Unipolar field charging of particles by electrical discharge: effect of particle shape

Aerosol Science 35 (2004) 965–979www.elsevier.com/locate/jaerosci

Unipolar eld charging of particles by electricaldischarge: e(ect of particle shape

L. Ungera, D. Boulaudb, J.P. Borraa ;∗

aLaboratoire de Physique des Gaz et des Plasmas, Equipe D�echarges Electriques et Environnement,UMR 8578 du CNRS, Ecole Sup�erieure d’Electricit�e, Plateau de Moulon,

Gif-Sur-Yvette Cedex 91192, FrancebInstitut de Radioprotection et de Suret�e Nucl�eaire, IPSN/DPEA/SERAC, BP 68,

Gif-Sur-Yvette Cedex 91192, France

Received 17 January 2003; accepted 23 January 2004

Abstract

In order to control the properties of the pollutant particles (diameter, charge, concentration, aerosol 4ow rate)to be collected in a coagulation device, a corona charger (negative wire cylinder discharge) has been designedand tested. This paper presents results of di ethyl hexyl sebacat (DEHS) and NaCl particle charging in a coronadischarge. The aerosol particles are charged in a high electric eld (¿ 106 Vm−1) so as to check the validityof the eld charging law. A special care is taken to characterise accurately the discharge, to calculate, for eachexperimental condition, the gaseous ion density and electric eld in which particles get charged. The rst pointis that the eld charging law ts well with experimental charging data for spherical particles in the intermediatesize range (0.44–1:13 �m). Nevertheless, for cubic NaCl particles in the same charging conditions (i.e. iondensity and transit time), the experimental charge level appears to be greater than predicted by classical eldcharging law. The only di(erence between DEHS and NaCl particles seems to be the particle shape, that couldlead to an increase of saturation charge in the case of cubic particles, due to local electric eld enhancement.? 2004 Elsevier Ltd. All rights reserved.

Keywords: Corona discharge; Field charging; Particles shape

1. Introduction

In the context of electro-coagulation of sub-micron-sized particles on bigger oppositely chargedparticles, a corona charger has been designed and calibrated. Indeed, one needs to control boththe sub-micron-sized particles and the micron-sized water droplets physical characteristics (sizes,

∗ Corresponding author. Tel.: +33-1-69-85-17-91; fax: +33-1-69-41-03-34.E-mail address: [email protected] (J.P. Borra).

0021-8502/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.jaerosci.2004.01.006

mailto:[email protected]

966 L. Unger et al. / Aerosol Science 35 (2004) 965–979

charges, concentrations, and relative velocity) to know the coagulation conditions and be able todetermine which parameters are important to control the coagulation eDciency. This paper focuseson the wire–cylinder corona charger using negative electrical discharge. Charging of particles inunipolar gaseous ion density is usually described in terms of di(usion charging (e(ect of thermalagitation of ions, preponderant for small particles and/or low applied electric elds, see Bricard,1949; White, 1963, Chapter 5) and eld charging preponderant for larger particles and higher electric elds (e(ect of ion 4ux due to an applied electric eld; see Pauthenier & Moreau-Hanot, 1932).Here, approximations underlying eld charging theory are met: electric elds are above 106 V=mand particles size ranges from 0.47 to 1:13 �m.It has to be emphasised that besides the theoretical works on the mathematical expressions, an

other way is useful to study the charging laws: one can use the existing charging law and determineaccurately the charging conditions met experimentally by particles, in order to compare experimentaland theoretical levels of charge (see Gallimberti, 1997 for instance). Indeed, in most cases, experi-mental charging conditions are not accurately de ned and/or are taken as average values of the veryinhomogeneous physical conditions.One important physical parameter is not included in these laws: the shape of particles. Almost all

airborne particles are non-spherical, especially pollutants to be removed in electrostatic precipitator.Experimental data have to be collected on non-spherical particles in order to take into account thisparameter in charging laws. In the context of asbestos removal, a few studies have been done, bothexperimental and theoretical (see Han & Gentry, 1993), but only for di(usion charging. Moreover,these studies concern brous aerosol, and models are based on cylindrical shape. Data on moreregular shape are needed to develop models. To our knowledge, no study have been made on thee(ect of particle shape on the eld charging level. We meet here the experimental conditions requiredto apply the eld charging law, so we are able to (i) verify the charging law on spherical particlesand (ii) test the e(ect of particle shape on their level of charge.The rst part of this paper gives a brief call-back of the eld charging law, and of the physical

approximations allowing to use this law.The second part describes the experimental set-up (aerosol production and characterisation, elec-

trical discharge characterisation and control). Set-up for the determination of the electrical chargeon particles will be detailed (gaseousions/charged particles separation, loss of particles in the lines).The third part gives experimental results, and is divided in two parts: (i) electrical discharge

control and (ii) as the discharge is stable, comparison between experimental results and theoreticalpredictions. A precise knowledge of the discharge functioning conditions is required, as the gaseousion spatial distribution and the electric eld pro le are given by the discharge regime. Most studieson eld charging using electrical discharges neglect the e(ect of particle deposition on the chargingconditions. The evolution of the discharge current (and regime) due to particle deposition have tobe understood to control the charging conditions, in order to compare calculations and experimentalresults, obtained in reproducible conditions.

2. Theoretical background

The classical eld charging mechanism describes the charging rate of a spherical particle, in ahighly concentrated gaseous ion density (˙ 2 × 1016 ionsm−3), with an applied electric eld. Ions

L. Unger et al. / Aerosol Science 35 (2004) 965–979 967

in the electric eld travel along the eld lines and collide on the particle where the eld linesintersect the particle. As the particle gets charged, the number of eld lines which intersect theparticle diminishes, so as the subsequent charging rate, until the saturation charge is reached. Onlythe di(usion charging mechanism can then add charges to the particle. The saturation charge ns ofa particle (radius rp and dielectric constant �) in an electric eld Eo, is given by (Pauthenier &Moreau-Hanot, 1932):

ns =(1 +

2(� − 1)(�+ 2)

) (4�0E0r2P

e

)(1)

the charging rate dnp=dt is

dnpdt

=eNi ins4�0

(1 − np

ns

)2

; (2)

where i and Ni are the electrical mobility and the density of the gaseous ions.If the particle is initially neutral, the level of charge reached after a time � spent in the ion density

is given by

np = ns × e iNi�(1 + e iNi�)

: (3)

This charging law is valid if the following assumption are met:

• The Knudsen number is ¡ 1 (Kn is de ned as the ratio of the ion’s mean free path to the particlediameter Kn = 2�=dp). We are in the so-called continuum regime (the gaseous medium can beconsidered as continuous medium since the mean free path of the gaseous ions is smaller thanparticles diameter). In our case, the particles diameter are ranged from 0.44 to 1:13 �m, whichmeans that the Kn number is between 0.025 and 0.065 (when taking 10 nm for the mean freepath of gaseous ions). The continuum regime approximation is valid with these particle sizes.

• Particles are spherical. In our case, the di ethyl hexyl sebacat (DEHS) (liquid) particles arespherical (even with 100 elementary charges, a 0:45 �m particle is charged at less than a fewpercent of the Rayleigh charge limit, which is the maximum number of charges on a dropletbefore it shatters under the strong electrical repulsion forces; particles can then be considered notdeformed by repulsion forces). On the contrary, the NaCl (solid) particles have a cubic shape,due to the properties of the NaCl crystal, and the slow evaporation rate.

• The electric eld where the particles get charged is uniform (spatially constant), and is suDcientlystrong (equal or greater than 105 Vm−1) so as to consider that di(usion charging can be neglected.In our case, electric eld in the discharge gap is about 106 Vm−1, and is very heterogeneousonly in the plasma region (also called the ionisation region; about 100 �m around the wire). Inthe so-called drift region (where the negative ions are moving from the ionisation zone to theearthen cylinder), the electric eld is less non-uniform, and the eld surrounding a particle canbe considered uniform.

• The gaseous ion concentration is orders of magnitude greater than the particle concentration, inorder to have gaseous ions excess. In our case, ion concentration in a corona discharge are about1016 m−3, compared to aerosol particle concentration ranged between 1010 and 1013 m−3. Thelarge excess of ion allows to charge eDciently the particles (as the time � spent by particles in


the drift region is about 10−3 s, the Ni×� product is about 106 s cm−3, which is enough to chargeparticles at 50% of the saturation charge).

3. Experimental set-up

The experimental set-up (depicted on Fig. 1) may be divided in three parts: aerosol production,corona charger and charged aerosol characterisation.

3.1. Monodisperse aerosol production

In order to characterise precisely the charge level of particles, one has to produce a monodisperseaerosol with controlled size dp, 4ow rate Qp and concentration Cp. Two generators were used inthis study, based on di(erent physical mechanisms:

• a Sinclair Lamer Generator (model Palas SLG) which produces a monodisperse aerosol of DEHSby atomisation of a NaCl solution, followed by heterogeneous condensation of DEHS on the dryNaCl residues

• a piezzo-electric generator (model Synaptec/URANUS) which produces a weakly polydisperseaerosol of NaCl by a vibrating piezzo-electric ceramic placed under the NaCl solution

The main characteristics of these generators are summarised in Table 1.

DryCompressed

Air MixingVolume

Aerosol generatorSinclair Lamer Generator

& Uranus (piezzo)

High Voltagegenerator

Coronacharger

Out

Oscilloscope

Electrometer

Particle current

Pump

185p/cc

CPC

Particle concentration2.456

Diffusion Battery

Monodisperse AerosolProduction

AerosolCharge

Electrical andgranulometric measurements

Kr 85Neutralizer

Dry Air

Humid Air

Discharge Current

Ionic Current

Applied potential

DryCompressed

Air MixingVolume

Aerosol generatorSinclair Lamer Generator

& Uranus (piezzo)

High Voltagegenerator

Coronacharger

Out

Oscilloscope

Electrometer

Particle current

Pump

185p/cc

CPC

Particle concentration2.456

Diffusion Battery

Monodisperse AerosolProduction

AerosolCharge

Electrical andgranulometric measurements

Kr 85Neutralizer

Dry Air

Humid Air

Discharge Current

Ionic Current

Applied potential

Fig. 1. Schematic of experimental set-up (size distribution measurements device is not shown).


Table 1Main characteristics of the aerosol generator used in this study; values correspond to range used here

Generator Principle Dp (�m) Qp (l=min) Cp (p=cc) Monodisperse

SLG Heterogeneous condensation 0.47–2 0–4.3 106 YesURANUS Piezoelectric 0.4–1.5 0–25 105 No

Insulating material

Metal

Aerosolflow

To high voltagesupply

Aerosolflow

Electrical measurement of thedischarge current Id(oscilloscope)

Electrical measurement of the ionic outputcurrent Ii (oscilloscope and/or KeithleyElectrometer)

Particle Concentration and Charged ParticlesCurrent Measurements Cp and Ip

Calculus of <np>

Metallic wire at high voltage

Fig. 2. Schematic of wire–cylinder charger and measurements.

Two other streams of dry and humidi ed air allow to control the total 4ow rate and relativehumidity of the aerosol 4ow (see discharge characterisation) in the charger.

3.2. Corona charger

This charger is based on an electrical discharge created between a wire (held to high potential)and an earthen cylinder. The aerosol passes through the discharge, and is charged by gaseous ionspresent in the gap. The only way to control the charging conditions of the particles is to controlthe electrical discharge regime. A schematic diagram of the wire–cylinder charger can be seenon Fig. 2.


It has to be emphasised, that the control of the discharge is a critical point of these type ofcharger: as the ion density is produced by the discharge, and as their spatial distribution is determinedby the discharge, a special care has to be taken about the discharge characterisation (measurementsof voltage and current, but also determination of the regime by fast measurements of frequencyand amount of charge of the Trichel pulses). All these points will be described in the next section“Electrical discharge characterisation”.The discharge has to be well characterised in order to know as precisely as possible the charging

conditions of the particles. The evolution of charging conditions (i.e. discharge regime modi cation)due to particle deposition will be detailed in the next section, but we can precise here the electricalparameters which are measured with an oscilloscope (Tektronix 24-40, 500 MHz) in this study:

• the applied voltage Va via a high voltage probe (Tektronix P6015)• the mean discharge current Id, frequency �tric and charge Qtric of the Trichel pulses• ionic current Ii at the system output (also measured with a Keithley electrometer)

3.3. Aerosol properties

The particles have to be characterised before and after the charger to quantify (i) the chargeacquired by the particles in the discharge and (ii) the e(ect of aerosol characteristics on the dischargeoperation. Two ways of characterisation are necessary in this kind of study: granulometric (beforethe charger) and electrical (after the charger). The size distribution were measured by an ElectricalLow Pressure Impactor (ELPI dekati) and/or a Particle Counting System (PCS model Palas 2010).Fig. 3 shows an example of the distribution obtained.The particle charge is measured by a CPC coupled with an electrometer. The particle concentration

Cp and the total aerosol current Ie measured by the electrometer allow to calculate the mean charge

0.E+00

1.E-04

2.E-04

3.E-04

4.E-04

5.E-04

6.E-04

7.E-04

8.E-04

9.E-04

1.E-03

0.1 1 10

dp (µm)

dN

/N

Fig. 3. Example of size distribution obtained with the PCS (DEHS aerosol, 〈dp〉 = 0:44 �m, sigma = 1:13).


number by

〈np〉 = IeQeCpe

; (4)

where Qe is the 4ow rate in the electrometer and e the elementary charge. This is a good approxi-mation as far as:

• the aerosol is monodisperse or weakly non-monodisperse (� = 1:3), which is the case here; themean level of charge, calculated this way from the total electrical charged particles current, is thelevel of charge of the mean diameter particles,

• no gaseous ions are mixed with the charged particles 4ow in the electrometer (which wouldlead to an overestimated electrical current, and to a wrong calculated charge); this is done byusing a metallic tube—placed between the exit of the charger and sampling—which allows, dueto the very di(erent electrical mobilities between gaseous ions (2 × 10−4 m2 V−1 s−1) and thecharged particles (10−9–10−7 m2 V−1 s−1) to precipitate the ions before sampling; the gaseousion precipitate during the travel through the tube by space charge self-repulsion, and the currentmeasured is only due to charged particles,

• losses during transport (by di(usion and self-repulsion) must be (i) the same in both the CPCline and the Electrometer line and (ii) quanti ed to be able to know the particle concentration atthe exit of the metallic tube; 4ow rates in both sampling lines are xed identical, and the losseswere measured and compared with theoretical laws, see Kasper (1980); only a few percent of thecharged particles cloud are lost during transport, allowing to use this method of measurement; itis so possible to consider that the concentration and electrical current measured are those at thesampling point,

• no parasite particles are measured in the CPC (which would lead to a wrong calculated charge);electrical discharges can produce ne nanometric particles when lamentary (see Borra, Goldman,Goldman, & Boulaud, 1998); to prevent a possible ne particles production when the discharge isat high voltage (not far from arcing), a di(usion battery was placed before the CPC, and losses inthe battery were measured to calculate the charged particles concentration at the sampling point.

All results shown below are the levels of charge calculated this way with the particle concentrationand electrical current measured (respectively, with the CPC and the electrometer) at the exit of thecharger (isokinetic sampling point on Fig. 2).

4. Experimental results

4.1. Electrical discharge characterisation

4.1.1. Without particles—eAect of polarisation on the discharge operationAn electrical discharge is characterised by its regime which de nes the spatio-temporal charac-

teristics of the ion distribution. One way to characterise the regime is to measure and separate thecontinuous current (mainly proportional to the density of ions moving in the drift region) and theimpulse current (mainly due to Trichel pulses: electronic avalanches creating large number of ion-epairs in the ionisation zone). To charge the particles eDciently, the ion density has to be the more


1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

0 2 4 6 8 10 12 14 16

Valim (kV)

Id (A

)

No DischargeSelf-sustained

Discharge

Non Self-sustainedDischarge

Arc

ing

1.E-12

1.E-11

1.E-10

1.E-

1.E-

1.E-

1.E-

1.E-

1.E-

0 2 4 6 8 10 12 14 16

Valim (kV)

Id (A

)

No DischargeSelf-sustained

Discharge

Non Self-sustainedDischarge

Arc

ing

Fig. 4. I = f(V ) characteristic of the system (die = 15 mm, rc = 165 �m, h= 2 mm).

Table 2Values of the electrical parameters of the charger (rc = 165 �m, die = 15 × 10−3 m, h= 2 × 10−3 m)

Value and/or range of variation

Va (V) Vth (V) Vtric (V) Varc (V) Id (A) Ii (A) �tric (Hz) Qtric (C)

0–16 × 103 5:8 × 103 7:55 × 103 16 × 103 0–60 × 10−6 0–300 × 10−9 0–105 0–425 × 10−12

homogeneous as possible. The discharge regime is then a high-frequency Trichel regime (as glowis not possible in wire cylinder geometry unless the surface of the wire is very smooth and clean,cf. Vuhuu & Comsa, 1969), where the ion density is very homogeneous.The most common way to characterise a discharge is to draw its I=f(V ) graph, with the di(erent

discharge regimes on it (regimes are de ned by the nature of the continuous and impulse current).This allow, for a given geometry (distance die between electrodes, curvature radius rc of the wireand height h of the cylinder), to know the potential required to reach a given regime (Fig. 4).Beside the applied voltage, the best mean to control the electrical discharge regime is to modify

the geometry of the electrodes. By taking small curvature radius rc of the wire and large cylinderdiameter die, one can increase the voltage range of the interesting regime (here, the Trichel regime).Here, die =15 mm diameter and rc=165 �m, allowing large voltage ranges and tting with technicalrequirements (solidity of the wire, total size of the charger). These data are summarised in Table 2as well as the variation range of the di(erent voltage and currents, where Va is the wire voltage,Vth; Vtric and Varc, respectively the threshold voltages of the discharge, of the Trichel regime and ofthe arc, Id the discharge current, Ii the ionic current measured at the system output, and �tric and Qtric,respectively, the frequency and the charge by pulse of the Trichel pulses. It has to be emphasisedthat all insulating surfaces near the discharge gets polarised under the in4uence of the strong ionicdensity in the discharge vicinity. This polarisation has two important consequences:

1. The polarisation of surfaces can destabilise the discharge: our preliminary study showed that thismechanism can be controlled by controlling the surface resistivity of the insulating part; the use


1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

0 2 4 6 8 10 12 14 16

Valim (kV)

Ou

tpu

t co

nce

ntr

atio

n (

cm-3

)

0

10

20

30

40

50

60

70

80

90

100

<np

> m

ean

nu

mb

er o

f el

emen

tary

ch

arg

es

Cp

Np

Fig. 5. Concentration Cp and mean number of charge on particles 〈np〉 at the exit of the charger, as a function of appliedvoltage Valim (DEHS aerosol, 〈dp〉 = 0:44 �m, Qa = 10 l=min).

of humid air allows to diminish the surfaces potential and then allows the discharge to be morestable (for a given applied voltage, dId=dt → 0).

2. Gaseous ions at the exit of the system have to be collected before measuring the charged particlescurrent; the metallic tube after the charger plays the role of a ion precipitator (see above).

When these conditions are met (correct applied potential and humid air allowing the discharge towork in the desired regime), the stable discharge obtained can be used to charge aerosol particles.

4.2. EAect of particle charging and deposition

As aerosol 4ows through the charger, particles get charged and a part of them is collected on theelectrodes and—in a less extent—on the wall before being measured (see Fig. 5).As the applied voltage increases, both ion density and electric eld increase inducing a better

particle charging eDciency (and more particle losses). Particle collection on the earthen cylindercauses a great reduction of particle concentration; to use the charged particles 4ow, one has tochoose between concentration and level of charge. The e(ect of particle collection on the electrodesdepends on the nature of the particles: solid (NaCl) or liquid (DEHS).

4.3. EAect of NaCl particles deposition on the electrodes

4.3.1. On the discharge regimeThe losses of solid particles on the electrodes induce a great change in the electric eld around

the wire: the collection of particles on the wire changes its radius of curvature, and then modi es the


Fig. 6. Evolution of the mean discharge current with time (NaCl aerosol, dp = 100 nm, produced by collison atomiser,Cp = 107 p=cc).

discharge regime. This can be observed by measuring the temporal increase of the mean dischargecurrent (see Fig. 6), which nally ends by arcing of the charger.It has to be emphasised that the evolution observed on Fig. 6 is obtained with a highly concentrated

aerosol, leading to a quick destabilisation, as the evolution characteristic time is proportional withthe mass of particles collected on the electrodes. The phenomenon of deposition leads to (i) NaClparticles deposition on both electrodes (leading to a reduction of gap length) and (ii) NaCl depositionon the wire which reduces the apparent curvature radius (micro-dendrites formation). This lead toa lower discharge threshold voltage and to more frequent and (apparently) smaller Trichel pulses.This also leads to an increase of the discharge current for a given applied voltage, mainly due tonon-homogeneous discharge (trichel pulses).

4.3.2. On the particles level of chargeThe consequence of this evolution from a stable discharge to arcing (very heterogeneous discharge)

is a decrease of charging eDciency in the charger as can be seen in Fig. 7.In this case, the mean number of charge is constant for about 30 min, and then decreases contin-

uously while the discharge current increases: the mean discharge current is not a good parameter toquantify the charging conditions. The loss of homogeneity leads to (i) an increase of the dischargecurrent and (ii) a reduction of charging eDciency. When discharge is arcing (i.e. the dischargecurrent mainly transit via an inter-electrode lament, which corresponds to the worst conditions interm of ionic density homogeneity), mean particle charge tends to be zero. In order to work only incontrolled conditions, all results presented in this paper with NaCl aerosol are obtained during thestability period, where both discharge current and particle charge are constant.

4.4. EAect of DEHS particle deposition on the electrodes

Collection of liquid particles leads to a di(erent situation: DEHS particles depositionon the electrodes changes the equilibrium but does not destabilise the discharge. The charge


0

50

100

150

200

250

300

350

400

0 20 40 60 80 100

t (min)

<n

p>

mea

nch

0

50

100

150

200

250

300

350

400

0 20 40 60 80 100

t (min)

<n

p>

mea

n n

um

ber

of

elem

enta

rych

arge

s

Fig. 7. Temporal evolution of the mean number of charge (NaCl aerosol, 〈dp〉 = 1 m, Qa = 5 l=min, Valim = 13 kV,Cp = 105 p=cc).

level acquired by particles stays constant in time so experiments with DEHS were more easy tocarry out.

4.5. EAect of particle size on deposition

As concentration of particle is measured before and after the charger, the penetration in the charger(de ned as the ratio of the exit and inlet concentrations P=Cout=Cin) is known for every experimentalconditions. Getting rid of the losses due to impaction (charger o() allows to determine the electricallosses, which is the amount of particles collected on the electrodes due to electrical charge. Weobserved that losses get more important as the particle size decreases. The di(erences observedbetween di(erent particle size (i.e. for a given particle mobility, which should lead to comparablelosses, losses are more important for smaller particles) can be explained by two reasons:

• a given electrical mobility is obtained at di(erent applied voltages for the di(erent particle size, i.e.for di(erent electric elds; nevertheless, as the electric eld in the gap is not very in4uenced byapplied voltage above the threshold voltage, this is not enough to explain the important di(erenceobserved,

• the injection of particles in the discharge is done on a “small” section (leading to 4ow velocityof ≈3 m s−1); experimental results can then be explained by a di(erent injection pro le for thedi(erent particle size; smaller particles are indeed more sensitive to turbulence and then areinjected on a bigger section than the bigger particles; we’ll see below that this is coherent withthe levels of charge obtained, which are underestimated for the bigger particles—if the same meanion density is taken for identical experimental conditions.

4.6. Comparison between experimental and calculated level of charge

4.6.1. Calculation of the charging conditions (ion density and electric Deld strength)In order to compare experimental results to calculated level of charge using eld charging law,

one has to calculate the charging conditions of particles (mainly electric eld Eo and mean iondensity Ni) from the experimental conditions.


From the measured discharge current Id and applied voltage Valim, and with the geometrical prop-erties of the corona charger, it is possible to determine the electric eld pro le E(r) and the ionicdensity Ni(r) for each experimental condition. The electric eld in the discharge gap (at a distancer from the wire) is the sum of the geometric eld Egeom and of the space charge eld E� (due toionic density created in the discharge):

E(r) = Egeom + E� =Valim

r ln(R2=R1)+

1r�0

∫ r

R1

rNi(r) dr; (5)

where R1 and R2 are the radius of, respectively, the mass cylinder and the wire. In addition, thetotal discharge current can be expressed as a function of E(r) and Ni(r) as follows:

Id Secharge = 2rhNi(r) iE(r); (6)

where i is the electrical mobility of the gaseous ions (2 × 10−4 m2 V−1 s−1). We have:Id Secharge

2rhNi(r) i=

Valimr ln(R2=R1)

+1r�0

∫ r

R1

rNi(r) dr: (7)

This equation is discretised in 100 points (length step Tr=150 m), allowing to calculate the discreteion density nk . The integral term is written as follows:

Sk =k∑

l=1

rlnlTr = Sk−1 + rknkTr (8)

and the equation becomes a second-order polynomial equation:

n2k + nk

(Valim�0

rkTr ln(R2=R1)+

Sk−1

rkTr

)− Id�0

2 ihrkTr= 0 (9)

that can be integrated by taking S0 = 0 (no space charge eld at the wire’s surface). Electric eldis then recalculated with the rst equation of this paragraph. Each experimental point (Id ; Valim) canthen be used to calculate the electric eld and the ions density (i.e. the charging conditions met bythe particles). It has to be emphasised that this use of the experimental parameters is possible onlyif the discharge regime is controlled, i.e. if the mean current is constant in time and the ion densityis spatially uniform.Our goal is rst to calibrate the charger in order to use it in an electro-coagulator. The aim is

to know the aerosol physical characteristics at the output of the charger: size 〈dp〉, concentrationCp, 4ow rate Qa and mean number of charge 〈np〉. To this purpose, we studied parametrically thecharger, and compared the experimental values to those calculated with the classical eld charginglaw, from the experimental parameters Valim and Id.

4.6.2. EAect of the Ni� product and particle diameter dp (spherical particles)The in4uence of the ion density on the level of charge can be experimentally observed by changing

the applied voltage, for a given 4ow rate (see Fig. 8, where experimental results are given as afunction of Ni × � product). The Ni� product is calculated from the experimental conditions Id andValim as described in the previous section).One can see that the experimental points are quite well described by the eld charging law, except

for low values of Ni × � (under 5× 1011 sm−3, i.e. 5× 105 s cm−3), where the discharge is not in astable, self-sustained regime yet. The classical eld charging law allows to calculate—if the charging


1

10

100

1000

1.E+09 1.E+10 1.E+11 1.E+12 1.E+13

Ni*t (s.m-3)

<n

p>

me

an

nu

mb

er

of

ele

me

nta

ryc

ha

rge

snp exp (0.44µm)

np exp (0.58µm)

np exp (0.75µm)

np exp (0.92µm)

np exp (1.13µm)

Fig. 8. Mean number of elementary charge on particles as a function of the Ni × � product in the discharge gap, fordi(erent particle diameters (DEHS aerosol, Qa =10 l=min, Valim =6–14 kV); Dots stand for experimental values, and linesfor results of calculations.

conditions are well known—the level of charge of spherical particles. It has to be emphasised thatthe calculation gives better results with small particles (under 1 �m). Moreover, one can see thatparticles reach high level of charge (from 80% of saturation charge for the 0:44 �m particles, andabove saturation charge for 1:13 �m).

4.6.3. EAect of Ni� product and particle diameter dp (non-spherical particles)Same experiments are depicted in Fig. 9, but with NaCl solid particles instead of DEHS liquid

particles.Fig. 9 shows that for NaCl particles, the experimental charge number is greater than the calculated

one. The main assumption which is not met in this case is the spherical shape of the particles. Ithas to be emphasised that diameters shown are aerodynamic diameters.In this case, saturation charge seems to be reached for every size of particles, for Ni� products

higher than 1012 sm−3. As in the case of spherical particles, level of charge are even over thesaturation charge for the bigger particles.This shift between experimental and calculated level of charge is due to the shape of particles (cu-

bic) as every other parameter is the same as in the case of spherical particles. Three e(ects could bedue to cubic shape, and can then explain experimental results: eld reinforcement, change in the timespent in the discharge and particle rotation modi cation. The eld reinforcement could be responsibleof the charge shift observed experimentally, as the saturation charge depends linearly on the electric eld. A ‘point e(ect’ on the edges of the NaCl cube would lead to such a higher local electric eld.Besides that, the non-spherical shape could also change the time spent in the discharge by particles.Moreover, particle rotation in the high electric eld could appear (Zevenhoven, 1999), and is certainlydi(erent for spherical and non-spherical particles. So, particle shape has a strong in4uence on the


1

10

100

1000

10000

1.E+09 1.E+10 1.E+11 1.E+12 1.E+13

Ni*τ (cm-3.s)

<n

p>

mea

n n

um

ber

of

elem

enta

ry c

har

ges np exp NaCl (0.42µm)

np exp NaCl (0.72µm)

np exp NaCl (1.1µm)

Fig. 9. Number of elementary charges on NaCl particles as a function of Ni × � product for di(erent diameters (NaClaerosol, Qa = 10 l=min, V = 6–12 kV); Dots stand for experimental values, and lines for results of calculations.

level of electrical charge and further experimental and theoretical investigations are needed to showhow it modi es the level of charge. Field reinforcement seems to be the most probable explanation,because it can easily explain a strong di(erence between calculated and measured level of charge.

5. Conclusion and future work

A wire–cylinder negative electrical discharge has been used to charge sub-micron-sized aerosolparticles. A great care has been taken to de ne accurately both (i) the discharge setting point(by taking into account the surface polarisation and the e(ect of particle deposition on the dischargeregime, i.e. on the evolution of the charging conditions) and (ii) the mean level of charge of particlesafter the charger, by separating the gaseous ions from the charged particle 4ow and verifying thedi(usion and space charge losses during transport between the charger exit and the measurementsapparatus. This has allowed to calibrate the charger for a further use in an electro-coagulationreactor, and to verify the eld charging law in the case of spherical particles. Moreover, in the caseof cubic NaCl particles, the experimental levels of charge are underestimated by this law, which doesnot take into account the particle shape. More investigations are necessary to study more completelythis e(ect, and to include the shape factor in the eld charging law for sub-micron-sized particles,in a way that must be coherent with experimental results.

Acknowledgements

This study has been partially nanced by ElectricitSe De France. The authors would like to thankPr. Amouroux (Ecole Normale SupSerieure de Chimie de Paris, France) and Pr. Fauchais (Laboratoire


de MatSeriaux CSeramiques et Traitements de Surface de Limoges, France), which have allowed, bythe way of an ARC, to start the Electro-coagulation project.

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of Aerosol Science, 24(2), 211–226.Kasper, G. (1980). Electrostatic dispersion of homopolar charged aerosols. Journal of Colloid and Interface Science,

81(1), 32–40.Pauthenier, M. M., & Moreau-Hanot, M. (1932). La charge des particules sphSeriques dans un champ ionisSe. Journal de

Physique et le Radium, 3, 590.Vuhuu, Q., Comsa, R. P. (1969). In4uence of gap length on wire-plane corona. IEEE Transactions on Power Apparatus

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Unipolar field charging of particles by electrical discharge: effect of particle shape