eq. (15). As Fig. 8d (Nitrogen, 12.0 kV, neg. P corona) shows, this is the case. The estimation for single particle charging, nth , amounts to 18 elementary charges per particle, while the space charge limit is reached with 7.5 charges already. In the further discussion (compare Fig. 11) we shall understand that the P contribution from electronic diffusion charging is decisive to reach such high values of nth . Hence, the fast kinetics of electronic charging (see below) explains that corona quenching is much stronger with negative corona compared to positive corona, compare Fig. 10.

Fig. 9. Correlation between ion mass and ion electric mobility from different sources, including positive and negative polarity. The Adachi (1985) and Mohnen (1977) values are cited from (Reischl et al., 1996).

13

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

Fig. 10. Influence of the aerosol on the current-voltage characteristics for both polarities in technical nitrogen (detail from Fig. 4).

6.3. Charging by free electrons Third, we apply the theoretical considerations on particle charging by free electrons in order to analyse the charging results in technical nitrogen with negative polarity. As stated already in the discussion on the current-voltage characteristics for the particle-free gas phases, it appears that free electron contribution accounts to roundabout 50 % of the total current density in case of the negative corona in technical nitrogen. Based on the rate of electronic current to ionic current, we can compare the charging rate by electrons to that by gas ions. To do this, Eq. (11) is divided by its twin for ionic charging, Eq. (6), for a given particle diameter dp and a given number n of charges on the particle: �� �� �� dne =dt ce CN;e γe 1 Te Ti n e2 exp (16) ¼ k Te Ti dp 2 π ε0 dni =dt ci CN;i The first term may be rearranged as rffiffiffiffiffiffirffiffiffiffiffi ce CN;e je ce Zel;i je mi Te Zel;i γe ¼ γe ¼ γ ci CN;i ji ci Zel;e ji me Ti Zel;e e

(17)

where Zel is the electrical mobility. je and ji are the area-related current densities of ions or free electrons, respectively. With the numerical values for the mass of the electron, me ¼ 9.1⋅10-31 kg ¼ 5.48⋅10-4 amu, the mass of the ion mi ¼ 55 amu (Table 4) the electrical mobility of the electron Zel;e ¼ 592∙10-4 m2/(V∙s) (Raizer 1991, p. 11) in air at 298 K and with the negative ion mobility in air Zel;i ¼ 2.54∙10-4 m2/(V∙s) according to our own measurements, we finally find the ratio of charging rates as: rffiffiffiffi �� �� �� dne =dt je Te 1 Te Ti n e2 γ e exp (18) ¼ 1:36 dni =dt ji k Te Ti dp 2 π ε0 Ti This relation is valid for combined charging by free electrons and negative ions in air or nitrogen at atmospheric pressure and ambient temperature (298 K), whereby the temperature of free electrons depends on the electric field according to Eq. (5). The temperature of the ions is identical to the gas temperature. As a result, we see that the relative importance of electronic charging is growing fast when the electron temperature is high and the charge on the particle is increasing. A nominal value of the electron contribution to the current is obtained as follows: We assume that the contribution of electrons to the space charge is negligible because the electron mobility is much higher than the ion mobility. Second, we use a simplified approach, assuming that the ratio of electronic to ionic current is constant along the radius coordinate. Third, we assume that the Table 5 Total current I, current contribution Ie from electrons for neg. corona and electronic current share for different voltages are based on the CVCs for air and nitrogen shown in Fig. 4. Average electron temperature Te in technical nitrogen at four different voltages is based on Eq. (5). Voltage [kV]

Total Current I [μA]

Electronic Current Ie [μA]

12.0 39 10 12.5 75 29 13.0 112 49 16.0 443 230 Electronic contribution from apparent charge carrier mobilities

14

Electron. Curr. Contrib. Ie/I [-]

Electron Temp. Te [K]

0.256 0.387 0.438 0.519 0.564

2228 2320 2413 2971 –

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

mobility of negative gas ions in air and in nitrogen is approximately equal. Hence, we estimate the electronic current as the current value in nitrogen minus the current value in air for a given voltage with negative polarity and aerosol-free conditions (see Fig. 4). Table 5 gives an overview of the current contributions for the negative corona in nitrogen at four different voltages. The calculations indicate an electronic contribution decreasing from 52 % to 25 % with the voltage decreasing from 16.0 kV to 12.0 kV. Quite certainly, this calculation scheme gives an underestimation of the electronic contribution especially for the lower values of voltage, because the calculation does not incorporate the higher value of the corona onset voltage in technical nitrogen compared to air (see Table 2). On the other hand, the calculation neglects that the mobility of neg. ions in technical nitrogen probably is slightly higher than in air. This might lead to an overestimation of the electronic contribution. As an alternative, an average value of the electronic contribution might be estimated from the charge carrier mobilities given in Fig. 4. Assuming once again that negative ions have the same mobility in air and in technical nitrogen, the electronic contribution would be found as: Ie Zi;neg;N2 Zi;neg;air 5:82 2:54 ¼ 0:564 ¼ ¼ 5:82 Itot Zi;neg;N2

(19)

The advantage of this calculation scheme is that the variations of U0 have already been considered in the fitted current-voltage characteristics obtained with the MPP equation. Therefore, this value is used for the calculations of electronic charging. Further we assume that the electronic charging occurs by non-thermal free electrons according to Eq. (5). For example, with an average field of 2.6 kV/cm (at U ¼ 13.0 kV) we expect an electron temperature of around 2413 K. 6.4. Prediction of particle charge For the numerical prediction of the particle charge, the contributions from field charging, ionic charging and free electron charging have to be added appropriately. To do so, the three contributions are calculated for a given value of the particle charge and a short time step (non-integer numbers of elementary charges are admitted). By a stepwise integration, the particle charge can be determined as a function of time. Also, the charging rate for each of the mechanisms can be given as a function of the actual particle charge. The calculations are executed in a strongly simplified way: Charging is predicted for one representative particle diameter (which is d50;1 ¼ 279 nm as long as diffusion charging is predominant [Lübbert, 2011; Lübbert & Riebel, 2011a]). The values of electric field, current density, electron temperature etc. are taken for the average radius (rav ¼ 0.025 m); the time for charging is the average residence time. The accommodation coefficient γe for electron attachment was used as an adaptation parameter and was varied from 0.0 to 0.6 in steps of 0.001. Finally, γ e ¼ 0.05 was used for all calculations, giving a good fit for measured total particle charge. Fig. 11 gives insight into the kinetics of particle charging for the example of 13.0 kV in technical nitrogen, including a 56.4 % share of electronic current. In the beginning, at zero particle charge, diffusion charging by ions is the dominating mechanism. Field charging by ions and diffusion charging by free electrons contribute much less. However, field charging and diffusion charging by ions drop sharply while the particle charge increases. Beyond about 11 elementary charges, diffusion charging by free electrons is the only relevant mechanism. This corresponds to the theoretical considerations discussed above. P Going back to Fig. 8, we find that the theoretical predictions of the particle charge ( nth ) meet quite well with the experimental values from the Faraday Cup Electrometer (nFCE ) and the values calculated from particle precipitation (nPP ) with the assumption of Deutsch theory - in spite of the gross simplifications that have been made. For positive and negative corona with air, and for positive

Fig. 11. Charging rate from different mechanisms for the example of 13.0 kV neg. corona in technical nitrogen; particle diameter d50,1 is 279 nm. Gas temperature: 293 K, electron temperature: 2413 K, electronic current share 0.56, γe ¼ 0.05. 15

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

corona with technical nitrogen, we find that diffusion charging by positive or negative gas ions is the predominant charging mech­ anism, while field charging contributes only about 10 % to the final particle charge. With negative corona in technical nitrogen, we find that electronic charging contributes 89 %–93 % of the final charge in the experiments with 12.5 kV and 13.0 kV, respectively. With a growing voltage and a growing share of electronic charging, the total number of charges rises sharply, while the absolute number of charges contributed from ionic charging and field charging decreases. The increase of particle charge with increasing voltage is much more pronounced than in case of ionic charging. The reason is that with increasing voltage not only the current density is increasing (just as in case of ionic charging), but also the electron temperature is going up. In case of the experiment with 12.0 kV in technical nitrogen, the value predicted from charging kinetics is nearly twice the value found experimentally and about twice the value corresponding to the space charge limit (Eq. (15)). Again, this is in agreement with the previous statement that the corona discharge was operated in the quenched state. In fact, the quenched state can be reached only in case that the charging kinetics allows for a higher particle charge than the space charge limit. 7. Conclusions Experiments in air and in technical nitrogen (with about 3.6 % of oxygen and very low humidity) have shown that electronic charging of aerosols can be important in technical scale electrostatic precipitators (ESPs). In technical nitrogen, the contribution of the free electrons to the overall current is estimated to be in a range between 25 % and 56 % already at operation voltages just slightly above the corona onset voltage. Due to the high temperature of free electrons, diffusion charging by free electrons allows to reach exceptionally high particle charge and extremely high precipitation efficiency within a short time. Further, the ion mobilities observed in the ESP experiments are significantly higher than the values typically used to describe diffusion charging in air. This may be ascribed to the very dry gas phase and to the short average lifespan of the ions under ESP conditions, which is in the order of 1 ms. A strongly simplified theoretical model was developed, which predicts particle charge quite precisely based on averaged values of particle diameter, electric field strength and residence time. For diffusion charging by free electrons, the electronic share of current density and the electron temperature have to be considered. From the practical point of view, electronic charging might be relevant in a number of technical applications, including high temperature ESPs, ESP applications in dry and oxygen-free gases and pulsed corona systems. Declaration of competing interest None. Acknowledgement This research is a part of the project “Einsatz elektrohydrodynamisch getriebener Str€ omungen zur erweiterten Nutzung von Elektroabscheidern” (Utilization of EHD driven flows for extending the applications of electrostatic precipitators) with financial support from the European Union under grant EFRE-StaF 23035000, which is gratefully acknowledged. Further, the authors would like to express their gratitude to Mr. Florian Dubrau for executing the measurements and to Dr. Andreas Marquard for helpful comments. References Aliat, A., Hung, C.-T., Tsai, C.-J., & Wu, J.-S. (2009). Implementation of Fuchs’ model of ion diffusion charging of nanoparticles considering the electron contribution in dc-corona chargers in high charge densities. Journal of Physics D: Applied Physics, 42, 125206. Aliat, A., Tsai, C.-J., Hung, C.-T., & Wu, J.-S. (2008). Effect of free electrons on nanoparticle charging in a negative direct current corona charger. Applied Physics Letters, 93. https://doi.org/10.1063/1.2967470, 154103. Chen, J., & Davidson, J. H. (2003). Model of the negative DC corona plasma: Comparison to the positive DC corona plasma. Plasma Chemistry and Plasma Processing, 23, 83–102. Crynack, R. R., & Penney, G. W. (1974). Charging of fine particles in negative corona near sparkover. IEEE Transactions on Industry Applications, IA-10, 524–530. Fews, A. P., Holden, N. K., Keitch, P. A., & Henshaw, D. L. (2005). A novel high resolution small ion spectrometer to study ion nucleation of aerosols in ambient indoor and outdoor air. Atmospheric Research, 76, 29–48. Fitch, R. A., & Drummond, J. E. (1987). Enhanced charging of fine particles by electrons in pulse-energised electrical precipitators. IEEE Proceedings, 134, 37–44. Gallimberti, I. (1988). Impulse corona simulation for flue gas treatment. Pure and Applied Chemistry, 60, 663–674. Gentry, J., & Brock, J. R. (1967). Unipolar diffusion charging of small aerosol particles. The Journal of Chemical Physics, 47, 64–69. https://doi.org/10.1063/ 1.1711892. Hallquist, M., Wenger, J. C., Baltensperger, U., et al. (2009). The formation, properties and impact of secondary organic aerosol: Current and emerging issues. Atmospheric Chemistry and Physics, 9, 5155–5236. Hara, M., Suehiro, J., Sumiyoshitani, S., & Akazaki, M. (1988). Modes and characteristics of corona discharge in high-temperature air. Electrical Engineering in Japan, 108, 10–20. Hinds, W. C. (1999). Aerosol technology: Properties, behavior, and measurement of airborne particles (2nd ed.). London: Wiley-Interscience. Huertas, M. L., & Fontan, J. (1975). Evolution times of tropospheric positive ions. Atmospheric Environment, 9, 1018–1026. Kasper, G. (1981). Electrostatic dispersion of homopolar charged aerosols. Journal of Colloid and Interface Science, 81, 32–40. Lawless, P. A. (1996). Particle charging bounds, symmetry relations and analytic rate model for the continuum regime. Journal of Aerosol Science, 27, 191–215, 10.1016/0021-8502 (95)00541-2.

16

Journal of Aerosol Science 141 (2020) 105495

P. Bürger and U. Riebel

Leal Ferreira, G. F., Oliveira, O. N., & Giacometti, J. A. (1986). Point-to-plane corona: Current-voltage characteristics for positive and negative polarity with evidence of an electronic component. Journal of Applied Physics, 59, 3045–3049. Lübbert, C. (2011). Zur Charakterisierung des gequenchten Zustandes im Elektroabscheider [Characterization of the quenched state in electrostatic precipitators]. Doctoral Dissertation, BTU Cottbus. https://opus4.kobv.de/opus4-btu/frontdoor/index/index/docId/2285. Lübbert, C., & Riebel, U. (2011). Corona Quenching – elektroabscheider bei hohen Aerosolkonzentrationen [Corona quenching – electrostatic precipitators operated at high aerosol concentration]. Chemie Ingenieur Technik, 83(4), 525–534. Lübbert, C., & Riebel, U. (2011). Electrostatic precipitator operation at corona quenching conditions – theory, simulation and experiments. Journal of Plasma Environmental Science and Technology, 5, 196–201. Marquard, A. (2006). Unipolare Aufladung nanoskaliger Aerosolpartikeln bei hohen Ladungstr€ agerdichten [Unipolar charging of nanoscale aerosol particles at high charge carrier density]. Doctoral Dissertation. Cuvillier Verlag, G€ ottingen: Universit€ at Karlsruhe (TH). Marquard, A., Meyer, J., & Kasper, G. (2007). Unipolar field and diffusion charging in the transition regime—Part II: Charging experiments. Aerosol Science and Technology, 41(6), 611–623. https://doi.org/10.1080/02786820701272061. McDonald, J. R., Anderson, M. H., Mosley, R. B., & Sparks, L. E. (1980). Charge measurements on individual particles exiting laboratory precipitators with positive and negative corona at various temperatures. Journal of Applied Physics, 51, 3632–3643. Mnich, R., Riebel, U., & Toshev, P. (2008). Bio-elektrische Gasreinigung mit "BEGA" [Bio-electric gas cleaning with „BEGA“]. Gefahrstoffe Reinhaltung der Luft, 68, 167–172. Monrolin, N., Praud, O., & Plourabou� e, F. (2018). Revisiting the positive DC corona discharge theory: Beyond Peek’s and Townsend’s law. Physics of Plasmas, 25. https://doi.org/10.1063/1.5031780, 063503. Parker, K. R. (Ed.). (1997). Applied electrostatic precipitation. Dordrecht: Springer Netherlands. Pauthenier, M., & Moreau-Hanot, M. (1932). La charge des particules sph�eriques dans un champ ionis� e. J. Phys. Radium, 3, 590–613. https://doi.org/10.1051/ jphysrad:01932003012059000. Penney, G. W., & Lynch, R. D. (1957). Measurement of charge imparted to fine particles by a corona discharge. AIEE Transaction, 76, 294–299. Raizer, Y. P. (1991). Gas discharge physics. Berlin Heidelberg: Springer-Verlag. Reischl, G. P., M€ akel€ a, J. M., Karch, R., & Necid, J. (1996). Bipolar charging of ultrafine particles in the size range below 10 nm. Journal of Aerosol Science, 27, 931–949. Riebel, U., Lübbert, C., & Lebedynskyy, S. (2012). Elektroabscheider - Es gibt noch viel zu tun [Electrostatic precipitation – so much is left to do]. Chemie Ingenieur Technik, 84, 1099–1113. Robinson, M. (1971). Electrostatic precipitation. In W. Strauss (Ed.), Air pollution control, Part 1. New York: Wiley-Interscience, 227 - 335. Romay, F., & Pui, D. Y. H. (1992). Free electron charging of ultrafine aerosol particles. Journal of Aerosol Science, 23, 679–692. Villot, A., Gonthier, Y., Gonze, E., & Bernis, A. (2010). Numerical model of current-voltage curve for the wire-cylinder electrostatic precipitators in negative voltage in the presence of nonpolar gases. IEEE Transactions on Plasma Science, 38, 2031–2040. Villot, A., Gonthier, Y., Gonze, E., & Bernis, A. (2013). Effect of the experimental parameters on the number of free electrons in the drift region of a wire-cylinder electrostatic precipitator. Journal of Electrostatics, 71, 815–822. Weber, E., Hübner, K., Pape, H.-G., & Schulz, R. (1981). Gas cleaning under extreme conditions of temperature and pressure. Environment International, 6, 349–360. White, H. J. (1951). Particle charging in electrostatic precipitation. AIEE Transaction, 70, 1186–1191. White, H. J. (1963). Industrial electrostatic precipitation. Reading, MA: Addison-Wesley Publishing Company, Inc. Wiedensohler, A., Lütkemeier, E., Feldpausch, M., & Helsper, C. (1986). Investigation of the bipolar charge distribution at different gas conditions. Journal of Aerosol Science, 17, 413–416. Zouzou, N., & Moreau, E. (2011). Effect of a filamentary discharge on the particle trajectory in a plane-to-plane DBD precipitator. Journal of Physics D: Applied Physics, 44, 285204. https://doi.org/10.1088/0022-3727/44/28/285204.

17