EPA-600/2-77-173
August 1977
Environmental Protection Technology Series
FINE PARTICLE
CHARGING DEVELOPMENT
Industrial Environmental Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
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EPA-600/2-77-173
August 1977
FINE PARTICLE
CHARGING DEVELOPMENT
by
D.H. Pontius, L.G. Felix,
J.R. McDonald, and W.B. Smith
Southern Research Institute
2000 Ninth Avenue, South
Birmingham, Alabama 35205
Contract No. 68-02-1490
ROAP No. 21ADL-036
Program Element No. 1 ABO 12
EPA Project Officer: Leslie E. Sparks
Industrial Environmental Research Laboratory
Office of Energy, Minerals, and Industry
Research Triangle Park, N.C. 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, D.C. 20460
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EXECUTIVE SUMMARY
The general objectives of this research program were to
develop a new theory for the process of fine particle charging by
unipolar ions in an electric field, to expand the available base
of fine particle charging data, and to design, construct, and eval-
uate a pilot scale precharging device capable of handling 600 to
1000 ftvmin of flue gas.
The existing literature was reviewed in order to establish
a background for theoretical development and to compile a base
of available data.
A new particle charging theory, in which the thermal motion of
the ions is assumed to dominate the process, was developed.
In this theory the presence of an electric field has the effect
of modifying the ion distribution in the vicinity of each parti-
cle. The theory has a statistical basis, and therefore predicts
the average charge per particle in a large collection of particles
of the same size and material, subjected to identical charging
conditions.
Experimental determinations of particle charging were made
using an electrical mobility analyzer to find the end points of
particle trajectories in an electric field. Charging was accom-
plished with a unipolar ion field derived from an electrical coro-
na discharge. The apparatus used for the charging experiments
was designed to permit independent variations in charging field
strength, ion density, charging time, ion polarity, and tempera-
ture, as well as particle size and dielectric constant. Experi-
mental charging data were obtained for particles from 0.32 to 7 yni
diameter.
The experimental results generally substantiate the theory.
Agreement was usually within 20 percent. When the results of
charging by positive and negative corona are compared, however,
the difference is much larger than predicted by the theory. The
free electron contribution to the negative ion current may be re-
sponsible for this discrepancy. A more detailed study may be
required to determine an appropriate means for taking the free
electron contribution into consideration in the theory. The new
theory was used to model the performance of the pilot scale
charging device developed under this contract, and has also been
successfully incorporated into the EPA-SRI electrostatic pre-
cipitator computer model.
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A pilot scale precharging device capable of treating a total
gas volume of up to approximately 1000 ACFM was designed and con-
structed. Evaluation of charging effectiveness of the device was
carried out using redispersed flyash at ambient temperature. When
the precharger was installed at the inlet of a pilot scale electro-
static precipitator a significant improvement in the overall collec-
tion efficiency of the system was measured. Particle migration
velocities increased by values up to 60 percent over that of the
precipitator without precharger.
Analysis of the theoretical and experimental results indi-
cates that reductions in electrostatic precipitator size by as
much as a factor of three may be feasible by using a two-stage,
precharger-precipitator system without sacrifice in collection
efficiency or increase in energy requirements. The capital costs
could be reduced by approximately one half for the estimated size
reduction.
This report was submitted in fulfillment of Contract No.
68-02-1490 by Southern Research Institute under the sponsorship
of the U.S. Environmental Protection Agency. This report covers
a period from June 24, 1974 to August 31, 1976, and work was
completed as of September 29, 1976.
SOUTHERN RESEARCH INSTITUTE
iii
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CONTENTS
Executive Summary ii
Figures v
Tables xv
Acknowledgements xvi
1. Introduction 1
2. Summary and Recommendations 3
Analysis and Conclusions 4
Recommendations 4
3. Theoretical Development 6
4 . Laboratory Charging Experiments 30
Apparatus and Methodology 30
Experimental Results 47
5. Pilot Scale Experimental Work 73
6. Analysis and Evaluation of the Two-Stage
Precharger-ESP Concept 109
Particle Charging 109
General Precharger Design Considerations 123
Cost Estimates 135
References , 140
Appendices
A. Literature Review-Theory of Particle Charging 143
B. Literature Review-Particle Charging Data. . 196
C. Particle Charging Programs for Portable Calculators 216
IV
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FIGURES
Number
Two dimensional physical model for developing
a charging theory
2 Model for mathematical treatment of charging rate.
Along r=r0 and at 60- the radial component of the
electric field is equal to zero. The values of Eo,
a, n, and n were chosen arbitrarily for this
example 9
3 Relationship among the charging rates in Regions I,
II, and III and the total charging rate for a small
particle and low electric field 16
4 Relationship among the charging rates in Regions I,
II, and III and the total charging rate for an im-
mediate sized particle and moderate electric field... 17
5 Relationship among the charging rates in Regions I,
II, and III and the total charging rate for a lar-
ger particle and high electric field 18
6 Distribution of ions around the surface of a parti-
ally charged aerosol particle in the presence of an
applied electric field 19
7 Distribution of ions around the surface of a parti-
ally charged aerosol particle in the presence of
an applied electric field 20
8 Comparison of charging theories and Hewitt's exper-
imental data for a 0.18 ym diameter particle. In
all theories and experiment the ion mobility is
1.6x10""mVv* sec and the ion mean thermal/ speed is
500 m/sec 22
9 Comparison of charging theories and Hewitt's experi-
mental data for a 0.28 urn diameter particle.
U=1.6xlO~lfm2/V-sec and v = 500m/sec 23
v
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FIGURES (Cont'd)
Number Pa9e
10 Comparison of charging theories and Hewitt's exper-
imental data for 0.56 yjn diameter particle.
y=1.6xlO~"m2/V'sec and v = 500 m/sec 24
11 Comparison of charging theories and Hewitt's exper-
imental data for a 0.92 urn diameter particle,
y=1.6xlO~ltm2/V-sec and v = 500 m/sec 25
12 The dependence of charge upon particle size for a
low electric field. Nnt = 1x1013 sec/m3,
y=1.6xlO~'tm2/V'sec and v = 500 m/sec. The experi-
mental data are by Hewitt (1957) 26
13 The dependence of charge upon particle size for a
moderate electric field^ N0t = IxlO13 sec/m3,
y=1.6xlO~lfm2/V'sec and v = 500 m/sec. The experi-
mental data are by Hewitt (1957) 27
14 The dependence of charge upon particle size for a
high electric field. N^t = 1x1013 sec/m3,
y=1.6xlO Itm2/V*sec and v = 500 m/sec. The experi- a
mental data are by Hewitt 28
15 Mobility analyzer for measuring fine particle
charge 31
16 The Assembled SRI Mobility Analyzer 32
17 Schematic representation of the Vibrating Orifice
Aerosol Generator 34
18 Ammonium fluorescein aerosol particles generated
using the vibrating orifice generator. The parti-
cle diameters are 3.0 ym 37
19 Cylindrical geometry particle charger, after Hewitt.
Ions originating at the corona wire pass through
the screen electrode into the charging region
between the screen and the center plate electrode . 38
20 Fraction of time spent charging vs. charging voltage
for Hewitt charger. No resistors in parallel, 100
and 200 Hz 40
21 Nt as a function of corona current for various values
of the average fields in the charger 42
VI
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FIGURES (Cont'd.)
Number Page
22 Charger I-V characteristics for three conducting
media: (A) dry air, (B) water vapor in air, and
(C) methanol in air 44
23 Penetration of a 13 channel diffusion battery by
particles of various sizes as determined by mobility
analyzer measurements on singly charged particles.
The continuous line is the theoretical penetration
as a function of particle diameter 46
24 First part of sample printout of program used in
analyzing the experimental data 48
25 Second part of sample printout of program used in
analyzing the experimental data 49
26 Number of charges per particle as a function of
ion density-residence time product, (Nt) for a
0.56 ym diameter dioctyl phthalate (DOP) aerosol.
The continuous lines represent the theoretical
calculations corresponding to these charging
conditions 50
27 Number of charges per particle as a function of the
Nt product for a 1.4 ym diameter DOP aerosol. Four
different values of the charging field strength
were used. The blacked-in symbols denote the theo-
retical curves corresponding to the data plotted
with the open symbols of the same shape 51
28 Number of charges per particle as a function of
Nt product for a 1.0 ym diameter DOP aerosol. The
solid lines represent the SRI charging theory 53
29 Number of charges per particle as a function of
Nt product for a 1.0 ym diameter DOP aerosol 54
30 Comparison of experimental and theoretical values
of particle charge for a 2.0 ym diameter DOP aero-
sol 56
31 Number of charges per particle as a function of
Nt product for 4.0 ym diameter DOP particles 57
32 Number of charges per particle as a function of
Nt product for a 7.0 ym diameter DOP aerosol 58
SOUTHERN RESEARCH INSTITUTE
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FIGURES (Cont'd.)
Number
33 Theoretical and experimental values of charge per
particle as a function of Nt product for 2.0 ym
diameter stearic acid particles 59
34 Number of charges per particle as a function of
Nt product for a 2.06 ym diameter stearic acid
aerosol 60
35 Stearic acid aerosols, calculated diameter 2.0 ym
(a) no heating, (b) heated to approximately 100 F.... 62
36 Charge per particle as a function of Nt product
for a 2.0 ym glycerol aerosol. The relative die-
lectric constant for this material is 42.5 63
37 Comparison of particle charging as a function of
charging field strength for two different Hewitt-
type chargers. The Nt product was held constant
at l.OxlO*3 sec/m3 on the field was varied. Aero-
sols used were OOP, 1.0 ym and 2.0 ym in diameter.... 65
38 Charge per particle as a function of Nt product ^
for a 1.0 ym DOP aerosol. The second Hewitt
charger was used for these data 66
39 Charge per particle as a function of Nt product
for a 1.0 ym DOP aerosol, charged with the second
Hewitt-type charger 67
40 Number of charges per particle for polystyrene latex
particles of various sizes. The Nt product was held
constant at 5x1012 sec/m3 as the charging field was
varied. 68
41 Number of charges per particle as a function of
charging field strength for polystyrene latex
particles of four different sizes. Nt is l.OxlO13
sec/m2 69
42 Number of charges per particle as a function of
charging field strength for polystyrene latex
particles, with Nt=1.5xl013 sec/m3 70
43 Comparison of positive and negative corona charging
for 0.109 ym polystyrene latex spheres.... 72
Vlll
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FIGURES (Cont'd.)
Number Page
44 Conceptual sketch of pilot scale charging device.
Only the three-wire charging section is shown. A
second charging device with five corona wires and
six plates is located in the opposite end of the
enclosure 74
45 Sketch of electric field lines in (a) periodic
geometry of infinite extent employed in computer
program, and (b) pilot scale precharger section con-
taining one wire and having finite plate width 75
46 Current-voltage characteristics of both sections
of the pilot scale precharger with 0.0254 cm corona
wire at positive potential 77
47 Current-voltage characteristics of both sections of
the pilot scale precharger with 0.0254 cm corona wire
at negative potential 78
48 Electric field profiles for both sections of the
pilot scale precharger at the maximum experimental
current density, positive corona. 0.0254 cm diam-
eter corona wires were used 79
49 Electric field profiles for both sections of the
pilot scale precharger at the maximum experimental
current density, negative corona. 0.0254 cm diam-
eter corona wires were used 80
50 Comparison of current-voltage characteristics of
precharger with 0.0254 cm corona wire and with
0.127 cm corona wire, positive corona 81
51 Comparison of current-voltage characteristics of
precharger with 0.0254 cm corona wire and with
0.127 cm corona wire, negative corona 82
52 Current-voltage characteristic for the 3-wire
precharger section with no dust loading, negative
corona 83
53 Current-voltage characteristic for the 3-wire pre-
charger section under 6.85 grain/ft3 dust loading,
negative corona 84
54 Current-voltage characteristic for the 3-wire pre-
charger section under 11.8 grains/ft3 dust loading,
negative corona 85
IX
SOUTHERN RESEARCH INSTITUTE
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FIGURES (Cont'd.)
Number ?a9e
55 Comparison of the theoretical curves corresponding
to Figures 76 through 78 for the 3-wire precharger
section 8 6
56 Electric field profiles along a line from wire to
plate, normal to the plate, for the maximum values
of current and voltage plotted in Figure 79 87
57 Current-voltage characteristics of 5-wire precharger
section under various conditions, negative corona.... 88
58 Charge/mass ratio as a function of voltage applied
to precharger, negative corona 90
59 Charge/mass ratio as a function of precharger vol-
tage , positive corona 91
60 Size distributions of flyash at inlet, as measured
with Brink impactor and at outlet using Andersen
imp actor 92
61 Collection efficiency of pilot scale dry wall pre-
cipitator with 3-wire precharger section turned
on compared with efficiency obtained with the pre-
charger off 94
62 Charge/mass ratio as a function of precharger vol-
tage for various particle sizes in the 3-wire pre-
charger section, negative corona 95
63 Charge/mass ratio as a function of precharger vol-
tage for various particulate sizes in the 3-wire
precharger section, positive corona 96
64 Charge/mass ratio as a function of precharger vol-
tage for various particle sizes in the 5-wire pre-
charger section, negative corona 97
65 Charge/mass ratio as a function of precharger vol-
tage for various particle sizes in the 5-wire pre-
charger section, positive corona 93
66 Comparison of experiment with theory for overall
charge/mass ratio of flyash sample in 3-wire pre-
charger section, negative corona 99
x
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FIGURES (Cont'd.)
Number Page
67 Comparison of experiment with theory for overall
charge/mass ratio of flyash sample in 3-wire pre-
charger section, positive corona 100
68 Comparison of experiment with theory for overall
charge-mass ratio of flyash sample in 5-wire pre-
charger section, negative corona 101
69 Comparison of experiment with theory for overall
charge/mass ratio of flyash sample in 5-wire pre-
charger section, positive corona 102
70 Collection efficiency of the pilot scale electro-
static precipitator for various particle sizes. 104
71 Collection efficiency of the pilot scale electro-
static precipitator as a function of the voltage
on the 5-wire precharger section 105
72 Collection efficiency and migration velocity as a
function of precharger current density for various
particle sizes, using the 3-wire precharger 106
73 Collection efficiency and migration velocity as a
function of precharger current density for various
particle sizes, using the 5-wire precharger 107
74 Collection efficiency of pilot scale electrostatic
precipitator as main voltage is varied while main-
taining the 3-wire precharger voltage constant at
approximately 20 kV ; 108
75 Charge per particle as a function of electric field
for three particle sizes and two values of Not 110
76 Charge per particle as a function of ion concentra-
tion-residence time product for three particle sizes
and two values of electric field Ill
77 Current-voltage characteristics of a wire-plate corona
system for various sizes of corona wire, holding all
other parameters constant. S is wire-plate spacing,
S is wire-to-wire spacing, b is ion mobility, and
a^is corona wire diameter 113
XI
SOUTHERN RESEARCH INSTITUTE
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FIGURES (Cont'd)
Number Pa?e
78 Electric field at the plate electrode, Ep, and average
electric field, Ea, as a function of current density
at the plate for various wire sizes in a wire-plate
corona system • •
79 Current-voltage characteristics for a wire-plate coro-
na system for several values of wire-plate separation,
holding all other parameters constant 115
80 Maximum permissible current density before breakdown
as a function of resistivity for an assumed breakdown
strength of 10* V/cm. Back corona and loss of
particle charging effectiveness occurs for particle
resistivity and corona current density corresponding
to points above the diagonal line 117
81 Electric field profile in a duct geometry device for
various values of equivalent mobility, while holding
the average current density constant at the plate
electrode 122
82 Theoretical electric field profiles for various elec-
trode geometries, all normalized to a field of 5 kV/cm
at the passive electrode 124
83 Probability charging field as a function of distance
from corona electrode, calculated from the field
profiles shown in Figure 82 127
84 Experimental I-V characteristics for four corona
system geometries 129
85 Theoretical collection efficiencies for the Gorgas
full-scale precipitator compared to a precharger-
E.S.P. system 134
86 Particle mobility as a function of diameter for
shellac aerosol particles charged in a positive
ion field (After Cochet and Trillat18) 198
87 Charge per particle for a mineral oil aerosol
charged in a negative ion field (after Fuchs et
al2). Nt = 3.27 x 1011 sec/m 199
88 Charge per particle for a mineral oil aerosol
charged in a negative ion field (after Fuchs et
al2). Nt = 4.64 x 1011 sec/m 199
Xll
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FIGURES (Cont'd.)
Number Page
89 Charge per particle for a mineral oil aerosol
charge by negative ions (after Fuchs et al2).
Nt = 5.10 x 10ll sec/m3 200
90 Electrical mobility of dioctyl phthalate droplets
as a function of particle diameter (after Hewitt8).
Positive corona charging 201
91 Particle mobility as a function of charging field
strength for a dioctyl phthalate aerosol under
positive corona charging (after Hewitt8) 202
92 Charge per particle as a function of particle
diameter for a dioctyl phthalate aerosol under
positive corona charging (after Hewitt8) 203
93 Charge per particle as a function of ion density-
residence time product, Nt in a positive corona
(after Hewitt8) for 0.18 ym diameter dioctyl
phthalate particles 204
94 Charge per particle as a function of ion density-
residence time product, Nt in a positive corona for
0.28 ym diameter dioctyl phthalate particles (after
Hewitt8) . . 205
95 Particle charge as a function of charging field
strength for 0.28 ]im diameter dioctyl phthalate
particles (after Hewitt8) 206
96 Particle charge as a function of ion density-
residence time product for 0.56 ym diameter
dioctyl phthalate particles (after Hewitt8) 207
97 Particle charge as a function of ion dioctyl-
residence time product for 0.92 ym diameter
dioctyl phthalate aerosol particles (after
Hewitt8) 208
98 The spread of the mobility analyzer response
curve for fixed values of Nt, particle size and
charging field strength (after Hewitt8) 209
99 Particle charge as a function of particle diam-
eter for a dioctyl phthalate aerosol (after
Penney and Lynch") 210
Xlll
SOUTHERN RESEARCH INSTITUTE
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FIGURES (Cont'd.)
Number Page
100 Particle charge as a function of charging field
strength for 0.30 ym diameter dioctyl phthalate
particles in a positive corona (after Penney and
Lynch7 ) 211
101 Particle charge as a function of charging field
strength and ion density-time product for a
0.30 ym diameter dioctyl phthalate aerosol in a
negative ion field (after Penney and Lynch7) 212
102 Comparison of particle charging for negative and
positive corona acting on 0.30 ym diameter dioctyl
phthalate particles (after Penney and Lynch7) 213
103 Average charge per particle as a function of par-
ticle diameter. The curve derived from the calcu-
lator program is the simple sum of the field charg-
ing and diffusion charging results 223
xiv
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TABLES
Number Page
1 Effect of Changing Particle Size On The "Goodness
of Fit" Between Experiment and Theory. The Cal-
culated Diameter was 1.0 ym OOP 55
2 Electrical Operating Characteristics For Several
Plate-Wire-Plate Charger Geometries 131
3 Calculated Charge and Fractional Efficiency of the
Precharger-ESP System. The ESP Has An SCA of
28 ft2/1000 ACFM 133
4 Flange to Flange Cost Estimates of Particulate
Collection Systems (No Installation Costs Included)... 137
5 Estimated Cost Benefit Ratios For Precharger Collector
Systems 138
6 Comparison of Primary Power Requirements In Kilowatts -
900,000 ACFM 139
7 Summary of the Published Experimental Data On Particle
Charging 197
8 Comparison of Experimental Data. Number of Elementary
Charges as a Function of Nt 215
xv
SOUTHERN RESEARCH INSTITUTE
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ACKNOWLEDGMENTS
Dr. H. J, White provided essential background information
and insight regarding this charging project. We also consulted
with Dr. George Hewitt, who made several helpful suggestions con-
cerning the design of the aerosol charger used in this work.
Particle mobility measurements were carried out by Mr. David
Hussey, and assistance in high voltage electronic design work was
furnished by Mr. Preston Rice. The continuing encouragement and
assistance of Dr. Leslie Sparks is gratefully acknowledged.
xvi
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SECTION 1
INTRODUCTION
The process of charging airborne particles in a unipolar ion
field is fundamental to electrostatic precipitation. Once charged,
the particles can be forced toward a collecting surface by an
electric field. The overall efficiency of any electrostatic pre-
cipitator is thus intimately related to the effectiveness of par-
ticle charging in the system. A thorough understanding of the
mechanisms related to particle charging is important to the search
for improvements in electrostatic precipitator technology. This
report presents the results of the research efforts undertaken pur-
suant to Environmental Protection Agency Contract No. 68-02-1490,
which covers a joint theoretical-experimental study of fine particle
charging. The principal objectives of this study were: to develop
an adequate theory for the charging of fine particles in a unipolar
ion field with an applied electric field, to extend existing experi-
mental data on fine particle charging, and to design and construct a
pilot scale charging device in order to investigate the technical
and economic feasibility of improved collection of high resistivity
particulate matter by using a precharging section in conjunction
with a high field, low current density electrostatic precipitator.
A new charging theory developed as part of this work, pro-
vides improvements over existing theories in accuracy and flexi-
bility of application. Comparisons made between this new theory
and data drawn from the literature show better agreement, in
general, than was achieved with previous charging theories.
In order to expand the base of particle charging data for
comparison with the theory, an experimental program was carried
out. Specially generated monodisperse aerosols were charged under
various controlled conditions of ion density and electric field
strength. The average charge per particle was determined in each
case by means of a mobility analyzer, a device in which the
trajectory of a charged particle under the combined influences of
a laminar gas flow and an electric field can be measured. Airborne
particle charging in a unipolar ion field depends upon ion density,
electric field strength, particle residence time in the ion field,
particle diameter, and electrical characteristics of the parti-
culate material. Experimental tests to verify the charging theory
were done, varying each of these parameters. The charging experi-
ments were generally successful and consistent with the theory,
although some additional work is needed in the regime of ultrafine
particles, negative corona, and elevated temperatures and pressure.
SOUTHERN RESEARCH INSTITUTE
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This new theory was used to model the performance of the
pilot scale precharger developed under this contract, and was also
incorporated into the EPA-SRI electrostatic precipitator computer
model, thus allowing more accurate predictions of E.S.P. perform-
ance.
The particle charging theory and the two-stage electrostatic
precipitator concept were tested with a pilot scale device capable
of handling up to 1000 ft3/min of flue gas. The two-stage
electrostatic precipitator concept is based on separation of the
particle charging and collection functions. In the first stage,
or precharger, a high ion density and high electric field strength
are maintained to provide optimum charging effectiveness. Particle
collection in the precharger should be minimized, since an ac-
cumulated dust layer affects the electrical characteristics of a
corona system, particularly if the electrical resistivity of the
dust layer is very high. Particle collection is reserved for the
second stage, which operates with a high electric field strength
and low current density. In practice, however, some particle
collection in the precharger section is virtually inevitable.
Calculations based on the results of the pilot scale pre-
charger study show that precharger-ESP systems can be reduced
in size to limits determined by mechanical, rather than electri-
cal considerations. Theoretically, an ESP located downstream from
a precharger could be reduced in size by almost a factor of 10.
Because of ash handling problems and reentrainment we estimate
that a factor of 3 might be more realistic.
Basically, a precharger would work best where an ESP works
best; i.e., with moderate particulate loadings and low resistivity
ashes. The chief advantage, excluding size and cost, is the poten-
tial for alleviating the high resistivity problem by means which
are too expensive or complicated to be applied to full scale ESP
installations. This is primarily because the small precharger
units can be more carefully aligned, can be of more complex design,
and extraordinary means can be used to overcome the high resistivity
problem. In addition, the precharger could be utilized to improve
the performance of scrubbers, existing ESP's, and perhaps baghouses
or novel collection devices.
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SECTION 2
SUMMARY AND RECOMMENDATIONS
A study of particle charging in a unipolar ion field was
carried out using a combined program of theoretical and experi-
mental investigations. An extensive literature review, presented
in the Appendix, provided the necessary background information for
both the theoretical development and the experimental design.
A new charging theory based on kinetic theory was developed.
In the new theory the charging rate is calculated in terms of the
probability of collisions between aerosol particles and ions. In
order to simplify the mathematics the surface of the particle is
considered as being divided into three charging regions and separate
charging rates are calculated for each region. The total charging
rate is the sum of these three individual rates. For large parti-
cles and high electric fields this theory predicts essentially
the same charging rate as the classical field charging equations
of Rohmann5 and Pauthenierx7. For low electric fields the theo-
ry reduces to White's27 diffusional charging equation. In this
new theory the charging process is considered to be dominated by
the thermal motion of the ions. The principal effect of the field
is to modify the ion distribution in the vicinity of the particle.
Experimental verification of the theory was undertaken using
apparatus and methodology similar to that employed by Hewitt.8
Three different charging devices were constructed in the course
of the experimental work. The basic requirements of charger
design included separate control of charging field strength and
ion density in the charging region.
Particle charge measurements were made with a mobility ana-
lyzer which was designed and constructed for this project. In
this device, described in Section 5, the trajectories of charged
particles in an electric field were determined. The particle
mobility was then calculated, and, using the particle diameter,
the charge per particle was calculated using Stokes1 law.
Among the variables investigated in the charging experiments
were the charging field strength, ion density-residence time pro-
duct, particle diameter and dielectric constant and ion polarity
in the charging region.
SOUTHERN RESEARCH INSTITUTE
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The results of the charging experiments agreed, in general,
within approximately 20 percent of the theoretical charging results
Detailed comparisons between theory and experiment are presented
in Section 5.
A particle charging device designed for installation at the
inlet of a pilot scale electrostatic precipitator was tested and
evaluated in terms of charging effectiveness and relative improve-
ment of overall precipitator collection efficiency. The charger
consists of two electrically independent sections, each contain-
ing a multiple wire-plate corona electrode system. Redispersed
flyash at ambient temperature was used for particulate loading up
to 27 g/m3, at a gas velocity of about 1.3 m/sec. The charging
performance of the device was measured by catching particulate
samples on a silver mesh filter connected to an electrometer.
The samples were weighed and the charge to mass ratio, Q/M was
computed. Values of Q/M up to 1.2 x 10~5 coul/g were found. A
theoretical calculation of Q/M as a function of charger voltage
was in good agreement with the experimental results. The char-
ger-precipitator combination was operated as a two-stage system,
and measurements of performance were compared with those for the
precipitator alone. The migration velocities of the particles
were found to be up to 60 percent larger for the two-stage system
than for the single-stage precipitator.
ANALYSIS AND CONCLUSIONS
An analysis of the two stage precharger-ESP concept was
carried out on the basis of the experimental and theoretical re-
sults obtained in this project. The effects of corona electrode
geometry, applications to high resistivity particulate, and space
charge resulting from large concentrations of fine particles in
the gas stream were taken into consideration. The conclusions de-
tailed in Section 7 indicate that size reduction by a factor of
approximately three in overall size of an industrial electrostatic
precipitator may be achieved by using a high current density pre-
charger stage operated upstream from a conventional, low current
density ESP. No sacrifice in collection efficiency or increased
energy expenditures would be required for such a system.
RECOMMENDATIONS
Although the particle charging experiments and theoretical
development were generally successful; additional work is needed
to investigate the effects of certain parameters more intensively,
and to apply the results to full scale precipitators where non-
ideal conditions exist. The specific topics which need further
WOJTJC 3.X* 6 •
-------
1. Further experiments need to be done and modelled which
relate the charging theory to precipitator geometries
when the electric field, ion density, and charging time
are non-uniform.
2. Further experiments need to be done and modelled to
isolate the effects of free electrons on particle
charging.
3. Further experiments need to be done and modelled to
investigate the effects of elevated temperature on
particle charging.
4. Further experiments need to be done to study the effect
of larger variations in particle dielectric constant on
particle charging.
5. Further experiments need to be done which allow us to
interpret the theoretical predictions of fractional unit
charges on ultrafine particles.
6. Further work to modify the theory to include any significant
effects found in the experimental work which are not already
included needs to be done.
Because of the possible improvements in electrostatic preci-
pitator performance with the addition of a precharger stage, fur-
ther work in precharger design should be pursued. Of particular
importance is the control or elimination of back corona, which
limits the cur-rent density in any corona system where high resis-
tivity particulate material is present.
Finally, the two stage precharger-ESP concept should be subjec-
ted to tests involving actual industrial emissions for comparison
with conventional control devices and systems.
SOUTHERN RESEARCH INSTITUTE
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SECTION 3
THEORETICAL DEVELOPMENT
BACKGROUND
The processes resulting in attachment of ions to airborne
particles in a unipolar ion field include effects caused by the
thermal motion of the ions as well as those related to the pres-
ence of an electric field. Previous theories, discussed in detail
in the Appendix, have dealt with both the diffusion charging
mechanism and the field charging process. In general, those
theories which attempt to include both charging mechanisms have
produced results which are either a linear combination of the two
effects10, or have given rise to mathematical expressions difficult
to evaluate *'2 . Theories which treat the two charging processes
separately are too limited for general application3'**. It is
apparent, then, that further theoretical development is required
to provide an accurate and useful model for particle charging.
The basic mechanism for our charging theory is similar to
that described by Murphy et al1 where charging is largely attri-
buted to the thermal motion of the ions, and the electric field
acts as a perturbation on the thermal charging process. As
Murphy et, al^ pointed out, the field can influence the charging
rate in two ways: (1) the ions can gain kinetic energy from the
applied field which will help overcome the repulsive force of
the charged particle, and (2) the ion distribution near the par-
ticle may be altered. Although in practical situations the ki-
netic energy of the ions due to their random thermal velocity is
always much greater than the kinetic energy gained from the ex-
ternal electric field, experiments show that the charging rate is
greatly enhanced by the application of an electric field. This
is due mainly to item (2) above.
Formulation of the Theory
Our theory predicts the charging rate of particles in an
ion field on a statistical basis. For given charging conditions,
the instantaneous charge depends upon the ion density-time pro-
duct or "exposure" to the ions (N0t) . In experimental charging
studies the time t is equal to the residence time in the charging
-------
region. The ion density is determined experimentally by measur-
ing the current density j and the electric field E in the charg-
ing region and then using the relationship
N0 =
eyE '
where y is the ion mobility and e is the electronic charge .
Figure 1 shows a two-dimensional diagram of the physical
model which is used as the basis for the development of the theo-
ry described in the following paragraphs. The particle shown in
this sketch, and its environment, are considered to be represen-
tative of the average of a large number of similar systems which
make up the aerosol under investigation. Because the ion con-
centration may only be 10-100 times as large as the particle
concentration and because of the screening effect of neighboring
charged particles , macroscopic theories based on diffusion due to
ion concentration gradients are not applicable. It is possible,
however, to apply some ideas from kinetic theory of gases in
order to calculate the charging rate in terms of the probability
of collisions between ions and the particle of interest.
The nomenclature used in the development of the theory is
defined in Figure 2. The physical description, however, will be
based on the conceptual representation shown, in Figure 1 where
the particle of interest is surrounded by gas molecules, ions,
and other charged particles. The particle is assumed to be " '£
spherical and only components of the electric field due to charge
on the particle and the applied field are considered. The external
electric field is taken to be uniform and directed along the nega-
tive z axis. The dashed line in Figure 2, labeled ro, corresponds
to points in space where the radial component of the total electric
field is equal to zero. The angle 9o corresponds to the azimuthal
angle at which ro is equal to the particle radius, a. The point
of intersection between ro and the particle surface will always
lie on the hemisphere defined by 0o <. ir/2. . As the charge on the
particle increases, 80 will go to zero and ro will exceed the
particle radius for all angles.
If the space charge in the region outside the volume of in-
terest is homogeneous, we can write down an expression for the
radial component of the electric field very near the particle as
follows:
= Eo cose
r3 4We0r
SOUTHERN RESEARCH INSTITUTE
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o
o
o
O
Figure 1. Two dimensional physical model for developing
a charging theory.
-------
Z AXIS
REGION III
E = 900 kV/m
a = 0.46//m
n= 160elementary charges
n = 285 elementary charges
9
Figure 2. Model for mathematical treatment of charging rate.
Along r=r0 and at 90, the radial component of the
electric field is equal to zero. The values of EO,
a, n, and ns were chosen arbitrarily for this
example.
SOUTHERN RESEARCH INSTITUTE
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where E = radial component of electric field (V/m) ,
EO = external field (V/m) ,
K = particle dielectric constant,
r = radial distance to point of interest (m) , and
6 = the azimuthal angle measured from the z axis,
and the other symbols have been previously defined.
For the purpose of discussion we will define three areas of
interest on the particle surface. One area, designated by Region
I, is that bounded by 6 = 0 and 0 = 0o; a second region, Region
II, is bounded by 9 = 0 o and 6= ir/2; and the third region of in-
terest, Region III, is the "dark side" of the particle where
6 > tr/2. Our approach to arriving at an equation for the charg-
ing rate, dq/dt, is to estimate the probability that ions can
reach the particle surface in each of these three regions.
The rate at which ions reach the particle surface is
where P = the probability that a given ion will
move in a direction to impact with the
particle. From kinetic theory, P=%vA.
(Here v is mean thermal speed of the ions
and A is the surface area of the particle
on which the ions may impinge) , and
N (Eo/a,8) = the ion concentration near the particle surface.
s
Again, from classical kinetic theory, Ns(E0,a,9) can be related
to the average ion concentration, N0, by the expression
Ns(E0,a,9) = Noe-AV(Eo,a
where AV(E0/a,9) is the energy difference between the particle
surface (r=a) and some point in space where the average ion dis-
tribution is undisturbed (r=rf).
Thus, for diffusion to the entire surface of a spherical
particle, we write
10
-------
Up to this point the derivation is similar to that given by
White for the classical diffusional charging rate. For classical
diffusional charging, AV is set equal to neV4Tre0a, the potential
energy at the particle surface, and the influence of the applied
field is not taken into account (in this case, r1 = °°) .
Because of collisions with neutral molecules, the energy of
the ions is not conserved and hence, there is no potential energy
function associated with the electric field given by equation
(1) « We can say, however, that a minimum amount of work must
be done in moving an ion from some point in space (defined by
r=r') to the particle surface. This minimum work is given by
af af ( \r=a
AV(E0,a,9) = / F-dr = / eE dr =< . ne + eE0rcos8 |l-i=i
«
-------
different approximations are used to calculate the charging rate
in each region and the rates are then added to yield the total
charging rate:
t
Equation (3) was developed using expressions from kinetic
theory which, in turn, are based on the assumption that the sys-
tem is in equilibrium. In solving equation (3) for the charge
as a function of time we will assume that the charging dynamics
can be approximated by a series of steady states so that these
expressions may be applied. Nevertheless, in reaching the ulti-
mate expression for q(N0t), we will consider the motion of the
ions due to the applied field.
Calculation of the Particle Charging Rate
Region I —
In Region I the argument of the exponential in equation "(4)
becomes positive. In this case, equation (2) predicts charg-
ing rates which are too large, to be approximated by steady state
solutions because of the finite source of ions. In fact, the
charging rate is limited to the rate at which ions are brought
into the system by the external field. This rate is given by
the product of the current density and the surface area (Aj) of
Region I :
(6)
(a?) - /V-dA! = jieN'o / E
i A! "A!
This is identical to the charging equation developed by Pau
thenier which we refer to as the classical field charging equa-
tion. We may write this equation in a more conventional and use
ful form as
n
dt
-L s
where ns =(1 +
e0 = arc cos (n/ng) , (9)
and the other symbols are as previously defined.
When n > n , r0 is greater than the particle radius for all
^ *' (<3q/dt)I ±S Zer°' That is' fiel* Bargin
12
-------
Region II—
In Region II, charge is acquired by the particle due to ion
diffusion which is enhanced by the presence of the applied elec-
tric field. In this case equations (2) and (4) apply and the
charging rate is
where Ns(E0,a,9) is given by equation (5). Using this expres-
sion for Ns and writing AH in terms of a and Q, we find
y «•
(at)IZ - 4 / •.(2».'.me>de
or
•fv/2
/dg\ e7ra2N0v / f /ne2(r0-a)
ldt/TT 2 / P L i4ireokTar
11 o o
+ [3ar02-r03 (K+2)+a3 (K-l)] eE0cos9n sin0d6
kTr02(K+2) '-"
(10)
For each value of the particle charge ne, a value of 60 is
calculated using equation (9) and the integration of equation
(10) is performed. The integration is complicated by the depen-
dence of r0 on the angle 9. Thus for each value of 6, a value
of ro must be calculated. The magnitude of ro is found from the
condition that for r=r0, Er(E0,a,9) = 0.
Region III —
In Region III (the particle surface between the angles
9 = TT/2 and 9 = IT) , the electric fields due to the particle charge
and the external field are in the same direction and there is no
radial point ro for which the total electric field is equal to
zero. In this case, equations (2 and 4) would predict that
no charging could occur on this side of the particle. This is a
result of our application of equilibrium thermodynamics to a dy-
namic problem. Physically this means that the ions move in the
direction of the electric force and are swept from the system.
In reality, additional ions are swept into the system by the same
electric field, effectively creating a steady state charge den-
sity. As Murphy et al1 and Liu and Yeh5 have pointed out
the change in the ion density (and hence, charging rate) near
13
SOUTHERN RESEARCH INSTITUTE
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the particle surface is much greater for small values of 6 than
for the region 9 > ir/2 when an electric field is applied. Since
the change in ion density in Region III is relatively small, the
effects of the applied field are neglected and the classical dif-
fusional equation is used as an approximation to calculate the
charging rate:
/dg\ = TTa2veN0 exp (-ne2/4Tre0akT) .
Vdt/III 2
In the preceding paragraphs we have developed charging
theories for each of three charging regions on the surface of
the particle. The charging rate of the particle is the sum of
these rates:
n e-tra2vNo
dg , , 2 ,A N n 4. e-travo exr>_ ne2(r0-a)
|£ = (N0unse2/4eo) I1'— + - 2 - exp
+ [3ar02 - r03(K+2) + a3 (K-l)] eE0
kTr02(K+2)
exP(-ne2/4-ire0akT) . (11)
Equation (11) is integrated numerically using the quartic
Runge-Kutta method in the following procedure:
(a) The initial conditions are taken to be n = 0 at
t = 0.
(b) ns is calculated using equation (8) .
(c) For each increment in the Runge-Kutta scheme, a
value of 80 is calculated from equation (9) .
(d) The integral over 0 in equation (11) is performed
using Simpson's Rule, and for each value of 6
which is chosen for this integration, r0 is cal-
culated.
(e) The three individual charging rates are calculated
and then added to give the total instantaneous
charging rate for a particular value of n.
(f) Procedures (b) through (e) are repeated for each in-
crement of time until the integration is completed.
14
-------
Theoretical Results
Figures 3-5 show how the charging mechanisms in each region
contribute to the overall charging rate. Figure 3 shows data for
a small particle and low electric field. (See also Figure 8).
In this extreme case, charging is dominated by the diffusional
mechanisms in Regions II and III. Figure 4 shows a small particle
with a moderate applied field (also Figure 9). For values of
Not larger than about 1012 sec/m3, charging is dominated by the
field enhanced diffusion in Region II. Figure 5 shows data for
the largest particle size tested by Hewitt (also Figure 11).
The charging rate is again higher in Region II, for large Not,
but field charging in Region I does contribute significantly for
low values of N0t. The deviation from a smooth decreasing curve
for the total charging rate in Figures 4 and 5 appears because
we have used a macroscopic description of charging in Region I
which does not consider the thermal motion of the ions. Because
of this approximation the charging rates in Regions I and II
near 8=60 are different. However, this does not significantly
affect the integrated charge.
Figures 6 and 7 show the ion distribution at the surface of
a 0.28 diameter particle in an applied electric field for two
values of particle charge as predicted by the new theory and the
solutions to the quasi-steady diffusion equation obtained by Liu
and Yen6. Since the results obtained with the new theory are
based on a microscopic kinetic theory approach and those given
by Liu and Yen include a macroscopic diffusional process, it is
difficult to make a quantitative comparison. Figures 6 and 7
show that both formalisms yield ion distributions over the
particle surface which are very non-uniform, with ion concentra-
tion at 6 = 0 being three or more orders of magnitude higher than
the ion concentration at 6 = 180°. The two formalisms differ in
that the new theory predicts higher ion concentrations at smaller
values of 6 and lower ion concentrations at larger values. How-
ever, the quantity of interest is the area under the curves
since, in effect, this represents the number of ions at the par-
ticle surface and hence, the number of ions available for charg-
ing. The areas predicted by the two formalisms are in reasonable
agreement.
Comparison With Hewitt's Data
There has been a wide range of values reported in the litera-
ture for the mobility of ions created in a corona discharge. Liu
et al7 measured ion mobilities of 1.1 x 10-*in2/Vsec in
their experimental arrangement. Hewitt8 used a value of
1.6 x 10~lfm2/V«sec to calculate N0 from the measured values of
current density and electric field in his aerosol charger. Also,
the mobility of ions in laboratory air has been shown to decrease
15
SOUTHERN RESEARCH INSTITUTE
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10
PARTICLE DIA.-O.I8nnT-
10
Not,(sec/m3)
Figure 3. Relationship among the charging rates in Regions I,
II, and III and the total charging rate for a small
particle and low electric field.
16
-------
10'
10
-II
ISP
CD ^
II
5 w io'IJ
O UJ
I- ~
10"
PARTICLE DIA.-0.28um
= 3.6xl05v/m
TOTAL RATE
REGION II
\\REGION III
REGION I\\
10
10
10
II
Not,(sec/m3)
10
12
10
13
Figure 4. Relationship among the charging rates in Regions I,
II, and III and the total charging rate for an imme-
diate sized particle and moderate electric field.
17
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10
PARTICLE DIA.-0.92ym
_ \RE6ION III
I0l I 1012
Not ,(sec/m3)
Figure 5. Relationship among the charging rates in Regions I,
II, and III and the total charging rate for a larger
particle and high electric field.
18
-------
Figure 6
PARTICLE DIA.-0.28Mm
= 3.6xl05v/m
n=!5
ns= 10.5
THIS THEORY
\ \ LIUANDYEH
\\ (1969)
\
0
80
120 160 200
AZIMUTHAL ANGLE,Degrees
Distribution of ions around the surface of a parti-
ally charged aerosol particle in the presence of an
applied electric field.
19
SOUTHERN RESEARCH INSTITUTE
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QC
H
LJ
8
en
UJ
g
CO
z
UJ
s
Q
PARTICLE DIA.-0.28um
= 3.6xl05 v/m
n=35
nss!0.5
— THIS THEORY
LIU a YEH0969)
20 40 60 80 100
AZIMUTHAL ANGLE .Degrees
120
Figure 7. Distribution of ions around the surface of a parti-
ally charged aerosol particle in the presence of an
applied electric field.
20
-------
with time and to depend upon the gas constituency. For ion trans-
port times on the order of 1 msec, the range in mobilities (due
to different species) was reported by Bricard et al9 to be from
2.1 x 10~'*m2/V'sec to 1.35 x 10-lfm2/V«sec. Research conducted
by Loeb and his students10 indicates that a value of 2-2.2 x 10"1*
m /V'sec is representative of both positive and negative corona
in laboratory air. Thus, because of the uncertainty in ion
mobility, it is difficult to select a value which is characteris-
tic of corona discharge in general.
In order to make valid comparisons of theoretical results
with the experimental data reported by Hewitt, two methods are
possible. One approach is to choose a representative value for
the ion mobility y and then normalize both the experimental data
(N0t) and the theoretical results to this particular value. The
other approach is to use Hewitt's value in the theory. Since
Hewitt's value is well within the range reported by Bricard e_t al9
the latter approach has been used in making comparisons presented"
in this report and the value of 1.6 x 10~'*m2/V'sec has been used
for the ion mobility to obtain the theoretical results. Also,
Hewitt's value of 500 m/sec has been used for the mean thermal
speed v °f the ions in order to be consistent with the choice of
ion mobility. This causes much less agreement between the theory
of Liu and Yeh and Hewitt's experimental results than is observed
if low values for y and v" are used in the theory and high values
in the experiment, as was done by the individual workers. Never-
theless, the same values for y and v must be used in both the
theory and experiment for meaningful comparisons to be made.
Figures 8-14 compare the predictions of this new theory
with Hewitt's experimental data and with the theory of Liu and
Yeh for OOP particles with a dielectric constant of 5.1. Figures
8-11 show the charge accumulated by particles for different val-
ues of particle radius, applied electric field, and Not product.
Figures 12-14 show the dependence of charge upon particle size
for fixed values of the electric field where N0t = 1 x 1013 sec/
m3. In Figures 12-14, results obtained from the classical field
equations are shown for comparison.
The curves predicted by the new theory in Figures 8-11, in
most cases, follow the shape of the experimental data very close-
ly. That is, they rise with a very steep slope until N0t is
1 x 1013 sec/m3 and then for larger values of Not the slope de-
creases smoothly and not too fast so that the curves do not
flatten out quickly (as is the case in other approximate theo-
ries) . The close agreement in the predicted curves and the exper-
imental data for small values of Not indicates that this new
theory gives an adequate description of the charging process
during the time when both field and diffusional charging are
21
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PARTICLE DIA. -CXIS/im
= l.08xl06v/m
n
THIS THEORY
— LIUaYEH
Figure 8.
0.0
2.0 3.0 4.0
Not,(sec/m3xl013)
Comparison of charging theories and Hewitt's
experimental data for a 0.18 ym diameter particle.
In all theories and experiment the ion mobility is
1.6 x 10~l*m2/V«sec and the ion mean thermal
is 500 m/sec.
speed
22
-------
PARTICLE DIA.-0.28#m
A£=9.0xl05v/m
DE=3.6xl05v/m
THIS THEORY
--- LIU 8 YEH
2.0 3.0 4.0
Not,(sec/m3xl013)
Figure 9. Comparison of charging theories and Hewitt's
experimental data for a 0.2£ pm diameter particle.
p = 1.6 x 10~lfm2/V-sec and v = 500 m/sec.
23
SOUTHERN RESEARCH INSTITUTE
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no
PARTICLE
DIOCTYL PHTHALATE
AEROSOL
POSITIVE CORONA
CHARGING
THIS THEORY
2.0 3.0 4.0
Not,(sec/m3xl013)
Figure 10. Comparison of charging theories and Hewitt's
liameter pa
500 m/sec.
^^^^^*fcp^ **^JP» A*».^^^*«fr ^^ **• ^^******* •« ^b«&^4 ^- 4 1_^^~ ^^ ^^ ^, %j- •- ^ I
experimental data for 0.56 urn diameter particle.
y = 1.6 x 10~4m2/V-sec and v = 5
24
-------
PARTICLE DIA.-0.92//m
AE=9.0xl05v/m
= 3.6xl05v/m
6.0x!05v/m
THIS THEORY
LIU a YEH
Figure 11.
0.0 1.0 2.0 3.0 4.0
Not,(sec/m3xl013)
Comparison of charging theories and Hewitt's ex-
perimental data for a 0.92 j^m diameter particle.
y = 1.6 x lO^mVV'Sec and v = 500 m/sec.
25
SOUTHERN RESEARCH INSTITUTE
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= 6.0xl04v/m
NotslxlOl3sec/m3
LIUaYEH
THIS THEORY
DIFFUSIONAL
FIELD
Figure 12
0.2
0.4 0.6 0.8 1.0
PARTICLE DIAMETER (j/m)
The dependence of charge upon particle size
for a low electric field. N0t = 1 x 1013
sec/m3, y = 1.6 x I0~k m2/V-sec and v = 500
m/sec. The experimental data are by Hewitt
26
-------
I03
10*
UJ
I
UJ
UJ
o
o:
<
o
uj I01
o
o:
1 ~T
E=3.6xl05v/m
LIU a YEH
THIS THEORY
DIFFUSIONAL
FIELD
0.2 0.4 0.6 0.8 1.0 1.2
PARTICLE DIAMETER(»m)
1.4
Figure 13. The dependence of charge upon particle size for a
moderate electric field. N^t = 1 x 10J3 sec/m3,
Vi = 1.6 x 10~lfm2/V-sec and v = 500 m/sec. The exper-
imental data are by Hewitt
27
SOUTHERN RESEARCH INSTITUTE
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1
LU
UJ
UJ
UJ
O
a
o
1
i/V
E»l.08xl06v/m
Not»UIOl3sec/m3
LIU a YEH
THIS THEORY
DIFFUSIONAL
FIELD
0.4 0.6 0.8 1.0
PARTICLE DlAMETER(jim)
Figure 14. The dependence of charge upon particle size for a
^ _.__ . _ . — __ _ _ _ 1 Q .O
high electric field.
Not = 1 x 10
13
sec/m
y = 1.6 x 10~'*m2/V'sec and v = 500 m/sec.
imental data are by Hewitt.
The exper-
28
-------
active. Also, the agreement with experiment for values of Not
larger than 1 x 1013 sec/m3 indicates that the effect of the
external electric field on particle charging has been closely
approximated in the diffusion processes which occur on Regions II
and III of the particle's surface.
The curves of charge versus particle size given in Figures
12-14, indicate that the new theory gives good agreement with
experimental data over a wide range of particle sizes and elec-
tric field strengths. Agreement for particle sizes up to 0.5 ym
diameter is excellent for low, medium, and high fields. The
agreement between theory and experiment for particles larger than
0.5 um diameter improves as the electric field strength is in-
creased. For the high electric field strength the agreement is
excellent for all the particle sizes given. For the low electric
field strength the classical diffusional charging theory gives
good agreement with the experimental data for all particle sizes
given. Such agreement is reasonable because the effect of an
external electric field is not included in the classical dif-
fusional charging equation. Thus, it is to be expected that
agreement with the results predicted by the diffusion equation
should improve as the applied field strength is reduced.
The charging rate predicted by the new theory is in excellent
agreement with Hewitt's data for the 0.28 ym particle in an
applied field of 3.6 x 10s V/m, whereas the charging rate given
by Liu and Yeh using the ion distributions obtained from the quasi-
static diffusion equation yields a curve that lies below Hewitt's
data with considerable disagreement at certain practical values
of N0t.
The agreement between the new theory and Hewitt's experimen-
tal data is within 25% over the entire range of data that is
available and is within 15% for practical charging times in elec-
trostatic precipitators. Although the theory involves certain
approximations in describing the charging process, the agreement
with existing experimental data indicates that it can be used in
its present form to describe particle charging with an accuracy
comparable to the experimental accuracy of charge measurements.
29
SOUTHERN RESEARCH INSTITUTE
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SECTION 4
LABORATORY CHARGING EXPERIMENTS
APPARATUS AND METHODOLOGY
Because of the scope of measurements undertaken it was nec-
essary to use various techniques for generating aerosols and for
detecting them. The charge measurements were made, in general,
by determining the electrical mobility of aerosol samples after
subjecting them to controlled charging conditions. The labora-
tory setup for a given set of measurements thus consisted of an
aerosol source, a charging apparatus, a mobility-selective device
and a particle detector.
Mobility Analyzer
Measurements of electrical mobility of charged particles
were made by determining particle trajectories in an electric
field. Figure 15 is an assembly drawing of the mobility analy-
zer, and Figure 16 is a photograph of the assembled device. The
design is based on a concentric cylinder geometry, and is simi-
lar to that used by Hewitt8 in performing his experiments. Fil-
tered air flows the length of the mobility analyzer under laminar
flow conditions. Charged particles enter through a narrow annu-
lar passage, and experience a radial force toward the central
cylinder due to the applied field between the inner and outer
cylinder. By moving the scanning slit axially, the mobility of
the charged particles can be measured. Since the particle mo-
bility bears a well defined relationship to the charge on the
particle, a measurement of mobility is sufficient to determine
the charge. The overall dimensions of the instrument are dictated
by the resolution that is desired, and the requirement that laminar
flow be maintained between the concentric cylinders.
The relationship between particle trajectory length L, and
mobility M in the mobility analyzer is8
M •
where V = the applied voltage between inner and outer cylinder,
Q = the volume rate of air flow between cylinders, and
30
-------
U)
sis^:^s^s^
=~==s -'-
Figure 15. Mobility analyzer for measuring fine particle charge.
-------
•
I
Figure 16. The Assembled SRI Mobility Analyzer
-------
ri and r2 = the radii of the inner and outer cylinders,
respectively.
Stokes1 Law gives the mobility of a particle of radius a,
carrying n elementary charges as
where n = the viscosity of the air,
e = the electron charge, and
C = the Cunningham slip correction factor.
Setting the above two expressions for the mobility equal to each
other, we obtain
_ 3Qna , r_2_
CLVe r i
for the charge on a particle in terms of measurable quantities.
The factor C (Cunningham Correction factor) is dependent upon
particle radius, and may be expressed as
C = 1 + £-{l-2 + 0.4 exp [(-0.88a)/A]} ,
(14)
t
where \ is the mean free path of the air molecules.
Aerosol Generators
In order to cover the range of particle diameters required in
the charging experiments two different aerosol generators were
used. For particles greater than about 1 ym in diameter a vibra-
ting orifice aerosol generator was used, and a Collison Nebulizer
was used to produce particles less than 2 ym in diameter.
Vibrating Orifice Aerosol Generator (VOAG)—
Figure 17 is a schematic diagram of the vibrating orifice
aerosol generator (VOAG) which has been constructed for use on
this project. This particular device was designed and built at
Southern Research Institute, although similar devices have been
reported by several authors previously.11'12'13 A solution of
known concentration is forced through a small orifice (5, 10,
15, or 20 ym diameter). The orifice is attached to a piezoelec-
tric ceramic which, under oscillatory electrical stimulation,
will vibrate at a known frequency. This vibration imposes perio-
dic perturbations on the liquid jet causing it to break up into
uniformily-sized droplets. If the liquid flow rate and the
33
SOUTHERN RESEARCH INSTITUTE
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Plexiglass Drying
Chamber
Vibrating
Orifice
Flow
Meters
Control
Valves
Po210 Charge Neutralizer
Signal Generator
Membrane
Filter
Syringe
Pump
Dry Air
Figure 17. Schematic representation of the Vibrating Orifice
Aerosol Generator
34
-------
perturbation frequency are known, the droplet diameter can be
readily calculated. The solvent evaporates from the droplets leav-
ing the nonvolatile solute as a spherical residue. The ultimate
dry particle diameter is calculated from the droplet diameter and
the known concentration of the liquid solution.
To calculate the dry particle diameter, the expression
is used,11*
where C = the solution concentration or volume of solute/volume
of solution,
Q = the solution flow rate (cm3/min),
f - the perturbation frequency (Hz) , and
I = the volumetric fraction of nonvolatile impurities.
The solution flow rate and the perturbation frequency cannot
be varied independently without disturbing the monodispersity of
the aerosol. For a given orifice and solution flow rate the per-
turbation frequency must be adjusted so that one and only one
droplet breaks off the stream passing through the orifice in each
oscillation. If the frequency is set too low, droplets may break
off prematurely at random, and if the frequency is too high, not
enough solution will be available to produce a well-formed drop-
let for each cycle. The system must, therefore, be tuned to pro-
vide a monodisperse aerosol.
Monodispersity can be tested by blowing a well-defined jet
of air across the aerosol stream. Since the particle aerodynamics
are strongly dependent upon particle diameter a uniform deflection
of the particle stream indicates monodispersity. If the particles
are polydisperse, deflection by a transverse air jet will break
the stream up into two or more separate streams. By observing
the stream deflection and adjusting the perturbation frequency
one can produce a very monodisperse aerosol. The technique de-
scribed above was employed each time the VOAG was set up to pro-
duce an aerosol. During system operation the particle monodis-
persity was also checked by drawing off filter samples for
microscopic examination and measurement.
Because clogging was a severe problem with the smaller
orifices the 20 ym diameter orifice was used almost exclusively
in this work. In order to avoid clogging the orifices were washed
35
SOUTHERN RESEARCH INSTITUTE
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with ultrasonic agitation and rinsed in the solvent to be used
in aerosol generation. The liquid handling system was also
flushed with the solvent.
The VOAG orifice was operated at the bottom of a plenum
chamber made of a clear plastic cylinder six inches in diameter
and three feet high. Air was introduced at the bottom of the
cylinder to loft and disperse the particles. Sampling ports at
the top of the chamber were used to extract the airborne particles.
Figure 18 shows a 3.0 ym diameter test aerosol generated from a
solution of fluorescein in 0.1 N NHifOH.
Collison Nebulizer—
A spray of liquid droplets is produced by atomizer action in
the Collison nebulizer. As in the VOAG, the primary droplets,
made up of a dilute solution of the desired aerosol material, are
evaporated to leave a residue of much smaller size than the pri-
mary droplets. The diameter of the residual particles is a function
of the solution concentration. Because the atomizer action pro-
duces a spray of polydisperse particles the use of the Collison
Nebulizer was limited principally to dispersing suspensions of
pre-sized insoluble particles, such as polystyrene latex.
Particle Charging Devices
Requirements for a particle charger for these experiments
included independent control of the electric field strength and
the ion density in the charging region. Three chargers were con-
structed and used in the course of this project. The first
device was based on a wire-plate electrode geometry, and both of
the other two were designed in a cylindrical configuration
similar to Hewitt's device.8 Of the three charging devices con-
structed the most satisfactory performance was achieved with the
second "Hewitt-type" charger, illustrated in Figure 19.
In a simple corona system consisting of a corona electrode
and a passive electrode the ion density and electric field strength
cannot be varied independently of each other. For this reason,
the particle charging devices were designed with a screen elec-
trode between the discharge and passive electrodes. The space
between the screen and the passive electrode was then used as the
particle charging region.
In the Hewitt charger the screen and plate electrodes lie on
concentric cylinders, and a corona wire is located along the
cylinder axis. At first a shutter assembly was included to mask
part of the screen area so that the aerosol residence time could
be varied without adjusting the flow rate. The shutter had to
be removed, however, because it contributed to sparking.
36
-------
«
Figure 18.
Ammonium fluorescein aerosol particles generated
using the vibrating orifice generator. The particle
diameters are 3.0 ym.
37
-------
INSULATION
T
SQUARE
WAVE
DC HI6H
VOLTAGE
INSULATION
GAS FLOW
'""•
rrrj~rff"f
SCREEN ELECTRODE
Figure 19.
Cylindrical geometry particle charger, after Hewitt.8
Ions originating at the corona wire pass through the
screen electrode into the charging region between the
screen and the center plate electrode.
38
-------
Ions created in the corona region pass through the screen into
the charging volume where they may become attached to test aerosol
particles. In order to apply a charging field, a voltage is ap-
plied between the screen and plate. A dc voltage in this region
would result in the precipitation of a large fraction of the
particles on the plate. To avoid this, a square wave ac voltage
was applied. This creates a uniform field and ion concentration
during one half cycle, for charging, but reversing polarity limits
the transverse motion of the charged particles to small amplitudes,
thus minimizing the losses by precipitation. The ion density-time
produce (Not) can be varied by changing the gas flow rate or the
corona current, either independently or simultaneously.
Because the electric field in the charging region is applied
as a square wave the ion density-time product for particle
charging must be multiplied by the fraction of time f in each
cycle that the charging field is on. The corrected ion density-
time product Nt is therefore
Nt = f Not . (16)
c
The value of f was determined for various values of switching
frequency and voltage by measurement on oscillograms. The
period of time between the points at 90% of the maximum voltage
on the leading and trailing edges of the waveform divided by the
entire period of the wave was taken to be the value for f . Fig-
ure 20 shows the fraction f. as a function of applied voltage
between the screen and plate electrodes for switching frequencies
of 100 and 200 Hz.
The ion density, No, during the charging period is determined
from the applied electric field, E, across the charging region
and the ion current, i, between the screen and plate electrodes.
The ion density, electric field and current density, j, are
related by the expression
j = NoeyE, (17)
where e is the electronic charge, and y is the ion mobility. If
we let A be the area of the plate electrode, then
i = jA,
and, substituting into equation (17), we obtain
No =
eyAE
39
SOUTHERN RESEARCH INSTITUTE
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0.48
o
5 0.46
I
o
0.44
UJ
a.
en
UJ
2
h-
5 0.42
t-
o
(T
li.
0.40
O
100 Hz
200 Hz
Figure 20,
I 234567
CHARGING VOLTAGE , kV
Fraction of time spent charging vs. charging voltage for Hewitt
charger. No resistors in parallel, 100 and 200 Hz.
8
-------
Correcting for ac excitation with the fraction f , we may write
c
where t is the transit time of an aerosol particle through the
charging region.
Because various values for the ion mobility were found in
the literature it was ultimately necessary to make separate
determinations of ion mobility for the particular charger system
geometry used, the ion polarity and the gas constitution. The
method used to determine ion mobility will be discussed in
greater detail later in this section.
Figure 21 displays Nt as a function of corona current for
various values of average field in the charging region.
Ion Mobility Measurements
The aerosols used in the charging experiments are derived by
evaporation of solvent from solutions containing the desired aer-
osol material. Solvent molecules are thus present in the charger
and will affect the ion mobility. The solvents most frequently
used were HaO and methanol.
In order to determine the ion mobility, I-V characteristics
of the charger were measured with a solvent vapor present in the
concentration normally resulting from aerosol generation. A non-
linear curve fit was then applied, using the following theoreti-
cal expression relating the current and voltage in a cylindrical
corona system:
where b = cylinder radius,
a = corona wire radius,
L = length of corona wire,
V0 = corona inception voltage, and
Vi = ion mobility.
41
SOUTHERN RESEARCH INSTITUTE
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-------
The measured I-v characteristics of the Hewitt-type charger
are presented in Figure 22 for three media: dry air, H20 in air
and methanol in air. The curve for dry air exhibits a disconti-
nuity at approximately 21 kv. This effect may be a back corona
resulting from a thin oxide layer on the inside surface of the
cylinder, but in any case it is of no consequence in the charg-
ing experiments since a liquid solvent is invariably used in
aerosol generation for this work. The behavior of the curves for
methanol and H20 is stable up to current densities of about
4 x 10 5 A/cm2.
The curve fitting was applied to the lower part of each of
the curves (current less than 2 mA) where anomalous behavior,
such as inhomogeneous current, thermal effects, etc., are least
likely to occur. The resulting mobility values were 2.38
x 10~4m2/V-sec for H^O in air, and 2.03 x 10~'*m2/V-sec for metha-
nol. For dry air the best fit also produced a calculated value
of 2.38 x 10-*m2/V-sec.
Bricard9 has reported results of mobility measurements
which indicate effects of ion aging. When the ion lifetime is
increased, by decreasing the applied voltage or increasing the
electrode separation, the measured mobility decreases. Apparent-
ly the more mobile ion species are quickly depleted from the con-
ducting medium. For ion lifetimes less than 1 msec, as in our
charging device, Bricard reports a mobility of 2.3 x 10~'*m2/V-sec
for positive corona in dry air, which is within 5% of our deter-
mination.
Calibration of the Mobility Analyzer
A direct measurement of the ratio of charge to mass in a
monodisperse aerosol taken from the outlet of the charger would
provide data necessary for calculating a particle's electrical
mobility which would allow a calibration of the SRI mobility ana-
lyzer.
Attempts to measure charge and mass directly, using a mono-
disperse polystyrene latex aerosol, yielded poor results due to
particle leakage through (or around) the silver filter used to
collect the aerosol sample.
A second series of experiments was undertaken using a mono-
disperse fluorescein aerosol. The sampling was again accomplish-
ed using a silver filter in an insulating plastic holder. Accu-
mulated charge was measured with an electrometer.
43
SOUTHERN RESEARCH INSTITUTE
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10
8
<
E
OJ
oc
o
<
0
8 12 16 20 24
APPLIED VOLTAGE, kV
28
32
Figure 22
Charger I-V characteristics for three conducting
media: (A) dry air, (B) water vapor in air, and
(C) methanol in air.
44
-------
Approximately two hours run time was required to collect a
0.5 milligram sample with a corresponding charge accumulation of
about 5.4 x 10~9 coul. This corresponds to a collection rate of
only 7.5 x 10~13 coulomb/sec. By turning off the aerosol genera-
tor and leaving all other apparatus energized, a background cur-
rent of about 2 x 10~13 coul/sec was established. Fluctuations
in the background current could therefore introduce substantial
error in the measured charge. The Q/M measurements were thus not
sufficiently consistent to provide the degree of accuracy re-
quired for system calibration.
A comparison of measurements of singly-charged particle
diameters as determined by the mobility analyzer and by a dif-
fusion battery has provided the best verification of mobility
analyzer performance. The method of comparison is described in
the following:
In the range of particle diameters between 0.02 and 0.06 pm,
a Collison nebulizer was used to produce an aerosol which was
passed through a bipolar ionizing region produced by a Kr85 radi-
ation source. In the resulting equilibrium condition, all except
a negligibly small portion of the particles were, at most, singly
charged. These particles were then introduced into the mobility
analyzer.
For any fixed values of voltage and trajectory length in
the mobility analyzer, only those particles with the mobility
thus defined can pass through the analyzer. Since the particles
are, at most, singly charged, and those with zero charge are
eliminated by the mobility selection, the aerosol at the mobility
analyzer output is essentially monodisperse. The diameter of
the aerosol can be calculated from Stokes' law, using the value
of electrical mobility defined by the voltage and trajectory
length in the mobility analyzer.
By using various values for the voltage and trajectory
length in the mobility analyzer a number of different monodis-
perse aerosols were generated, with diameters between 0.02 and
0.06 ym. For each case the penetration through a 13 channel
diffusion battery was determined by measuring the diffusion bat-
tery inlet and outlet concentrations with a condensation nuclei
counter (Environment One, Model Rich 100). The data points
shown in Figure 23 indicate the measured values of diffusion
battery penetration as a function of the particle diameter, as
determined from the mobility analyzer parameters, and with the
assumption that the particles are singly charged. The solid
line is the theoretical diffusion battery penetration as a
function of particle diameter. There is considerable scatter
in these data, particularly for small values of diffusion
battery penetration. Aerosol source fluctuations are probably
responsible for at least some of the scatter, and for the smaller
values of penetration the condensation nuclei counter was operat-
ing in a less sensitive range than for the larger values.
45
SOUTHERN RESEARCH INSTITUTE
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lOOr
CTi
eof
cr
LU
a.
60
UJ 401
CD
CO
ID
LL
20
0.01
1 i i i i i i .
0.02 0.04
PARTICLE DIAMETER,
0.1
Figure 23. Penetration of a 13 channel diffusion battery by particles of
various sizes as determined by mobility analyzer measurements
on singly charged particles. The continuous line is the theo-
retical penetration as a function of particle diameter.
-------
Computer Program
A FORTRAN IV computer program was written which takes raw
experimental data as input, computes the mobility and charge
corresponding to each data point, averages the data taken for
each value of Nt, calculates standard deviations, determines the
charge predicted at that value of Nt by the SRI theory, and cal-
culates a percentage difference between the average charge and
predicted charge. Sample printouts, showing a tabulation of the
input data and the resulting statistical summary are presented
in Figures 24 and 25.
EXPERIMENTAL RESULTS
Rectangular Geometry Charger
The first measurements of particle mobility were made on
monodisperse aerosols of dioctyl phthalate (DOP), generated by a
VOAG, and charged by use of the rectangular charging system.
Values of ion density-residence time product (Nt) between 1.0
xlO12 and l.OxlO13 sec/m3 were used, with charging field strength
values of 6.0x10"* to 5.0x105 V/m. The number of charges per par-
ticle as a function of Nt product for two values of charging
field strength are presented in Figure 26 for a 0.56 ym diameter
DOP aerosol. The theoretical charging curves are also illustra-
ted for comparison. For this particle size the theory predicts
a larger number of charges per particle for a field strength of
6.0x10"* V/m, than the measured values. But for a charging field
strength of 2.0x105 V/m the theoretical values are lower than
those measured in the experiments.
Similar results are found for a 1.4 ym DOP aerosol, as shown
in Figure 27. Fairly good agreement between theory and experi-
ment occurs for intermediate values of the charging field. But
the theoretical values are below experiment for a high charging
field and above the measured values for a low charging field.
It was found that severe turbulence effects occur in this
charging device for large values of Nt, thus limiting the effec-
tive operating range of the charger. For this reason the rec-
tangular charger was replaced by a device of cylindrical geometry,
similar in design to those used by Hewitt8 in his charging exper-
iments .
First Hewitt Charger
Mobility measurements were made on charged monodisperse DOP
aerosols ranging from 1.0 to 7.0 ym in diameter. Charging field
strengths were between 8.0x103 to 8.0x105 V/m. The ion concen-
tration-residence time product (Nt) ranged from 2x1012 sec/m3 to
a maximum of 4x1013 sec/m3. Figures 28 through 31 show the
results of these experiments. The graphs are ordered by particle
47
SOUTHERN RESEARCH INSTITUTE
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S.IOOF + Of OH.LFCTRlf. CONSTANT
0* CHARGING FIELD STRENGTH, W/CM
).356f:+0
-------
l.OOOF + OU M]c»i)t. riA»«FTtR PARTICLE
8.000t+03 CHARGING FIFIO STRfcNGTH, VOlTS/C*
S.JOOF+00 tMFLHTKir. Ct'MSTAMt
2.200E+00 CM**2/fVnLT-SEC) ION MOBILITY
500,0 M/S MEAN TNFRMAL SPEED
298.0 DEGRFES K
POSTTTVF If!* CHARGING FOR OOP
2.99IF+0? SATURATION CHARGE
MT
VO
AVERAGE
MOBILITY
MOBILITY
STO-DEV'.
AVERAGE
CHARGE
CHA«fiE
STD-DEV.
SRI THEORY
CHARGE
CELEM UNITS) fF.LFM UNITS) (FLEM UNITS)
EXMT.-THEOMY
CHARGF
CELFM UNITS)
CHARUF
2.000E+1?
3.085E-07
3.6?5£-o7
7.00CF+12
8,f"0f>fc41 2
9.000E+1?
M.S70F-07
U.789t-n7
3.3««E-OP
a.moE-ne
5,t38F-0«
«.I22E-08
6.017E-08
6.901E-OH
6.219E-08
3.389E+02
3.72&E+02
3.BR3E*02
U.170E+02
a.?72E»02
U.62SE+02
U.698E+0?
5.083E+01
3.X55E+01
S.IHOE + Ot
5,fifl6E+01
6.052E+01
2,?61f:+02
3.«H?E+02
3,568E+02
3.63SE+0?
3.690E+02
3.736E+02
3.776E+02
! .955F+01
«,006F«0)
6.0?OE»01
6.372Ft01
7.868F + 01
8.RH8E+01
9.223F+01
2.«21E»01
S.938F+00
1.088t»OI
1.556E+0)
1.612F+01
^ .927E + 01
J.126E+OI
^.177E+01
in
O
c
X
m
71
m
in
m
Figure 25.
Second part of sample printout of program used in analyzing
the experimental data.
V)
-I
3
H
PI
-------
70
60
50
40
tn
u
o
OC
<
O
fi 20
00
10
1 T
O
O
0
Figure 26,
A
6 8
sec/m3 X I012
10
ION DENSITY X TIME,
Number of charges per particle as a function of ion
density-residence time product, (Nt) for a 0.56 pm
diameter dioctyl phthalate (DOP) aerosol. The con-
tinuous lines represent the theoretical calculations
corresponding to these charging conditions.
50
-------
1000
800
600
500
400
300
O O O
O O
UJ
x
o
200
oc
UJ
m
2
i 100
80
60
50(
Figure 27.
000000°!
2468
ION DENSITY X TIME , scc/m3 X I012
10
Number of charges per particle as a function of the
Nt product for a 1.4 ym diameter DOP aerosol. Four
different values of the charging field strength were
used. The blacked-in symbols denote the theoretical
curves corresponding to the data plotted with the
open symbols of the same shape.
51
SOUTHERN RESEARCH INSTITUTE
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diameter. Each graph shows the experimentally determined values
of charge per particle along with the values predicted by the
theory described in section 3.
Figures 28 and 29 present the results for a 1.0 ym DOP aero-
sol. As in our previous results the theoretical predictions of
charge are lower than those found in the experiments for large
values of the charging field, and higher than the experimental
values in the lowest range of charging fields.
Calculations were made to investigate the significance of
possible errors in particle size. Particle diameters from 0.8 ym
to 1.2 ym were used in the charging theory and compared with data
from a 1.0 ym diameter particle. It was found that for a charg-
ing field strength of 6.0x10^ V/m a 0.8 ym diameter particle pro-
duces a lower percentage difference between theory and experiment,
whereas at higher field strengths a 1.2 ym particle gives a better
fit. Table 1 summarizes this comparison. The concentration of
DOP in methanol required to produce a 1.2 ym diameter DOP aerosol
is approximately 2.7 times that required to produce a 1.0 ym dia-
meter DOP aerosol particle. Thus it is unlikely the particle di-
ameter was as large as 1.2 ym. Also, as particle diameter in-
creases the uncertainty of concentration decreases. We conclude
from this exercise that any lack of agreement between theory and
experiment is not due primarily to errors in particle diameter.
The source of the discrepancies may be related to a dependence of
ion mobility on the electric field strength.9 Since the calcu-
lation of the ion density depends upon the value determined for
the mobility of the ions, any uncertainty in the mobility will be
reflected in the Nt product, which will, in turn, affect the par-
ticle charging calculations.
Figure 30 shows the results for 2.0 ym diameter DOP particles.
In this case the tendency continues for experiment to rise from
below to above theory as the charging field strength is increased
from 0.6 kV/cm to 7.5 kV/cm. However, the effect is not as mark-
ed as with the 1.0 ym diameter aerosol.
The experimental results for 4.0 ym and 7.0 ym diameter DOP
particles are compared with, theoretical charge calculations in
Figures 31 and 32, respectively. In both of these cases the the-
ory predicts larger values of particle charging than are found
experimentally for all values of charging field strength.
Particle charging experiments were carried out with, aerosols
made from stearic acid and glycerol. Figures 133 and 34 show the
results for stearic acid aerosols 2.0 ym and 2.06 ym in diameter,
respectively. Agreement between theory and experiment for this
aerosol material was generally quite poor.
The source of the poor agreement between experiment and the-
ory is believed to be incomplete drying on the part of the. stearic
52
-------
250
200
150
CD
ce
<
6
o
cc
UJ
CO
5
50
n
E=3.6XIOpV/m
E* 8.0X10° V/m
1.0
ION DENSITY X TIME, sec/m3 X I01
Figure 28. Niomber of charges per particle as a function of Nt
product for a 1.0 ym diameter DOP aerosol. The
solid lines represent the SRI charging theory.
53
SOUTHERN RESEARCH INSTITUTE
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500
400
300
-------
TABLE 1. EFFECT OF A CHANGING PARTICLE SIZE ON THE "GOODNESS OF FIT"
BETWEEN EXPERIMENT AND THEORY. THE CALCULATED DIAMETER WAS
1.0 ym OOP
Particle Size Charging Field Strength
(microns) 80 V/cm 600 V/cm 3.6 kV/cm 5.0kV/cm 7.5 kV/cm 8.0 kV/cm
ui 0.8 Best Fit
Ul
0.9
1.0 Best Fit
1.1
1.2 Best Fit Best Fit Best Fit Best Fit
m
3)
3D
m
in
m
n
z
-I
H
m
-------
1600
1400
1200
1000
CD
ui
o
< 800
o
u.
O
IU
OQ
600
400
ZOO
E*7.5XI05 V/m
D
O 0
O O 0
i >
it
. i .
0 1.0 2.0 3.0 4.0
ION DENSITY X TIME , sec/m3 X IO13
Figure 30. Comparison of experimental and theoretical values of
particle charge for a 2.0 urn diameter DOP aerosol.
56
-------
5000
4000
3000
in
(0
IT
U
u. 2000
o
UJ
00
1000
' ' — ' i I i
= 7.5XI05V/m
i i — i — r— r
O
00
O
o
o o
oooo o o o
I I I I I I I I
01234
ION DENSITY X TIME, sec/m3XI013
Figure 31. Number of charges per particle as a function of Nt
product for 4.0 vim diameter DOP particles.
57
SOUTHERN RESEARCH INSTITUTE
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18
16
14
12
10
O
10
CO
UJ
I 8
o
£
ffi
1 1 1 1
T r—i—T
E*7.5X !05V/m
o o
5.0XI(T V/m
A
E*6.0XI04VAn
COO
I I I I I I I
0123
ION DENSITY X TIME, sec/m3X I013
Figure 32. Number of charges per particle as a function of Nt
product for a 7.0 jim diameter DOP aerosol.
58
-------
1400
1200
1000
to
o 800
oc
<
o
o 600
tr
2 400
200
Figure 33.
T 1 r
A
A
A
E*5.0X I05 Win.
ION
1.0
DENSITY X
2.0
TIME , sec/m3 X 10
13
Theoretical and experimental values of charge per
particle as a function of Nt product for 2.0 ym dia-
meter stearic acid particles.
59
SOUTHERN RESEARCH INSTITUTE
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1400
1200
1000
g 800
X
u
-------
acid aerosol. This was indicated by samples of stearic acid aero-
sol particles which were observed after impaction on microscope
cover glasses. The more usual technique of sampling a solid aero-
sol by catching it on a filter then coating the filter with immer-
sion oil to aid in observing the particles will not work in this
case, because the index of refraction of stearic acid and
immersion oil are very nearly the same. It was found that the
particles were nonspherical and much larger than their calculated
diameters.11 Figure 35(a) shows a photomicrograph of these parti-
cles. Other photomicrographs show that clumping and splattering
on impact also occurs. It was therefore concluded that the aero-
sol was not sufficiently dried. Heating the aerosol does not
appear to solve the problem although spherical particles can be
produced. Figure 35 (b) shows a photomicrograph of the same aero-
sol after being passed through a heated pyrex tube approximately
70 cm long and 1.8 cm in diameter. Temperature inside the tube
was approximately 41°c. Best results were obtained at this
temperature, with the aerosol becoming plastic and splattering
on impaction at higher temperatures.
The majority of aerosol particles are spherical, but some
nonspherical particles remain and evidence of impact splattering
and clustering still exist. These particles should be approxi-
mately 2.0 ym in diameter according to Berglund's11 equations;
however, 3.5 ym to 4.0 ym are more typical of what is seen.
Figure 36 presents the results of charging experiments per-
formed with aerosols of glycerol. This material has a relative
dielectric constant of 42.5, much higher than any of the other
materials used. The experimentally determined values of charge
are much lower than the theoretical values. This result may occur
because of an uncertainty in the determination of particle size.
Glycerol tends to wet almost any surface it contacts; therefore,
direct observation of glycerol aerosol particles is difficult.
Optical measurements of the sizes of the glycerol particles used
in these charging experiments indicated a size below the 2.0 ym
calculated from Berglund's equations. Because of this it was sus-
pected that some of the glycerol itself was evaporating along with
the solvent, methanol. Although glycerol has a low vapor pressure
(1 mm Hg at 125°C)l5 it is significantly higher than that of DOP
(0.028 mm Hg at l25°C).llf A diameter of 1.8 ym for the aerosol
provides the best theoretical fit to the data shown in Figure 36,
which indicates that as much as 25 percent of the glycerol may have
evaporated before charging took place. Because of the apparent
evaporation problem the use of glycerol as an aerosol material was
not pursued further.
Second Hewitt Charger
It became apparent during experiments with the first Hewitt-
type charger that certain modifications in the design could be
61
-------
(a)
;^^^ •-'•
Figure 35.
(b)
Stearic acid aerosols, calculated diameter
2.0 ym (a) no heating, (b) heated to approxi-
mately 100°F.
62
-------
1000
800-
600
(0
til
o
DC
<
X
0
u. 400
o
oc
UJ
00
200-
E* 5.0X10"V/m
JL
0.5 1.0
ION DENSITY X TIME ,
1.5
sec/m" XIO
2.0
.13
2.5
Figure 36.
Charge per particle as a function of Nt product for
a 2.0 pm glycerol aerosol. The relative dielectric
constant for this material is 42.5.
63
SOUTHERN RESEARCH INSTITUTE
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made to improve the electrical behavior and the gas flow character-
istics. A second Hewitt charger was designed, with special atten-
tion given to the elimination of sharp edges and corners which
might contribute to sparking. Smooth transition pieces, cast in
RTV 106 silicone rubber (General Electric), were made in order to
provide for reduced turbulence in the aerosol stream entering and
leaving the charging region.
When the first Hewitt charger was replaced by the second one
a number of measurements were repeated to compare the two devices.
Figure 37 shows the theoretical and experimental behavior of par-
ticle charging for OOP particles 1.0 ym and 2.0 ym in diameter as
the electric field strength in the charging region is varied
while holding the Nt product fixed at l.OxlO13 sec/m3. Data taken
with both Hewitt-type chargers is in reasonably good agreement
with theory for charging field strengths up to about 8x105 V/m.
At low field strengths the measured value of the charge falls be-
low the theory, and at high field strengths experimental values
are above the theoretical values. There are two possible sources
for this effect. First, there may be sufficient turbulence re-
lated to the corona wind at high field strengths to cause a sub-
stantial increase in the average particle residence time in the
charging region. Secondly, in view of Bricard's study^ concern-
ing the effects of aging on ion mobility, the enhancement of
charging above the theoretical predictions at high charging field
strengths may be at least partly due to an effective increase in
ion mobility.
Figures 38 and 39 show charge per particle for a 1.0 ym OOP
aerosol as a function of Nt for various values of the charging
field strength. The data taken with the two Hewitt chargers is
generally in good agreement (compare with Figures 28 and 29) with
the exception of the case for which the charging field strength is
3.6xlOs V/m, where the data taken using the second charger lies
much closer to the theory.
The results of charging experiments using polystyrene latex
(PSL) aerosols in the second Hewitt charger are presented, with
the theoretical charge predictions, in Figures 40, 41, and 42.
Four different particle sizes were used, ranging from 0.109 ym to
1.099 ym in diameter. The dielectric constant of this material
was taken to be 2.5, the value for bulk polystyrene.* * The the-
ory agrees well with experimentally determined charge for the
0.109 ym and 0.312 ym particles. For the larger particles the
agreement is not quite as good, but still falls within about 30
percent.
Negative Corona Charging
The ion mobility associated with a negative corona is gener-
ally slightly higher than that found for a positive corona. With
64
-------
1600
1400
1200
1000-
LU
CD
at 800
ac
UJ
oo
600-
400-
200
T
T
T
T~
A
O FIRST HEWITT CHARGER
^SECOND HEWITT CHARGER
I.Opm
8
ELECTRIC FIELD STRENGTH, kV/cm
Figure 37
Comparison of particle charging as a function of
charging field strength for two different Hewitt-type
chargers. The Nt product was held constant at 1.0
xlOJ sec/m3 on the field was varied. Aerosols used
were DOP, 1.0 ym and 2.0 ym in diameter.
65
SOUTHERN RESEARCH INSTITUTE
-------
300
200
CO
UJ
o
cc
<
X
o
u_
o
5 100
CD
3E
O O
O
= 5.0XIO°V/m
O
I
_L
I
0.5 1.0 1.5 2.0
ION DENSITY X TIME, sec/m3X I013
2.5
Figure 38.
Charge per particle as a function of Nt product for
a 1.0 jam DOP aerosol. The second Hewitt charger was
used for these data.
66
-------
500
200
100
50
UJ
o
x 20
UJ
OQ
10
a
d = 1.09 91
= 0.3l2jJm
Figure 40.
12345678
CHARGING FIELD STRENGTH, kV/cm
Number of charges per particle for polystyrene latex
particles of various sizes. The Nt product was held
constant at 5x1012 sec/m3 as the charging field was
varied.
68
-------
400
E«6.0XI05 V/m
300
E= 3.6X10 V/i
co 200
o
tc
X
o
U_
O
Q:
UJ
oo
100
Figure 39.
0.5 1.0 1.5 2.0 2.5
(ON DENSITY X TIME , stc/m3 XI013
Charge per particle as a function of Nt product for
a 1.0 vim DOP aerosol, charged with the second Hewitt-
type charger.
67
SOUTHERN RESEARCH INSTITUTE
-------
500
200-
2345678
CHARGING FIELD STRENGTH, kV/cm
Figure 41. Number of charges per particle as a function of charg-
ing field strength, for polystyrene latex particles
of four different sizes. Nt is l.OxlO13 sec/m2.
69
SOUTHERN RESEARCH INSTITUTE
-------
500
200
100
50
yj
o
g 20
x
o
u.
o
a:
ui
m
10
d * 1.099 m.
- 0.60pm -
d= 0.312 Mm.
d=0.109pm
Figure 42
123456
CHARGING FIELD STRENGTH, kV/cm
Number of charges per particle as a function of
charging field strength, for polystyrene latex parti-
cles, with Nt = l.SxlO13 sec/m3.
70
-------
the curve fitting technique employing Equation (18) a value of
2.70 x 10~4 m2/Vsec has been determined for negative corona char-
ging, as compared with 2.38 x 10"1* mz/V.sec for positive corona
under like conditions.
Figure 43 shows a comparison between the results of positive
and negative corona charging for 0.109 ym diameter PSL particles,
with the Nt product held at 5.0 x 1012 sec/m3 for both cases.
The charging theory predicts results which differ by less
than one percent for positive and negative corona charging under
the experimental conditions associated with Figure 43. But the
measured values of charge for negative corona charging average
approximately 1.5 times the values measures for positive charging.
The disparity increases as the charging field strength is increas-
ed.
It is not immediately apparent why the charge per particle
should be so much greater for negative corona than for the posi-
tive case. The principal difference between the two is that there
may be free electrons included with the negative ions. And since
the electron mass is extremely small in comparison with that of a
gas ion there is a very large difference in the mobilities of cur-
rent carrier species. It may not be appropriate, therefore to
treat the system as though a single "average" mobility is suffi-
cient to describe the combined effects of the carrier species. It
is concluded that the charging mechanisms described by the theory
are sound; however, further studies related to mobility measure-
ment and proper application of such measurements to the theory
may lead to a more complete understanding of the charging process.
SOUTHERN RESEARCH INSTITUTE
-------
Figure 43.
8
to
uj
o
oc
<
I
O
tr.
UJ
CD
A
A A
O
O O
O
i i i I i i i i I i
A NEGATIVE CORONA
O POSITIVE CORONA
I
8
CHARGING FIELD STRENGTH, kV/cm
Comparison of positive and negative corona charging
for 0.109 ym polystyrene latex spheres. For both
sets of data Nt is 5.0 x 1012 sec/m3. The theoreti-
cal curves for positive and negative corona, repre-
sented by the solid line, are indistinguishable on
this scale.
-------
SECTION 5
PILOT SCALE EXPERIMENTAL WORK
In order to test the charging theory and to demonstrate the
feasibility of particle charging in a high current density system
under various dust loading conditions a pilot scale charging de-
vice was designed and constructed for installation at the inlet
of an existing 600 - 1000 ACPM pilot scale electrostatic precipi-
tator. A multiple wire-plate electrode configuration was used,
with narrow electrode separation. An assembly drawing of the
precharger is presented in Figure 44. There are two separate
precharging sections, both of wire-plate geometry. The first
section has four 11.4 cm wide grounded plates and three corona
wires while the second section has six 6.9 cm wide grounded
plates and five corona wires. The grounded plates are construc-
ted of 0.32 cm thick stainless steel with smoothed corners. The
precharger is specifically designed to eliminate sneakage. A
teflon enclosure holds the two precharging sections and was de-
signed to interface with the dry-wall pilot scale precipitator
mentioned above.
For each of the two separate charging sections, current-
voltage characteristics were measured with 0.0254 cm and 0.127
cm corona wires. The results were compared with those of an
electric field computer simulation.
The computer simulation is based on an electrode geometry
consisting of a pair of infinitely long parallel plates with
evenly spaced parallel wires lying in the plane midway between
the plates. The precharger, on the other hand, has only a sin-
gle wire between each pair of narrow parallel plates. By repre-
senting the precharger section with one segment of the periodic
geometry simulated by the computer program a useful approximation
can be made. In Figure 45 sketches of the electric field lines
in the two configurations are compared. The correspondence is
not exact because of the edge effects in the precharger geometry.
Compensation for the edge effects was achieved by using a simula-
ted duct segment length (L in Figure 45) larger than the prechar-
ger plate width. Since no precise information on the edge ef-
fects is available the width in the simulation was treated as an
adjustable parameter until a good approximation to the experimen-
tal result was found for each of the .two sections. This "effec-
tive plate width" was then held constant for further calcula-
tions .
73
SOUTHERN RESEARCH INSTITUTE
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Figure 44.
CORONA
WIRES
Conceptual sketch of pilot scale charging device.
Only the three-wire charging section is shown. A
second charging device with five corona wires and
six plates is located in the opposite end of the
enclosure.
74
-------
(A) Periodic duct geometry used in computer simulation
W-actual width
Ws=simulation width
(B) Prechargcr section
Figure 45.
Sketch of electric field lines in (a) periodic
geometry of infinite extent employed in computer
program, and (b) pilot scale precharger section
containing one wire and having finite plate width.
75
SOUTHERN RESEARCH INSTITUTE
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Figures 46 and 47 show the experimental and theoretical re-
sults obtained with a 0.0254 cm corona wire, for positive and
negative corona, respectively. For the smaller precharger sec-
tion the actual plate width was 6.86 cm, and the width used in
the computer simulation was 9.4 cm. The larger section plate
width was 11.4 cm; the simulated width was 20.96 cm. The shapes
of the curves are dominated by the mobility of the ions, which
was taken to be 2.2 x 10~'*m2/V-sec for positive corona in air,
and 3.0 x 10~1*m2/V-sec for negative corona to achieve good fits.
Figures 48 and 49 show the variation in electric field along
the perpendicular line connecting the wire and plate. These the-
oretical curves are plotted for the maximum values of current
density achieved experimentally. The precharger section with the
smaller plates and spacing shows a more uniform electric field
and a much higher value of maximum current density than the lar-
ger section.
Figures 50 and 51 show comparison of experimental determina-
tion of current-voltage characteristics for two different corona
wire sizes. Average current density for the smaller corona wire
consistently exceeds that for the larger wire in both precharger
sections for both polarities and at all values of applied vol-
tage. Next, the pilot scale precharging device, fitted with
0.0254 cm diameter corona wires, was installed in the dry wall
pilot scale electrostatic precipitator. Current-voltage charac-
teristics were measured for both precharger sections under var-
ious dust loading conditions.
In Figures 52, 53, and 54 the electrical characteristics of
the three wire precharger section (1.46 in. wire-to-plate spac-
ing) are shown along with the corresponding theoretical curves.
Increases in dust loading cause a decrease in mobility and a
concomitant reduction in current for a given value of applied
voltage. Mobilities in the theoretical model were chosen to
provide the best approximation to the experimental results. The
theoretical curves are repeated together in Figure 55 for com-
parison. Electric field profiles at the maximum current density
for each of the three cases are shown in Figure 56.
The behavior of the 5-wire precharger section (0.85 in.
wire-to-plate spacing) was somewhat erratic in comparison with
the 3-wire-section as may be seen in Figure 57. The current was
higher at every value of voltage in the presence of dust loading
than in the "clean" system. It appears that an accumulation of
dust on the bottom of the precharger may be responsible for this
sort of aberration. After running the system long enough to ac-
cumulate a dust layer about % in. deep on the bottom of the pre-
charger, the dust blower was turned off and another measurement of
the current-voltage characteristic was made. The presence of the
dust layer provides an additional current path between the corona
wire and the plate, thus producing a greater apparent average current
76
-------
50r-
SRI theory
experimental,
O 2.17cm, wire to plate
3.70 cm, wire to plate
0
Figure 46
APPLIED VOLTAGE, kV
Current-voltage characteristics of both sections
of the pilot scale precharger with 0.0254 cm corona
wire at positive potential. Curves derived from
computer simulation are included for comparison with
the experimental results.
77
SOUTHERN RESEARCH INSTITUTE
-------
50r
•S40
£30
5
to
I20
LU
ec
oc
O
O
LU
0
2
O SRI theory
experimental,
O 2.17cm, wire to plate
3.70 cm, wire to plate
Figure 47.
10 20
APPLIED VOLTAGE,
30
Current-voltage characteristics of both sections
of the pilot scale precharger with 0.0254 cm corona
wire at negative potential. Solid lines are
computer generated curves.
78
-------
14
12
10
K)
b 8
X
E
UJ
° 2.17 cm, wire to plate
A 3.70 cm, wire to plate
Figure 48. Electric field profiles for both sections of the
pilot scale precharger at the maximum experimental
current density, positive corona. 0.0254 cm dia-
meter corona wires were used.
79
SOUTHERN RESEARCH INSTITUTE
-------
X
E
UJ
14
12
10
B
4
O 2.17 cm, wir*e to plate
A 3.70 cm, wire to plate
Figure 49.
Electric field profiles for both sections of the
pilot scale precharger at the maximum experimental
current density, negative corona. 0.0254 cm dia-
meter corona wires were used.
80
-------
50
40
CM
Q.
E
30
S
I20
ui
o
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oc
8 10
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2.17cm wire to plate,
O wire diameter s 0.0254 cm
• wire diameter = 0.127cm
3.70cm wire to plate,
A wire diameters0.0254cm
A wire diameter s 0.127cm
10
20
Figure 50.
APPLIED VOLTAGE, kV
Comparison of current-voltage characteristics of
precharger with 0.0254 cm corona wire and with 0.127
cm corona wire, positive corona.
81
SOUTHERN RESEARCH INSTITUTE
-------
5Qi— 2.17cm wire to plate,
owire diameter = 0.0254 cm
•wire diameter = 0.127cm
40
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3.70cm wire to plate
^ wire diameter - 0.0254cm
A wire diameter s o.l 27cm
10
20
30
APPLIED VOLTAGE, kV
Figure 51. Comparison of current-^voltage characteristics of pre-
charger with 0.0254 cm corona wire and with 0.127 cm
corona wire, negative corona.
82
-------
18
16
14
12
10
111
a
W
1*1
ae
fle
u
ui
ac
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6
2 -
6
10
14
18
26
BO
Figure 52
APPLIED VOLTAOE, KV
Current-voltage characteristic for the 3-wire pre-
charger section with no dust loading, negative corona,
The smooth curve is the SRI theory with mobility of
2.7 x IQ-4 m2/V-sec.
83
SOUTHERN RESEARCH INSTITUTE
-------
18
10
14 18 22
APPLIED VOLTAGE. KV
26
30
Figure 53
Current-voltage characteristic for the 3-wire
charger section under 6.85 grain/ft3 dust loading,
negative corona. Theoretical curve for mobility of
2.5 x 10-1* mVv-sec.
84
-------
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Figure 54
10
14
18
26
30
APPLIED VOLTAGE, KV
Current-voltage characteristic for the 3-wire pre-
charger section under 11.8 grains/ft3 dtast loading,
negative corona. Theoretical curve for mobility of
2.2 x 10-" m2/V-sec.
85
SOUTHERN RESEARCH INSTITUTE
-------
18
16
- O 27 g/m3, p » 2.2 x I0~4 m2/ V sec
CM
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Dl5.6g/m,
2.5xlO"4m2/Vsec
10 15 20
APPLIED VOLTAGE, NV
25
30
Figure 55. Comparison of the theoretical curves corresponding
to Figures 52 through 54 for the 3-wire precharger
section.
86
-------
12
10
8
m
'o
K
I6
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4
Figure 56
O mobility * 2.2 x IO"4 m2/Vsec
D mobility =2.5xlO"4m2/Vsee
A mobility * 2.7 x IO"4 m2/Vsec
Fraction of wire to plate distance, x/
D
Electric field profiles along a line from wire
to plate, normal to the plate, for the maximum
values of current and voltage plotted in Figure 55.
87
SOUTHERN RESEARCH INSTITUTE
-------
"
o
K
bl
10
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§
o
bi
K
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ri.8
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10
15
APPLIED VOLTAGE, KV
Figure 57. Current-voltage characteristics of 5-wire precharger
section under various conditions, negative corona.
88
-------
density than occurs in the "clean" precharger.
The three-wire precharger section is much less affected by
dust accumulation. Part of the reason for this may be found by
examining the dust layer after operating both precharger sec-
tions. A relatively clear area surrounds the corona wires in the
3-wire section, reaching almost to the plates. Apparently the
corona wind in that area tends to blow the dust away, providing a
sort of self-clearing effect. In the 5-wire section the maximum
applied voltage is lower, and hence the corona wind effect is
smaller.
A simple test of the charging effectiveness of the prechar-
ger was made by collecting flyash on an isolated metal filter.
The filter was connected to an electrometer so that the integra-
ted charge could be monitored for a sample of flyash which had
passed through the precharger.
A plastic filter holder, fitted with a nozzle for isokinetic
sampling, and containing a silver filter was placed in the duct
immediately downstream from the precharger. Preliminary tests
showed that when the precharger was turned on and no flyash was
being blown through the system, charge accumulation on the filter
was of the order of 10"11 coul/sec or less. Approximately the
same order of charge accumulation occurred with the precharger
turned off and with flyash blown through the duct. When the pre-
charger and flyash blower were both turned on the rate of charge
accumulation rose abruptly to more than 10~a coul/sec. For each
test point measured the precharger was set at a particular vol-
tage and then the flyash feed and blower were turned on until a
total charge of approximately 5x10"8 coul was accumulated on the
filter. The collected flyash was then weighed and the charge/
mass ratio was calculated. Figure 58 shows the results of these
measurements for negative corona and Figure 59 shows the positive
corona results.
A measurement of charge/mass ratio was also made at elevated
temperature. The precipitator system was heated to approximately
105"C and the negative corona charging test was repeated. The
results, shown in Figure 58 show a much reduced charging effec-
tiveness. Heating the flyash produced an increase in resistiv-
ity, and apparently back corona occurred at a voltage only very
slightly above the corona inception voltage.
Impactor data were taken to provide size distribution infor-
mation as well as to verify the effectiveness of the precharger
in improving the performance of the pilot scale precipitator.
Figure 60 shows inlet data for two Brink impactor runs made on
different days. An Andersen impactor was used to measure the
outlet size distribution. The data points for the smaller parti-
cle sizes at the outlet with the precharger on must be considered
less reliable because the samples collected by the impactor were
89
SOUTHERN RESEARCH INSTITUTE
-------
16
14
12
10
~ 8
o
4
I 5 wire section
J 3 wire section, T = 26 °C
A 3 wire section, T= 105 *C
I
-10 -20
PRECHAR6ER APPLIED VOLTAGE, KV
-30
Figure 58. Charge/mass ratio as a function of voltage applied to
precharger; negative corona.
90
-------
10
X
0»
o
o
e
5 5
5WIRE SECTION
3 WIRE SECTION
5 10 15 20
PRECHARGER APPLIED VOLTAGE, kV
Figure 59. Charge/mass ratio as a function of precharger
voltage, positive corona.
91
SOUTHERN RESEARCH INSTITUTE
-------
12
10
10
CO
UJ
o »
1°
o
o»
JO
•o
Z G
* ios
8
10
0.1
x \ PRECHARGER OFF
OUTLET, \ \
PRECHARGER ON \ %
ll
j L
J_
I III
Figure 60.
1.0 10
PARTICLE DIAMETER,
Size distributions of flyash at inlet, as measured
with Brink impactor and at outlet using Andersen
impactor.
100
92
-------
very small. A broken corona wire in the precharger required that
the sampling time be cut short.
The collection efficiency curves presented in Figure 61 were
derived from the information in Figure 60. The pilot scale pre-
cipitator was operating at a current density of approximately
270 yA/m2. The three-wire precharger section was set at appro-
ximately 8 mA/m2. An inlet mass loading of approximately 3.4 g/
m3 was used for these measurements.
The SRI charging theory was used to compute the charge/mass
ratio obtained with the precharger for comparison with the meas-
ured results. The computer program calculates the total charge
per particle of a specified diameter. Input information includes
average charging field, ion density, and residence time in the
charging region. These quantities were derived directly from the
measured current-voltage characteristics of the precharger and
the flow rate through the charging region. Using a density of
2.25 g/cm3 , the charge/mass ratio was computed for eight particle
sizes in the range 0.25 ym to 32 ym diameter, with various vol-
tages applied. The results of these calculations are shown in
Figures 62, 63, 64 and 65. The four cases include each of the
precharger sections under both positive and negative corona con-
ditions. In the range of particle sizes considered, field char-
ging dominates over the diffusion charging process. Since the
charging rate depends on the square of the radius and the mass
increases as the cube of the radius the charge/mass is inversely
proportional to the particle radius.
In order to compare the theoretical results with experimen-
tal measurements a sum was taken over the range of particle si-
zes, weighted in accordance with the measured particle size dis-
tribution. Thus, for a particulate sample having mass M and a
size distribution such that there are N^ particles per gram in
the ith size range, with average charge q^ per particle,
The theoretical values of charge/mass ratio are shown in
Figures 66, 67, 68, and 69 along with the experimentally deter-
mined values. The scatter in the theoretical points arises from
the fact that empirically derived input information was used in
the charging theory. In nearly all cases the theoretical values
are somewhat higher than those determined experimentally. But,
considering the magnitude of statistical errors involved, the a-
greement between theory and experiment appears to be reasonable.
The effects of the precharger on overall precipitator per-
formance were investigated under various voltage conditions by
making outlet particulate load measurements with a Climet
93
SOUTHERN RESEARCH INSTITUTE
-------
50
40
30
20
10
cc
fc
uj 1.0
O.I
0.01
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I I I I I 1111 I I I I I 11 I 111 (I III) I I
PRECHARGER OFF
PRECHARGER
111 iiii I
111 ii I mil i j
0.5 1.0 2 5
PARTICLE DIAMETER , pm
10
Figure 61.
Penetration of pilot scale dry wall pre-
cipitator with 3-wire precharger section
turned on compared with efficiency obtained
with the precharger off. Precipitator cur-
rent density was held at 270 iaA/m2 through-
out these measurements'.
94
-------
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10
c-5
§
u
o
oc
8 I06
i
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10'
-5
-25
Figure 62.
-10 -15 -20
APPLIED VOLTAGE, kV
Charge/mass ratio as a function of precharger voltage
for various particle sizes in the 3-wire precharger
section, negative corona. Low resistivity flyash.
95
SOUTHERN RESEARCH INSTITUTE
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10
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J.
-4
-8 -12 -16
APPLIED VOLTAGE, kV
Figure 64. Charge/mass ratio as a function of precharger
voltage for various particle sizes in the 5-wire
precharger section, negative corona.
-20
97
SOUTHERN RESEARCH INSTITUTE
-------
-4
10
g
o
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tr
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en
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8 12 16
APPLIED VOLTAGE, kV
20
Figure 65. Charge/mass ratio as a function of prec&arger voltage
for various particle sizes in the 5-wire precharger
section, positive corona.
98
-------
16
14
12
o»
X.
o
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8
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Figure
SRI CHARGING
THEORY
10 20
PRECHARGER VOLTAGE. kV
Comparison of experiment with theory for overall
charge/mass ratio of flyash sample in 3-wire pre-
charger section, negative corona.
99
SOUTHERN RESEARCH INSTITUTE
-------
SRI CHARGING
THEORY
10 20
PRECHARGER VOLTAGE, kV
Figure 67. Comparison of experiment with theory for overall
charge/mass ratio of flyash sample in 3-wire prechar-
ger section, positive corona.
100
-------
SRI CHARGING
THEORY
10 20
PRECHARGER VOLTAGE, kV
Figure 68. Comparison of experiment with theory for overall
charge/mass ratio of flyash sample in 5-wire prechar-
ger section, negative corona-.
101
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16
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SRI CHARGING.
THEORY
10 20
PRECHARGER VOLTAGE, kV
Figure 69. Comparison of experiment vcith. theory for overall
charge/mass ratio of f lyash. sample in 5-wire prechar-
ger section, positive corona.
102
-------
Instruments Model 208 optical particle counter. A significant
increase in collection efficiency was observed for all particle
sizes as the precharger voltage was increased while holding the
precipitator voltage constant. Figure 70 shows the results for
the 3-wire precharger section and Figure 71 shows the 5-wire sec-
tion results. In both cases the pilot scale precipitator was op-
erated near the maximum voltage which could be applied without
excessive sparkover; approximately 40 kV. Both precharger sec-
tions were capable of producing improved collection efficiency,
but the 3-wire geometry was clearly the more effective of the
two.
Figures 72 .and 73 present the same data shown in the pre-
vious two graphs, except that the collection efficiency is given
as a function of the current density in the precharger. The mi-
gration velocity is also shown as a function of precharger cur-
rent density in these plots.
In Figure 74 the performance of the precharger - precipita-
tor combination is indicated for various values of precipitator
voltage with the precharger voltage held at approximately 20 kV.
When the precipitator voltage was removed completely some parti-
cle collection was achieved. The efficiency increased as the
field in the precipitator was increased, but much greater in-
crease in efficiency occurred as the corona current in the pre-
cipitator became substantial.
103
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2.4-4.8jJm
-2 -4 -6 -8 -10
PRECHARGER APPLIED VOLTAGE, W
-12
Figure 71.
Penetration of the pilot scale electrostatic
pre1ip?ta?or as a fSuction.of the voltage on
the 5-wire precharger section.
105
SOUTHERN RESEARCH INSTITUTE
-------
0.01
5 10 15
PRECHARGER CURRENT DENSITY, mA/m2
Figure 72.
Penetration as a function of precharger cur-
rent density for various particle sizes, using
the 3-wire precharger.
106
-------
100
2 4 6 8 10
PRECHAR6ER CURRENT DENSITY, mA/m2
Figure 73. Penetration as a function of precharger cur-
rent density for various particle sizes, using
the 5-wire precharger.
107
SOUTHERN RESEARCH INSTITUTE
-------
0.01
-10 -20 -30 -40
PRECIPITATOR VOLTAGE, kV
-50
Figure 74. Penetration of pilot scale electrostatic pre-
cipitator as main voltage is varied while
maintaining the 3-wire precharger voltage
constant at approximately 20 kV.
108
-------
SECTION 6
ANALYSIS AND EVALUATION OF THE TWO-STAGE,
PRECHARGER-ESP CONCEPT
PARTICLE CHARGING
In a two-stage precharger-ESP the particle charging and
collection functions are carried out separately. An important
factor in the operation of a two-stage system is effective parti-
cle charging in the precharger stage. The theory shows that
large values of both electric field strength and ion density-
residence time product are required to provide a suitable level
of particle charging effectiveness in a precharger. Practical
limitations on the performance of a precharger may arise from
two principal sources: (1) the presence of particulate material
having high electrical resistivity, and (2) the effects of space
charge on the electrical characteristics of the system. The
importance of the various factors related to particle charging
are discussed-in the following paragraphs.
Electrical Parameters
The results of the charging theory may be used to examine
the effects of variation of charging parameters. In,the follow-
ing discussion the effects of the electric field strength, the ion
density-residence time product, and the corona geometry for a wire-
plate system are examined.
The graph shown in Figure 75 presents the charge per parti-
cle as a function of the average field for two values of ion den-
sity-time product and for various particle sizes. The effect of
varying Nt is more pronounced for small particles than for the
larger ones. The effect of field charging with increasing parti-
cle size is evident from the difference in the shape of the curves
for the different particle sizes.
Figure 76 indicates the charging behavior as a function of
the ion density-residence time product, Nt, for fields of 5 kV/cm
and 10 kV/cm for three particle sizes. It can be seen that in-
creasing Nt above approximately 1013 sec/cm3 will produce little
increase in the charge accumulated, particularly for the larger
particles, where field charging dominates.
109
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104
103
102
10
- 2.0urn DIAMETER
• Nt = 2.0x1013 sec/m3
A Nt = 0.5 x 1Q13 sec/m3
0.5Mtn DIAMETER
K = 100
O Nt = 2.0x1013 sec/m3
A Nt = 0.5 x 1Q13 sec/m3
0.05 Mm DIAMETER
K = 100
Nt = 0.5 x 1013 sec/n.3
2 4 6 8 10
CHARGING FIELD STRENGTH, kV/cm
12
Figure 75. Charge per particle as a function of electric field
for three particle sizes and two values of Nt.
110
-------
104
103
I
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Ul
u
Ul
cc
<
CL
102
10
0.5Aim DIAMETER
K = 100
0.05Aim DIAMETER
K = 100
E = 10kV/cm
E = 5kV/cm
€ E = 10kV/cm
A E = 5kV/cm
O E = 10kV/cm
A E = 5kV/cm
2.0urn DIAMETER
K = 100
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
Figure 76.
Charge per particle as a function of ion concentra-
tion-residence time product for three particle
sizes and two values of electric field.
Ill
SOUTHERN RESEARCH INSTITUTE
-------
Figures 77-79 show calculated effects of variations
in wire diameter and wire-plate spacing in a duct-type charging
geometry. Increasing the wire diameter increases the corona
inception voltage (see Figure 77). The slope of the current
voltage curve also increases slightly for larger wire sizes. In
Figure 78 the average field and the field strength at the plate
are plotted as a function of wire diameter. For a given current
density the average field increases much more than the field at
the plate as the wire size is decreased.
Variations in the wire-plate spacing produce changes in the
current-voltage characteristic as illustrated in Figure 79. In
this case there is only a slight change in corona inception vol-
tage and a large change in the slope of the I-V characteristic
as the wire-plate spacing varies. This may be contrasted with
Figure 77. The average field and the field at the plate are shown
as functions of the current density in Figure 78. It is interesting
to note that increasing the wire-plate spacing increases the
field at the plate but decreases the average field. We may
choose, for example, a narrow wire-plate spacing and moderate
wire diameter in order to achieve high charging fields and high
current density.
High Resistivity Particulate Material
The difficulties in electrostatic precipitation of high
resistivity particles arises principally from the behavior of
the corona system when the passive electrode becomes coated with
the material. The effectiveness of the particle charging process
becomes reduced, and the corona current tends to behave erratically.
The result is a reduction in overall efficiency of the precipitator.
The problem of dealing with high resistivity particulate materials
and some possible approaches to the solution of the problem are
discussed in the following paragraphs.
Electrical conduction through a dust layer on an electrode
may be described by Ohm's law:
E = jp
The resistivity, p, depends upon the type of particulate
material, temperature, humidity and other factors such as the
presence of conditioning agents. A layer of high resistivity
material behaves as a resistor in series with the corona system,
which causes a reduction in current for a given applied voltage.
But, more importantly, the field in even a thin particulate layer
may become great enough to cause breakdown to occur. Localized
high field regions at breakdown sites may then produce ionization,
resulting in back corona.
112
-------
o
«• 7
I 1 —
• o = l.27xKr4m
__ "0 = 1.27x10-301
^k ^^ ^B A . _. _ df
X
CM
V a =5.08 x 10" 3 m
E
N fiU- A .
1 | -
1 1
b =2.2 xlO-4rr.2 /volt-sec
SX = O.I 143m
SY = O.II43m
A
n
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§
OL
CO
ui
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UJ
oc
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UJ
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30 40 50 60
APPLIED VOLTAGE,kV
70
80
Figure 77.
Current-voltage characteristics of a wire-plate
corona system for various sizes of corona wire,
holding all other parameters constant. Sx is
wire-plate spacing, Sy is wire-to-wire spacing,
b is ion mobility, and a is corona wire diameter.
113
SOUTHERN RESEARCH INSTITUTE
-------
8
I I
• a = l.27x!0~4m
»a = l.27xlCT3m
Aa=2.54xlO~3m
o = 5.08 x I0~3 m
E
I 1 I
b =2.2xlO~4m2/volt-sec
Sx = O.II43m
SY=O.II43m
0123456
AVERAGE CURRENT DENSITY AT PLATE , A/m2x!06
Figure 78. Electric field at the plate electrode, ED, and
average electric field, Ea as a function of current
density at the plate for various wire sizes in a
wire-plate corona system. (a = wire diameter;
b = ion mobility; Sy = one half distance between
wires; Sx = wire-plate spacing.)
114
-------
g
X
I 6
Ul
I
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UJ
o
UJ
o
Ul
(E
uj 2
I 1—
• Sx =0.0508 m SY = 0.!l43m
• Sx =0.1016 m d = l.27xlO~3m
ASX = O.I524m b *2.2 xlO'4™2/volt-sec
VSX = 0.2032m
• Sx = 0.2540m
10
I
1 !
/ _
I I 1 /
20 30 40 50
APPLIED VOLTAGE,kV
60
70
Figure 79.
Current-voltage characteristics for a wire-plate
corona system for several values of wire-plate sepa-
ration, holding all other parameters constant.
115
SOUTHERN RESEARCH INSTITUTE
-------
When back corona occurs, ions of one species are injected
at the corona electrode and ions of the opposite type originate
at the passive electrode. The overall current increases, but the
charging effectiveness is reduced severely by the competing
effects of the oppositely charcred ions.
The maximum allowable current density at the passive elec-
trode in a corona system depends only upon the resistivity, p,
and breakdown strength E of the deposited material:
The breakdown strength is typically of the order of 10 ** V/cm.
The maximum current density at the plate electrodes is plotted as
a function of resistivity for this value of Et, in Figure 80. Thus
for example, if a corona system is operated in the presence of a
dust having resistivity of 10 10 ohm-cm, the current must be limited
to a maximum of 10 3 nA/cm2 . All other conditions remaining con-
stant, an increase in particle resistivity requires a decrease in
maximum operating current, which, in turn reduces the particle
charging effectiveness.
Because the condition for back corona at a given value of
current density at the passive electrode depends only upon the
resistivity and electric breakdown strength of the accumulated
particles, back corona can occur with a very thin layer of high
resistivity material on a collecting surface. Efforts to control
back corona must, therefore, be directed toward either maintain-
ing the passive electrodes completely free of dust accumulation,
or conditioning any collected dust in such a manner that the
resistivity is reduced to an acceptable value.
Possible Solutions to the High Resistivity Problem
a. Mechanical removal of high resistivity particulate
i. Aerodynamic design. In order to produce effective scour-
ing of the electrode surfaces the gas velocity must be
much higher than that which occurs in a conventional pre-
cipitator. Thus, the gas would have to be forced through
a region of reduced cross sectional area. No data are
currently available to indicate how high the velocity
must be to produce effective scouring.
ii. Continuous rapping. Thick accumulations of dust in the
precharger can be removed by rapping; however, the ad-
hesive forces on the first few monolayers of dust are
extremely strong. Continuous energetic rapping with
116
-------
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z
111
Q
I-
IU
tc
cc
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5
D
I I I Hill 1 1 I I! Ml
108
1010 1Q11
RESISTIVITY, ohm-cm
1012
ID"
Figure 80. Maximum permissible current density before break-
down as a function of resistivity for an assumed
breakdown strength of 10 ** V/cm. Back corona and
loss of particle charging effectiveness occurs for
particle resistivity and corona current density
corresponsing to points above the diagonal line.
117
SOUTHERN RESEARCH INSTITUTE
-------
accelerations of the order of several hundred times g
would be required to break loose these particles. If
the plate is vibrated continuously at frequency f , with
amplitude A cm, the peak acceleration is
a
_ 4ir2f2A
max -- 980~
If the plate is made to vibrate in a resonant mode, the
driving power would be limited to that required to replace
thermal losses. For example, vibration at 100 Hz with
an amplitude of 0 . 1 mm would produce a maximum accelera-
tion of approximately 400 g.
A combination of best aerodynamic design and continuous
rapping may serve to keep the precharger electrodes sufficiently
clean to avoid back corona, or at least to limit the amount of
dust which must be conditioned.
b. Steam injection
This method would use low pressure steam forced through a
porous electrode to treat and/or remove the deposited high resis-
tivity material. It might also be possible to use a conventional
electrode and inject the steam on the upstream side.
i. Advantages: In many applications (e.g., coal or oil
fired boilers) steam is readily available. In any
case it is easily generated. Although the principal
reason for the steam is to lower the resistivity of
the deposited material frequent pulses of increased
steam pressure might dislodge at least a large part
of the dust and prevent clogging of the pores.
ii. Possible Disadvantages: There might be a problem in
maintaining uniform steam injection through a porous
electrode. Localized clogging may become severe,
resulting in the build-up of thick patches of dust.
Aerodynamic shielding of the passive electrodes
might help to alleviate problems of this nature.
118
-------
c. Na-glass electrodes
Glass can be fabricated with a large enough concentration
of sodium to produce a resistivity ^ 106 ohm cm. If a high resis-
tivity glassy particulate layer resides on the surface of such a
material in the presence of a large electric field, the Na+ ions
would tend to be driven into the particles, thus reducing the
resistivity of the particulate layer.
A Na-glass electrode could be constructed with an imbedded
wire mesh for making contact to ground. In this case, the sodium
ions would be depleted gradually, requiring periodic replacement
of the electrode.
i. Advantages: Only a small amount of conditioning agent
would be required to provide mobile ions for the de-
posited particulate matter. It is almost certain that
a system of this type could be made to work on some
mass loading scale, but the overall ion migration
rate into a deposited particulate layer is uncertain.
A large Na ion density would be available at the
glass surface because of the applied field; but in
order to produce the desired effect, the ions would
have to be transferred very quickly into the particles
arriving at the surface.
ii. Possible Disadvantages: If the necessary reactions
proceed too slowly, it may not be possible to accom-
modate realistic levels of high resistivity mass
loading. In addition, a glass electrode is intrinsi-
cally somewhat fragile. Rapping to remove any col-
lected material would probably not be possible.
119
SOUTHERN RESEARCH INSTITUTE
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SPACE CHARGE EFFECTS
General Nature of the Problem
The presence of charged particles in a corona system re-
duces the effective mobility of a conducting medium and therefore
reduces the current density in the system for a given applied
potential. The effect is most pronounced where there exists a
large number density of fine particles. The problem is essenti-
ally a loading of the corona current by comparatively very massive
charge carriers. Ions which become attached to particles no
longer move with their original mobility, but travel with the
much slower particle drift velocity.
The charging theory does not account for the fact that
a fraction of the corona current is carried by ions attached to
particles. In most cases the assumption that the particle current
is negligibly small compared with the ion current serves as a
good approximation. But, if the density of charge attached to
the particles is a significant fraction of the total charge
density the apparent mobility associated with the corona current
is reduced, and the particle charging processes are impeded.
The total current density in the system (neglecting free
electron current) is:
j = yegNE = y-N^E + EypNpnpeE (20)
where y = particle mobility,
y = equivalent mobility of the system,
y. = ion mobility,
N = total charge density,
N. = ion density,
N = density of particles of diameter p, and
n = number of elementary charges per particle of diameter
P P-
Now,
N=N.e+ZNne
i P P P
and so, solving equation (20) for y , we have
120
-------
N
1 + £ rj
P N.
n
Consider the case for which EN n < ION., since y.
the sum in the numerator may be neglected, and hence 1
» y
"
eg
~ EN n
Ni p P PJ
But EN n e = Q, the total charge on the particulate material in
the system, so
-i
eq
In terms of the specific charge Q/M, where M is the total mass
per unit volume,
eq
(21)
The ratio Q/M increases for decreasing particle diameter as
shown in Figure 62, Section 5. Thus, the equivalent mobility
decreases as the particle size is made smaller, for a given
mass loading M. The effect of changing mobility for a fixed
current density and particle size distribution is shown in
Figure 81. It is also fairly accurate to say that the
maximum current density decreases by the same amount as the
equivalent mobility, i.e.,
J/j
max
(22)
If, for example, we have a flue gas with 1.0 g/m3 of 0.5, ym
diameter particles where the charging process has produced an
average charge/mass ratio of 5 x 10 5 coul/g, in a region where
the ion density is 10
llf
m
~3
the reduction in current is
j/j max =
121
SOUTHERN RESEARCH INSTITUTE
-------
E, kV/cm
Figure 81.
1 —
4/6
5/6
WIRE TO PLATE DISTANCE, x/d
Electric field profile in a duct geometry device
for various values of equivalent mobility, while
holding the average current density constant at
the plate electrode. The parameter p is the ratio
Meg/Pi-
122
-------
or
j/j max = 0.24 .
Clearly, in this case a severe degradation in particle charqincr
performance would result.
Practical Operating Conditions
The reduction in equivalent mobility of a system containing
charged particles depends very strongly upon the fraction of the
total charge density which resides on the particles. For a given
mass loading the space charge problem is more severe as the par-
ticle size is reduced, because the ratio of charge to mass is
generally an inverse function of particle diameter. Because of
the fundamental nature of the effect it appears that the only way
in which it can be minimized is to use a corona electrode geome-
try which will produce a maximum ion density for a given electric
field. This generally requires small wire-plate spacing (see
Figures 50 and 79) . The numbers shown above were chosen for
convenience because they are related to data obtained on a partic-
ular pilot scale precharger. They should not be taken as absolute
limits because of the dependence on charger geometry and operating
conditions.
GENERAL PRECHARGER DESIGN CONSIDERATIONS
Large values of both electric field strength and ion density
are required in order to produce a suitable level of particle
charging for electrostatic precipitation. In those cases where
high resistivity particles or space charge effects do not present
special difficulties, the principal consideration in precharger
design is optimization of the electric field profile and current
density in the charging region. In the following discussion
theoretical calculations of electrical characteristics for various
electrode geometries are made and compared, some limited experi-
mental data are presented, and comparative performance estimates
are given.
Electrode Configurations - Theoretical
A comparison of static electric field profiles was made for
several electrode geometries. The spacing between corona elec-
trode and passive electrode was made the same for all cases, and
the limiting field at the passive electrode was set at 5 kV/cm
for each system. The field profiles for the configurations de-
scribed in the following are plotted in Figure 82.
a. Duct geometry. The Cooperman expression was used to
provide the field profile for the duct geometry, with
wire-plate spacing of 5 cm.
123
SOUTHERN RESEARCH INSTITUTE
-------
Figure 82.
l5
cc
o
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OC
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111
10
IRE-CYLINDER
RECTANGULAR DUCT
DISC-CYLINDER
WIRE-SINGLE PLATE
~0 I 2345
DISTANCE FROM CORONA ELECTRODE, cm
Theoretical electric field profiles for various
electrode geometries, all normalized to a field
of 5 kV/cm at the passive electrode.
124
-------
Single plate-wire. Although this geometry has little
to recommend it in practice, a field profile is includ-
ed for the case of a corona wire parallel to a single
plate, at a distance of 5 cm. The expression for the
field as a function of x, the distance from the corona
wire on a line normal to the plate and passing through
the wire is
E
(x) x(2d-x)
(23)
where d is the wire-plate spacing, and ki is a constant,
depending upon the linear charge density of the wire.
Wire-cylinder system. The field as a function of radi-
al distance, r, from a wire along the axis of a ground-
ed cylinder is
E
(r)
where kz is a constant depending upon the boundary
conditions. In this case, end effects are ignored.
The cylinder radius is 5 cm.
d. Disc-cylinder geometry. A sharp-edged disc and a
grounded cylinder with coincident axes form an elec-
trode system where the field in the annular region
between the disc and cylinder as a function of the
radial distance, x, from the edge of the disc is
E
(x)
(a + x)
In5
1 -
a + x
In'
_i
Again, k3 is a constant depending upon the boundary con-
ditions; a is the disc radius and b is the cylinder
radius.
The arithmetic average field (i.e., applied voltage divided
by electrode spacing) is probably not the best way to compare the
above systems for a short precharger section, because in the cy-
lindrical geometries there is a much higher probability that a
particle will pass through a low field region near the plate
than through a higher field region near the corona electrode.
These considerations can be taken into account by defining the
mean charging field as
125
SOUTHERN RESEARCH INSTITUTE
-------
= JP(s)E(s)ds (24)
R
where P(s) is probability that a particle will pass through an
element of volume ds where the field is E(s). The integral is
carried out over the charging region A, and P(s) is normalized
to unity over R. The integral depends very strongly, in general,
upon the radius of the discharge wire (or radius of curvature of
an edge used as a corona electrode). For this reason a more rea-
sonable comparison of can be made by observing the areas under
the curves of the products P(s)E(s) for each of the corona sys-
tems, as shown in Figure 83.
These curves are derived directly from the field profiles
shown in Figure 82. The probability function P(sJ for both wire-
plate geometries is simply a constant. And for the cylindrical
systems,
P(r) = kn(r)
where kn is the normalizing function for the particular system.
For example, normalizing P(r) over an annular region in the disc-
cylinder device requires
P(r) = 2E_ (25)
a2+b2-J d2
where r = x + a.
Because of the asymptotic behavior of the curves in Figure
81, estimates of the integrated values are not immediately
apparent (area under curves), except in the case of the wire-
cylinder system, where, clearly = 10 kV/cm. The value of
for the rectangular duct geometry is certainly greater than
that of the single plate-wire system, but the relative values
of other pairs depend upon the point where the maximum equipoten-
tial is chosen at the corona electrode. If that point is taken
to be at less than approximately x = 0.8 cm, the rectangular duct
system has an greater than the disc-cylinder, but less than
the wire-cylinder.
The above analysis does not include space charge effects,
but may serve at least as a qualitative guide in the investigation
of corona system geometries. Variations on the type of corona
discharge electrode (i.e., barbed wire or helix) may provide some
improvement on any general corona geometry, but they are generally
beyond the available theory and must be tested experimentally.
126
-------
Figure 83.
' ' I ! | I I I I | I I I I | I I I
RECTANGULAR
DUCT GEOMETRY
WIRE-SINGLE PLATE
WIRE-CYLINDER
^CYLINDER
(b/a*3)
12345
DISTANCE FROM CORONA ELECTRODE,cm
Probability charging field as a function of distance
from corona electrode, calculated from the field
profiles shown in Figure 106. The area under each
curve is the mean charging field .
127
SOUTHERN RESEARCH INSTITUTE
-------
For a particular current density at the passive electrode,
a cylindrical geometry may offer some advantage since the average
ion density in the charging region will be higher than that found
in a rectangular geometry.
Electrical Configurations - Experimental
In the preceding section a theoretical comparison of elec-
trical field profiles, neglecting space charge, was presented
for several corona electrode systems. A limited experimental
study has also been carried out.
A disc with 1.9 inch diameter was mounted centrally inside
a 5.5 inch i.d. pipe, 18 inches long. The disc axis was aligned
with the axis of the pipe. The disc was approximately 1/32 inch
thick and the edge was sharpened. The I-V characteristic for
this geometry is shown in Figure 84. (Current density in all
cases on this graph is based on the assumption that all of the
current is restricted to a strip 1 cm wide on the passive
electrode, parallel to the edge of the corona electrode.) For
the geometry described above, a maximum of 74 kV was applied be-
fore sparking occurred, and a current density of approximately
7 x 10 nA/cm2 was achieved.
A second experiment was carried out using a similar disc,
but with a thickness of 0.1 inch, and rounded edge. The maximum
voltage before sparking was somewhat lower (65 kV) than that for
the sharp-edged disc, and the maximum current density was approx-
imately 3.5 x 101* nA/cm2.
Two experiments were done using a flat plate 17 inches x
14 inches for the ground electrode. First, a 0.1 inch diameter
wire was located approximately 1.9 inch above the plate. In order
to minimize field concentrations at the ends of the wire, 1 inch
radius bends were made near both ends of the wire, directed away
from the plate. The length of the wire between the centers of
the bends was approximately 9 inches. The current increased more
rapidly with increasing voltage than in the other systems, but
the maximum voltage before sparking was only 52 kV, even though
the minimum distance between electrodes was the same as for the
cylindrical geometry.
Finally, the sharpened edge of a thin (approximately 0.01
inch) plate was used as a corona electrode. The plate was cut so
that the edge was the shape of the bent wire electrode described
above. The plane of this electrode was mounted perpendicularly
to the flat grounded electrode with a 1.9 inch space between the
electrode edge and ground plane. As shown in Figure 84, the I-V
characteristic for this electrode geometry lies between those
found for the disc-cylinder arrangement and the wire-plate elec-
trodes.
128
-------
I
oc
GC
THICK" DISC
O THIN DISC
O THIN PLATE
X 0.1"WIRE
Figure 84.
APPLIED VOLTAGE, kV
Experimental I-V characteristics for four corona
system geometries.
129
SOUTHERN RESEARCH INSTITUTE
-------
Optimization of a Plate-Wire-Plate Design
The final geometry of the pilot scale precharger system
will depend largely upon the results of laboratory evaluations
and careful consideration of cost, ease of fabrication, mainten-
ance, etc. The following analysis is done for a plate-wire-plate
system because we have a more complete theory at the moment for
that geometry. The foregoing generalized analysis of different
geometries indicates that the results predicted for the plate-wire-
plate system will be comparable to those predicted for the other
systems.
It is assumed in this section that the electrical character-
istics are not limited by the resistivity of the dust. This is a
necessary assumption because it is clear that the high current
densities required for charging particles in a short time or
space cannot be sustained if even minute amounts of high resisti-
vity dust remain on the passive electrodes. Thus, the resistivity
of troublesome dusts must be modified or the dust removed.
The space charge effect is a more fundamental problem and
the electrical design of the Charger-ESP system must be optimized
to reduce dust effect if a small size distribution is to be collec-
ted effectively. This simply means that the effective mobility
(ions and particles) must not fall below some critical value. If
this does happen sparking will occur at reduced current densities.
In general, for best charging it is desirable to have a high aver-
age field and high ion density. For a given Nt product, it is
preferable to have N large and t small.
Table 2 shows the predicted performance for several plate-
wire-plate chargers which have different wire sizes and plate
spacings. The criterion used to generate this table and for com-
parison of the different geometries is that the field at the
plate reach 15 kV/cm. This seems to be a reasonable value to
achieve at or near sparkover. One can see from the table that,
over the range at parameters shown, the current density and
charging field change very little. Of course, for extremely dif-
ferent values this is not true. Table 2, however, covers the
range of interest to us. For mechanical strength and stability
we would probably choose the larger spacing and wire diameter.
Estimated Size and Performance
In this analysis we shall assume a value of 1.0 x 1013
sec/m3 for Nt in the charger, at an electric field strength of
1.0 x 106 V/m.
Figure 14, Section 3 shows the approximate charge that would
be acquired by particles of various sizes. Because of the high
electric field, charges are much higher than would be expected
for normal ESP operation.
130
-------
u>
c
X
PI
TJ
71
5!
n
n
X
tn
TABLE 2. ELECTRICAL OPERATING CHARACTERISTICS FOR SEVERAL PLATE-WIRE-PLATE CHARGER
GEOMETRIES
Wire-Plate
Spacing (cm)
3.175
4.064
5.08
Wire Diameter
(in/ram)
(nA/cm2)
Electric Field
(kV/cm)
(ave)
0.04/1.02
12
0.06/1.52
12
0.08/2.03
/
Voltage (V)
Current Density
(nA/cm2)
Electric Field
(kV/cm)
(ave)
Voltage (V)
Current Density
(nA/cm2)
Electric Field
(kV/cm)
(ave)
Voltage (V)
Current Density
38478
3423
12
48701
3399
12
59313
3188
41524
3439
13
50788
3225
13
62467
3207
43565
3225
14
54038
3225
13
65901
3226
13
-I
ni
-------
For the purposes of this study it is assumed that the down-
stream collector (ESP) is maximized with regard to the field at
the collecting plate and that only enough current is used to
charge reentrained dust. A field of 10 kV/cm is assumed in the
ESP. Similar calculations were done at a field of 5 kV/cm to sim
ulate a high resistivity dust or other difficult situations.
The basic equation applicable to Charger-ESP system is
_a(E Not, a) A
Efficiency = 1 - e ? - - Ep.^.C (26)
where q(EcN0t,a) = the average charge on a particle of radius a
(coulombs) ,
Ec = the average charging field (V/m) ,
NO = the average ion density in the charger (m~3)7
t = the average charging time (sec) ,
a = the particle radius (m) ,
n = the viscosity of the gas (kg/m sec) ,
Ep = the average electric field at the collecting
zone (V/m) ,
A = the downstream collector area (m2) ,
V = the volumetric flow rate (m3/sec) , and
C = the slip (Cunningham) correction factor.
Table 3 shows charge data taken from Figure 61 and effi-
ciencies and migration velocities calculated for the different
particle sizes. The SCA for the downstream ESP was calculated
by selecting the efficiency to match that of the full scale ESP
on Unit 10 at Gorgas. That ESP has an overall mass efficiency of
approximately 99.70%. The theoretical fractional efficiency
curves for the Gorgas ESP and the proposed system are shown in
Figure 85.
This analysis can be criticized because the calculated
migration velocities are so high that the Deutsch equation is no
longer valid. On the other hand, the velocity component of the
particles toward the collecting plate will be such that calcula-
tions of trajectories would also predict very low SCA's.
132
-------
in
O
c.
-4
m
33
Z
a
0
TABLE 3. CALCULATED CHARGE AND FRACTIONAL EFFICIENCY OF THE PRECHARGER-ESP
SYSTEM. THE ESP HAS AN SCA OF 28 ft2/1000 ACFM.
Particle
Diameter
GJ
U)
0.1
0.5
1.0
1.5
2.0
Charge (coul.)
1.44 x 10~18
2.2 x 10~17
8.6 x 10~17
1.8 x 10~16
3.2 x 10-16
Collection Efficiency
68
79
93%
96.8
98.7
Migration
Velocity (cm/sec)
20 cm/sec
21 cm/sec
41 cm/sec
58 cm/sec
77 cm/sec
-i
c
-------
00
u
z
111
LL
LU
O
O
LU
_J
_l
O
O
Figure 85.
99.99
99.90
99.8
99
98
95
90
80
70
60
50
40
30
20
10
0.1
1.0
PARTICLE DIAMETER, urn
10.0
Theoretical collection efficiencies for the Gorgas full-scale precipitator
compared to a precharger-E.S.P. system.
-------
The theory, then predicts SCA's of about 1/10 of the value
which one would expect for a normal ESP installation. Taken at
face value, for example, this means that the Gorgas ESP could
be shortened to about 3 ft in length. This is obviously imprac-
tical because the ash could not be handled and reentrainment
would be a problem.
In summary, if the high current density charger operates
as predicted, the size of the downstream collector is determined
by mechanical, not electrical, considerations. For costing, we
have thus arbitrarily assumed that the dust can be collected and
removed, and reentrained dust recollected with a minimum SCA of
120 ft2/1000 acfm for new installations and 240 ft2/1000 acfm
for difficult dust installations, or about a factor of 3 less
than a normal ESP.
COST ESTIMATES
Since the potential value of an electrostatic collection
system employing a precharger will depend to a large extent upon
the relative costs of such a system compared with existing
technology, we have prepared cost estimates of two different types
of precharger-precipitator systems for comparison with convention-
al electrostatic precipitator installations. The following cases
were selected for comparison:
Case No-
1. A wire-pipe precharger followed by a modified precipi-
tator with a specific collecting area of 23.6 m2/m3 sec
(120 ft2/1000 cfm).
2. A wire-pipe precharger followed by a modified precipi-
tator with a specific collecting area of 47.2 m2/m3/sec
(240 ft2/1000 cfm).
3. A wire-plate precharger followed by a modified precipi-
tator with a specific collecting area of 23.6 mVm3/sec
(120 ft2/1000 cfm).
4. A wire-plate precharger followed by a modified precipi-
tator with a specific collecting area of 47.2 mVm3/sec
(240 ft2/1000 cfm).
5. A conventional electrostatic precipitator with a speci-
fic collecting area of 59 m2/m3/sec (300 ft2/1000 cfm).
6. A conventional electrostatic precipitator with a speci-
fic collecting area of 118 m2/m3/sec (600 ft2/1000 cfm).
The cost estimates for the precharger assemblies and the
conventional precipitators are based on the following assumptions:
SOUTHERN RESEARCH INSTITUTE
-------
1. Flange to flange costs of conventional precipitator
without erection = $6.67/ft2 of plate area.
2. Wire-tube precharger array consisting of 4" pipe on 8"
centers is estimated to cost $227/ft2 of inlet area.
This includes a contingency factor equal to about four
times the material and fabrication costs to allow for
a means of lowering the resistivity of dust collected
in the precharger, removing excessive accumulations,
and electrical supplies.
3. Wire-plate precharger consisting of 2" nominal wire-to-
plate spacing with diamond section plate assemblies
(for stiffness required) 8" long x 4" thick is estimat-
ed to cost $80/ft of inlet area. This concludes a
contingency factor of four as described above.
4. The particulate collection system will collect 99.5%
or greater of the mass loading in the flue gas. The
precipitator sections consist of conventional plates
and relatively large diameter discharge electrodes.
For the 120 SCA case, the precipitator is 108 ft wide,
25 ft long, and 15 ft high with 144 gas passages.
The plate height is doubled to 30 ft to obtain an SCA
of 240.
Cases 1, 3, and 5 are considered to be applicable to dusts
in which resistivity does not severely limit conventional precipi-
tator operating conditions, whereas Cases 2, 4, and 6 are con-
sidered to be applicable to dust with a resistivity of 5 x 1010
or greater. Tables 4 and 5 give comparisons of cost estimates
for the six cases described earlier. The installations with
prechargers are estimated to cost approximately 50% to 60% as
much as a conventional precipitator under comparable operating
conditions based on flange to flange costs with no installation
charges included.
Table 6 gives a comparison of projected power requirements
for Case 4 and Case 5. This shows that the precharger system
does not cause increased power consumption over that experienced
with conventional precipitators.
136
-------
c
-i
m
X
Z
(A
C!
a
n
x
to
3
c
m
TABLE 4. FLANGE TO FLANGE COST ESTIMATES OF PARTICULATE COLLECTION
SYSTEMS
(NO INSTALLATION COSTS INCLUDED)
Collector
Total Flange
Precharger Specific Collecting Area To Flange
Case No. Type m2/m3/sec f:t2/1000 cfm Cost $
1
2
3
4
5
6
Wire-pipe
Wire-pipe
Wire-plate
Wire-plate
None
None
23.6
47.2
23.6
47.2
59.1
118
120
240
120
240
300
600
1,088,100
2,176,200
850,000
1,700,000
1,800,000
3,600,000
Precharger
Cost
$
367,740
735,480
129,600
259,200
Collector
Cost
$
720,360
1,440,720
720,360
1,440,720
1,800,000
3,600,000
-------
FIGURE 5. ESTIMATED COST BENEFIT RATIOS FOR PRECHARGER COLLECTOR SYSTEMS
Case No. Comparisons Ratio of Conventional System to Precharger System
5 to 1 1.65
6 to 2 1.65
£ 5 to 3 2.12
00
6 to 4 2.12
All systems assumed to have collection efficiency of 99.5% or greater on a typical
coal-fired power plant fly ash on 900,000 acfm of flue gas.
-------
o
c
X
m
a
m
10
ni
50
n
x
in
H
C
PI
TABLE 6. COMPARISON OF PRIMARY POWER REQUIREMENTS IN KILOWATTS - 900,000 ACFM
Precharger System
Precharger Collector Total Conventional Precipitator
408 88 496 520
Assumptions:
1. Geometry of Case 4 used for precharger system. Case 5 used for conventional
precipitator.
2. Precharger operating conditions: 1760 x 10~9 amps/cm2, 50 kV.
3. Collector operating condition: 5 x 10~9 amps/cm2, 57 kV.
4. Conventional precipitator operating conditions: 30 x 10~9 amps/cm2, 45 kV.
5. Conversion efficiency of T-R sets = 65%.
-------
REFERENCES
1. Murphy, A.T., F.T. Adler, and G.W. Penney. A Theoretical
Analysis of the Effects of an Electric Field On Charging of
Fine Particles. AIEE Trans. 318-326, Sept. 1959.
2. Mirzabekyan, G.Z. Aerosol Charging in a Corona-Discharge
Field. In: Strong Electric Fields in Technological Pro-
cesses (Ion Technology), V.I. Popkov, ed. Energy Publishing
House, Moscow, 1968. pp. 20-38.
3. Pauthenier, M.M., and M. Moreau-Hanot. Charging of Spherical
Particles in an Ionizing Field. Journal de Physique et le
Radium, 7(3):590-613, 1932.
4. White, H.J. Particle Charging in Electrostatic Precipitation.
AIEE. 1186-1191, May 1951.
5. Liu, B.Y.H., and H. Yeh. On the Theory of Charging Aerosol
Particles in an Electric Field. J. Appl. Phys. 39(3):1396-
1402, 1968.
6. McDaniel, E.W. Collision Phenomena in Ionized Gases. John
Wiley and Sons, New York, 1964. p. 473.
7. L_iu, B.Y.H., K.T. Whitby, and H.H.S. Yu. Diffusion Charging
of Aerosol Particles at Low Pressures. J. Appl. Phys.
38(4) :1592-1597, 1967.
8. Hewitt, G.W. The Charging of Small Particles for Electrosta-
tic Precipitation. AIEE. 76:300-306, 1957.
9. Bricard, J. Formation and Properties of Neutral Ultrafine
Particles and Small Ions Conditioned by Gaseous Impurities
of the Air. Ins Aerosols and Atmospheric Chemistry,
G.M. Hidy, ed. Academic Press, New York, 1972.
10. Loeb, L.B. Electrical Coronas. University of California
Press, Berkeley, California, 1965. 694 pp.
11. Berglund, R.N., and B.Y.H. Liu. Generation of Monodisperse
Aerosol Standards. Environmental Science and Technology.
7(2):147-152, 1973.
12. Lindblad, N.R., and J.M. Schneider. Production of Uniform-
Sized Liquid Droplets. J. Sci. Instr. 42:635-638, 1965.
140
-------
13. Strom, L. The Generation of Monodisperse Aerosols by Means
of a Disintegrated Jet of Liquid. Rev. Sci. Instr. 40(6),
1969.
14. Letter, Kodak Chemical Products, Inc. Coatings Chemicals
Division, Kingsport, Tennessee.
15. Handbook of Chemistry and Physics, 45th ed. Chemical Rubber
Publishing Company, Cleveland, Ohio. D-106, 1966.
16. Bundy, R.H., et al. Styrene: Its Polymers, Copolymers and
Derivatives. ACS Monograph Series R.
17. Fuchs, N. , I. Petrjanoff, and B. Rotzeig. On the Rate of
Charging of Droplets by an Ionic Current. Transactions,
Faraday Society. 1131-1138, Feb. 1936.
18. Arendt, P., and H. Kallmann. The Mechanism of Charging of
Cloud Particles. Zeitschrift fur Physik. 35:836-897, 1935.
19. Rohmann, H. Method of Size Measurement for Suspended Parti-
cles. Zeitschrift fur Physik. 17:253-265, 1923.
20. Ladenburg, R. Research on the Physical Basis of Electrical
Gas Purification. Annalen der Physik. 4:863-897, 1930.
21. Penney, G.W., and R.D. Lynch. Measurements of Charge
Imparted to Fine Particles by a Corona Discharge. AIEE.
76:294-299, July 1957.
22. Drozin, V.G-, and V.K. LaMer. The Determination of the
Particle Size Distribution of Aerosols by Precipitation of
Charged Particles. J. Colloid Science. 14:74-90, 1959.
23. Liu, B.Y.H., K.T. Whitby, and H.H.S. Yu. On the Charging
of Aerosol Particles by Unipolar Ions in the Absence of an
Applied Electric Field. J. Colloid Sci. 23:367-378, 1967.
24. Cochet, R. Law of Charging of Fine (Submicron) Particles;
Theoretical Studies; Recent Controls; Particle Spectra. In:
Collogue International-La Physique des Forces Electrostatiques
et leurs Applications. Centre National de la Recherche
Scientifique, Paris, 1961. pp. 331-338.
25. Millikan, R.A. The General Law of Fall of a Small Body
Through a Gas and its Bearing upon the Nature of Molecular
Reflection From Surfaces. Phys. Rev. 22:1-23, 1923.
26. Cochet, R. Theory of Charging of Submicron Particles in
Electrically Ionized Fields; Rate of Precipitation of the
Particles. Compt. Rend. Acad. Sci. 243:243-246, 1956.
141 SOUTHERN RESEARCH INSTITUTE
-------
27. Cochet, R. and J. Trillat. Charging of Submicron Particles
in Electrically Ionized Fields; Measurement of the Rate of
Precipitation in a Uniform Electric Field. Compt. Rend.
Acad. Sci. 250:2164-2166, 1960.
28. Knudson, E.G. The Distribution of Electrical Ch-rge
Among the Particles of an Artificially Charged Aerosol.
Ph.D. Thesis, University of Minnesota, Minneapolis, Minneso-
ta, 1971.
29. Smith, W.B., K.M. Gushing and J.D. McCain. Particulate
Sizing Techniques for Control Device Evaluation.
EPA-650/2-74-102, U.S. Environmental Protection Agency,
Research Triangle Park, N.C. July, 1974. p. 83.
142
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APPENDIX A
LITERATURE REVIEW - THEORY OF PARTICLE CHARGING
The works summarized and discussed in this section include
the principal previous contributions related to the topic of par-
ticle charging. This material has provided the background and
insight for the theoretical development -presented in Section 3
of this report. The range of experimental data in the literature
has indicated a need for a comprehensive study of particle charg-
ing under various conditions of electric field strengths and ion
density for a variety of aerosol materials and sizes.
GENERAL REVIEW
M. Pauthenier & M. Moreau-Hanot (1932)3
Discussion—
A theoretical and experimental study is made to examine par-
ticle charging by a cylindrically symmetric electric field for
spherical particles down to several microns in diameter. The
theory is used to derive a "law" of charging of particles with
time and to determine the maximum charge these particles can ac-
quire. Both conducting and insulating particles are considered
and thermal charge is considered to be negligible. The theory is
tested over a wide range of particle sizes, field strengths and
particle materials, with results which indicate the theory is
applicable for particles with diameters down to several microns,
where the effects of ion diffusion on the maximum charge start to
be observed.
Basic Equations—
Potential—The cylindrically symmetric electric field is
constructed by grounding a conducting cylinder of inner radius R0
and by placing a fine wire of radius r0 along its axis at a po-
tential Vm. Inside the cylinder the density of negative charge
p(r) is
p(r) = i/27rryE (27)
where i = ionization current per unit length,
r = radial distance measured from the cylinder,
143
SOUTHERN RESEARCH INSTITUTE
-------
U = ion mobility, and
E = electric field strength.
Solving Poisson's equation using (27) as the charge density gives
2! h
li + — (28)
_y r2J
and
V(r) = F(r) - F(R0) (29)
for
R0 ^_ corona wire diameter,
where ^
F(r) = Clnr + C2 + 2^r - ClnlfC2 + 2" + c) (30)
and C is determined by the condition that22
Vm = V(ro) ~ v(Ro> <31)
In the case where i is very small, a zero current approxi-
mation of E can be found from (28) which when inserted in (27)
gives a low current approximation of p(r). Integrating Poisson's
equation gives the low current results:
E = -| f1 + —i— r2) , (32)
which is a first order expansion of equation (2), and
v = cln IT + Tcf (r2-R°2) (33)
On the other hand, series expansions of (28) and (30) give the
high current results:
2ir^ " \2irz / J
and
V = *(r) - *(r0) (35)
where
^/?ll 1 \\C*^" 1 /! I P1 ^ \ I
(36)
l l ^°2 + L /^C2 \ 4- T
± - ff + -H-T- [ 1 + . . .
2 2ir2 W \2ir2/ J
144
-------
In many instances in (34), the term yC2/4ir* is small, so the po-
tential curve is practically linear over most of its length.
Thus, the field due to space charge is approximately constant
for high currents.
Travel time—In a constant field, an ion of mobility y,
traveTs a distance H in the time
t0 =
JL.
yv
(37)
where V is the potential difference between departure and arri-
val points.
If the field E varies in the space considered, then the time
of travel t is
(38)
which in every case is higher than to for constant applied vol-
tage. The effect of ionization is to lower this time. The more
intense the corona, the closer the value of t is to to.
The charging of conducting particles—The capture of ions
by a particle which already carries a charge of the same sign
takes place by two processes:
1. Under the influence of thermal agitation, an ion
can acquire sufficient kinetic energy to overcome
the Coulomb repulsion of the particle, and be
attracted by its image charge. This may be the
dominant mechanism for particles whose diameter
is less than one micron.
2. In the presence of an applied electric field, ions
move along electric field lines and are attracted
to their image charges on the particle. For
larger particles, which can acquire a larger
maximum charge, this is the dominant charging
mechanism.
The second case is considered here. A conducting sphere of
radius a and negative charge Q is placed in an electric field
E0. Nearby, a negative ion of charge e is situated. The loca-
tion of the ion is (6, a(l+v)) with respect to the center of
the particle.
The uniform field E0
component is
exerts a force on the ion whose radial
= -eE0 cos
(39)
145
SOUTHERN RESEARCH INSTITUTE
-------
Due to the field E0f the charge Q on the sphere is unequally dis-
tributed and gives rise to a second force on the ion whose radial
component is
F2 = _ 2E0e cos 9 (40)
The charge Q on the sphere repels the ion with a radial force
equal to
Fa - 26Q a (41)
a2 (1+v)2
And finally, the ion induces an image charge on the particles
which exerts a force of attraction expressed by
-l - (42)
4a2v2 (1+v) 3(l+v/2)2
which for small values of v reduces to:
F* a -e2/4a2v2 (43)
The ion approaches the sphere if
F = FI + F2 + F3 + F^ < 0 (44)
If Q is small, F is negative regardless of the distance a (1+v),
with the condition that 6 is smaller than some limit 8 0 . As the
charge Q increases, 60 decreases and eventually the sphere is
completely surrounded by a repulsive zone which the ions cannot
penetrate, except when thermal agitation provides them with suf-
ficient kinetic energy.
The equation F = 0 cannot be solved for 9o at v = 0. How-
ever, (18) is always negative if Q is less than 3E0a2, and in the
region where
v « 1 (45)
and
e2
4a2v2
2
« 1 (46)
concurrently, Q = SEoa^ leads to a very small value for (44).
Setting
Q = 3E0a2A, (47)
146
-------
where X is a dimensionless parameter, allows one to rewrite (44)
as:
F = EQCOS 6 yi + (X-l)y2 %L (48)
a'
where yi, yi, and y3 depend only on v.
A graphical study of (48) shows that the repulsive zone
completely envelopes the sphere for values of X slightly greater
than unity. Increasing X tends to rapidly enlarge the repulsive
region.
For spheres with radii larger than ten microns, X is essen-
tially unity. However, when particle radii are on the order of
one micron, then X»l.l. The conclusion is that at this size
that the effects of thermal agitation are being observed.
The law of charging of particles with time—The above dis-
cussion shows that thermal agitation has an insignificant influ-
ence on the limit charge of a large particle in an ionized
field. Therefore, for large particles (a >_ 10 y) thermal effects
cannot be considered as dominating in the evaluation of the time
necessary for a particle to acquire a charge. Indeed, a simple
calculation shows that even in the region of maximum charge
density there are not enough ions to appreciably influence the
charging rate of a large particle by diffusional effects alone.
The larger part of the charge is formed by ions entrained by the
field with a speed of viE.
The charge brought to the particle in time dt is proportion-
al to the flux $ of radial force F across a spherical segment
limited by the edge of the repulsive zone. We choose a spherical
segment very near the particle but far enough away from the sur-
face so that (42) is negligible. Then the limit of integration
8 o is defined by
cos 60 = sU- = A (49)
and
3E0a2
Bor
I (3E0cose- ——) . 2ira2sin9d6
•fn 9
= -e / (3E0cose *—). 2TTazsin9d6 (50)
0 a2
= -3TTE0ea2(l-X)2 (51)
The negative charge -dQ acquired equal to
-dQ = -3E0a2dX (52)
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and the charge density at a distance r from the cylinder axis is
(53)
lirr
So in a time dt, the negative charge acquired is
Eo
y$dt (54)
4irre
From which one obtains the differential equation
_r^^-*0/3J- / EX EC \
with solution
X = -t- (56)
where
T = -£— (57)
is the time required to reach half the limit charge. We see that
(55) does not depend on a. Therefore, the charging time is in->
dependent of particle size.
The charging of dielectric spheres—The charging of dielec-
tric spheres in an electric field proceeds in a manner analogous
to that for the conducting case. It is sufficient to replace
the induced charge on a conducting particle by the polarization
charge of the dielectric. A rigorous treatment would also re-
quire modification of (42); but the final results above are
essentially independent of this term so it is not included here.
Thus, the limit charge is now
Qo = pE0a2 (58)
where
and k is the dielectric constant of the particle.
Application to electrostatic precipitation—When this theory
is applied to electrostatic precipitators with a vertical corona
wire and planar precipitation electrode, an analysis of particle
trajectories to determine collection time and point of impact
shows:
a. For negligible air resistance, i.e., large particles,
and with laminar gas flow numerical solutions of the
equations of motion show that particles are collected
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according to size. The relationship between
particle size and collection time is double
valued. It is found that at a particular
point on the planar electrode collection
begins with a certain size particle with both
larger and smaller ones being collected at
later times.
b. For very light particles which quickly reach
their terminal velocity, the time necessary
for precipitation is independent of density
and inversely proportional to the radius.
Selection according to particle size is very
noticeable.
Experimental Results—
A cylindrically symmetric electric field was generated in a
grounded conducting cylinder 30 cm in diameter with an axial wire
which could be kept at a desired potential Vm with respect to
ground (12 kV <_ Vm <_ 48 kV) . The potential was measured at
points in the field for weak (1.15 yA) and stronger (13.2 yA) io-
nization currents. In the corona region, the theory developed
above was in good agreement with the experimental results.
In order to measure the limit charge for spherical particles
moving through the electric field, two procedures are used:
first, to measure the limit charge for large particles, conduct-
ing and insulating spheres with diameters on the order of 1 mm
to 1 cm were dropped from rest through the cylinder. Their
acquired charge was measured by discharge through an electrometer,
The theory was verified to within an experimental uncertainty of
1 to 2%. Second, small conducting and insulating spheres with
diameters on the order of .20 ym to 200 ym were dropped from rest
in the field and their trajectories were photographed. These
were analyzed for deviation from a theoretically determined
trajectory based on the effects of gravity and field charging
rate, corrected for viscous forces and initial charge. Once
again, the experimental results and theoretical predictions are
in good agreement. This second method is called the "method of
trajectories". Particles were also collected on the side of the
cylinder on wet gelatin plates. This allowed accurate measure-
ments of the number of particles of a particular size which
move through a precisely determined vertical distance.
Conclusions—
The theoretical and experimental results lead to the
following conclusions:
a. For particles with radii larger than several
microns, the limit charge acquired is primarily
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due to the electric field and is given
accurately by the equations developed above.
b. The law of charging accurately predicts the
charging rate for large particles (a _> 50 y) ,
and when trajectories are corrected for viscous
effects agreement between theory and experiment
can be extended to particles whose radii are on
the order of several microns.
c. The underlying principles of electrostatic
precipitation of large particles (a >. 5 y) ,
are adequately explained by the theoretical
analysis of particle trajectories in an
electric field.
Comments and Remarks--
This paper is definitive with regard to field charging
phenomena. The authors limit their attention to particles large
enough so that no diffusional charging effects need be consider-
ed. In some of the numerical analysis fairly crude assumptions
are made in order to obtain results but these do not affect the
conclusions drawn. The experimental work was carefully done and
clearly designed to test the theory.
N. Fuchs, I. Petrjanoff, & B. Rotzeig (1936)17
Discussion—
An experimental investigation was made into the kinetics of
the particle-charging process. Particles ranging from approxi-
mately 1.0 ym to 6.0 ym in diameter were examined. Curves for
particle charge as a function of particle size were obtained for
different values of ion concentration, electric field strength,
ion current density, and time. The data were to be compared with
the field-charging equation
« % *• "-rs^i^f I •"-"•«• % T i »•,_ . I i r f\ \
for agreement, where
Q = particle charge,
K = dielectric constant of particles,
E = external field strength,
a = particle radius,
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N = ion density,
y = ion mobility,
e = elementary unit of charge, and
t = time.
It was suspected that for smaller particles, the agreement
between equation (34) and experiment would be less because of
the increased influence of ion diffusion and image forces.
In the experiment, uncharged oil mist droplets were charged
by passing a narrow air-jet containing the oil mist through a
short trajectory along the axis of a wire pipe precipitator near
the collecting surface. The oil mist was formed by taking a hot
air-stream saturated with oil vapors and mixing it with a cold
air-stream. The cloud produced by condensation was then diluted
by mixing with clean air in order to obtain a suitable concen-
tration of droplets. By adjusting the hot and cold airstream
flows, clouds containing different particle sizes could be gener-
ated.
The velocity and width of the aerosol jet were adjusted
until a jet was produced that had maximum stability and a width
that remained essentially constant over its trajectory. Under
these conditions, the linear velocity of the jet was assumed con-
stant. The average velocity of the jet was obtained from the
rate of flow of the oil mist before it entered the charging re-
gion and the cross-sectional area of the jet. Using the average
velocity and the length of the trajectory, the average residence
time of the droplets within the charging region could be deter-
mined.
The ionic current density intersecting the aerosol jet was
calculated from the average current flowing through the inner
section of the three-section precipitator. Measurements were
made to ensure that the tubes, introduced into the precipitator
to produce the jet and carry it off, did not appreciably alter
the ionic current density in the region of the jet.
After passing through the charging region, the jet was
pulled into an ultramicroscopic cell where both the size and
charge of the droplets were determined by the "photographic os-
cillation method". In this method, the droplets were allowed to
fall under the influence of gravity and simultaneously were
forced by an alternating electric field to oscillate in a hori-
zontal direction. By photographing the zig-zag paths of the
droplets, the size is first determined from the rate of fall and
then charge is found from the horizontal velocity.
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Conclusions--
The experimental results were plotted and compared with
those predicted by equation (34) with j/E substituted for yNe.
The mobility y was taken to be 1.75 x 10"'*m2/V-sec to give best
agreement with theory. The electric field strength E was not
measured directly but was determined from
(61)
where j is the current density at the surface of the pipe, and
r is the radius of the pipe.
The mean values of the measured charges lie satisfactorily
on the theoretical curves. However, insufficient data were ob-
tained to determine the validity of equation (60) for particles
having radii less than one micron.
Comments and Remarks—
The jet employed in the experiment was greatly affected by
the corona discharge and suffered deviation from a straight-line
path and dispersion sooner for increasing current density. This
limited the measurements to rather low values of external field
strength and ion concentration. The deflection and spreading of
the jet, due to the charges acquired by the droplets, limited
this method of measurement to low values of particle charge.
Charge on the droplets up to about 1/3 of the saturation charge
could be measured.
H. J. White (1951)^
Discussion—
An account was given of the work done on particle charging
up until the time of publication. Existing theories were pre-
sented and the pertinent experimental studies discussed briefly.
The theories were compared with experiment for agreement. In
addition, some previously unpublished results were given.
Studies involving electric charges associated with indus-
trial aerosols yielded the following findings:
a. The majority of industrial aerosols are charged.
b. The charge usually is equally distributed between
positive and negative charges so that the aero-
sol as a whole is electrically neutral.
152
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c. The average particle charge is comparatively
small although not negligible.
The above facts indicate clearly that electrostatic precipi-
tation must include particle charging as an inherent part of the
process.
The existing theories considered two particle-charging mech-
anisms to be important in the unipolar corona discharge.
a. Bombardment of the particles by ions moving
in the d-c field.
b. Attachment of ions to the particles by ion
diffusion.
The first mechanism was considered to be of primary impor-
tance in electrostatic precipitation and the latter process ordi-
narily was considered to be important only for particles smaller
than about 0.2 ym in diameter.
Basic Equations—
The theoretical equations were based on the following
assumptions:
a. The particles were assumed to be spherical.
b. Particle spacing was assumed large compared
to particle diameter.
c. Ion concentration and electric field in the
region of any given particle were assumed
uniform.
Charging by ion bombardment — In the ion bombardment process,
the ions move along the electric lines of force, strike the par-
ticle, and impart charge by attachment. This charge on the par-
ticle in turn produces a repulsive force which alters the field
configuration and lowers the charging rate by reducing the elec-
tric flux entering the particle. Ultimately, sufficient charge
is acquired to completely counteract the external field. At
this point, the electric flux entering the particle is zero and
charging ceases. The charging equation for this process is given
by
to
(62)
l ;
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where
_2
(.
and
In the equations,
n = particle charge,
n = saturation charge,
s
t = time,
to = particle charging time constant,
No = undisturbed ion concentration,
e = elementary unit of charge,
U = ion mobility,
K = dielectric constant of particle,
a = radius of particle, and
Eo = external field strength.
Equations (62)-(64) indicate the following features of this
type of charging process:
a. The particle charge n approaches the saturation
value ns for large values of t.
b. The saturation charge ns is directly proportional
to both the electric field strength EO and to the
surface area represented by a2.
c. The charging time constant to is inversely propor-^
tional to both ion concentration NO and to ion
mobility y.
Charging by ion diffusion—Equations based on ion diffusion
give reasonable results for particles of 0.1 ym or less in
diameter. In this mechanism, the thermal energies of the ions
cause them to diffuse through the gas and suffer collisions with
molecules and particles. Upon collision with a particle, the
ions adhere to the particle due to the attractive electrical
154
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image forces present. The diffusion process will occur in the
absence of an external electric field although the presence of an
external field will enhance charging. As the particle acquires
charge by diffusion, it sets up a repelling field which tends to
keep additional charges from reaching the particles. Thus, the
charging rate decreases as the particle accumulates charge and
ultimately becomes negligible.
Arendt and Kallman18 made the first significant study of
particle charging by diffusion of unipolar ions and derived the
equation
-ne 2/akT
to describe the mechanism, where
dn/dt = charging rate,
c = mean thermal speed of ions,
k = Boltzmann's constant,
T = absolute temperature,
and the other symbols are as defined previously. Equation (65)
is long in derivation, valid only for the case where the parti-
cle has already acquired appreciable charge, and must be solved
numerically.
A simpler derivation and equation is presented which gives
essentially the same results as equation (65) and where
n =
In equation (66) , n=0 at t=0 so that the particle is ini-
tially uncharged. From equation (66), it is seen that the par-
ticle charge will depend on the thermal energies of the ions, on
the particle size, and on the time of exposure.
Comparison of theoretical equations with experiment—Experi-
mental measurements essentially validate the equations presented
for ion bombardment and ion diffusion. Experiments by Rohmann,19
Ladenburg,20 Pauthenier and Moreau-Hanot,3 Arendt and Kallman,18
Fuchs and Petrjanoff,*7 and White can be described reasonably well
by one or the other of the charging mechanisms.
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Conclusions—
In general, the particle-charging mechanism is mainly that
of field charging for particles larger than about 0.5 ym in
diameter and the ion diffusion process predominates for particles
smaller than about 0.2 ym in diameter. An exact theory
should account simultaneously for both charging mechanisms/ but
this approach leads to mathematical difficulties.
Comments and Remarks—
The ion diffusion mechanism presented does not account for
the effects of the external field, which are appreciable. Dif-
fusion charging can occur simultaneously with field charging,
and this is not taken into account.
Gaylord W. Penney^& Robert D. Lynch (1957)21
Discussion—
An experimental investigation was made into the charging
of fine particles by both positive and negative corona discharge.
Experimental results were given for particle charge as a func-
tion of particle radius, electric field strength, and time.
Particle sizes range from 0.15 ym to 0.32 ym in radius. Electric
field strengths were varied from 1.2 to 3.8 kV/cm at the collec-
ting surface.
The experimental apparatus and methods can be summarized
as follows:
a. Aerosol Generator and Particle Size Determination -
The generator employed could produce a dioctyl phthalate
aerosol containing particles largely uniform in size.
The particle size was determined by an optical instru-
ment called the "owl." This instrument passes white
light through the aerosol and particle size informa-
tion is inferred from the angular scattering pattern.
b. Particle Charger and Charge Determination - The parti-
cles were charged by a concentric wire and pipe corona
discharge in most of the tests. Also, some tests were
run with a special particle charger that used the elec-
tric field between parallel screens for charging the
particle. Results from the tests using the screen
charger could be compared with charging theories because
both the electric field and ion concentration were
essentially uniform over the charging region. The
particles were passed through the charging region and
the resulting particle charge was determined by two
different methods.
156
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i. Weight Method - The charged aerosol is drawn
through a filter and the weight increase is that of
the particles. The current collected due to the
particles is measured by a galvanometer so that the
total charge can be found from the integral of the
current over time. From the total weight, total
charge, and particle size, the charge per particle
can be determined. This method was unfavorable
because too long a time was required to collect a
weighable number of particles and certain variables
could not be kept constant over this period of time.
ii. Mobility Method - The mobility of the particles is
determined by measuring the efficiency when the
charged particles are passed through a special
parallel-plate precipitator having a uniform elec-
tric field between the plates, and designed to
minimize turbulence. A linear relation exists be-
tween the plate efficiency and the potential be-
tween the plates and the mobility is determined
from a plot of this relationship. Knowing the
mobility and particle size, the charge per particle
can be found from Stokes1 Law. Data obtained from
the weight and mobility methods showed reasonable
agreement. The mobility method was preferable
since it yielded results more conveniently.
Conclusions—
The following are some results and conclusions from certain
tests.
a. With positive corona in the cylindrical charger, the
particle charge was measured as a function of electric
field strength. At a field strength of 4,000 V/cm and
Nt = 108 sec/cm3, the measured charge was approximately
twice that predicted by theory which neglected field
effects. Thus, in this case, the field has a signifi-
cant effect on the charging process.
b. With negative corona in the screen charger, the
particle charge was measured as a function of
electric field strength. At approximately a field
strength of 5,400 V/cm and Nt = 2.1 x 107 sec/cm3,
the measured charge was approximately twice that
predicted by theory which neglected field effects.
Again, field effects are important.
c. At an electric strength of 1,600 V/cm and Nt = 3.3
x 107 sec/cm3, both the positive corona in the cy-
lindrical charger and the negative corona in the
screen charger give both the same charge. These
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results indicate that at low electric fields, the
charging by positive and negative corona is approxi-
mately the same.
d. With negative corona in the cylindrical charger,
the particle charge was measured as a function
of electric field strength. At low voltage, the
charge due to negative corona was only a little
greater than that given by positive corona. As
the voltage was increased, the charge due to
negative corona increased much more rapidly than
that due to positive corona. At 13 kV the nega-
tive charge was 50% higher than the positive
charge. This behavior is attributed to the
possible presence of free electrons in the
negative corona discharge at high voltages.
e. The charge was measured as a function of Nt for
both positive and negative corona in the cylin-
drical charger at a potential of 11 kV. Here
both experimental charging curves were well above
the curve predicted by theory neglecting field
effects. Also, the charging due to negative
corona was greater and increased more rapidly
than that for positive corona. The effects of
the electric field and the possible presence
of free electrons is reflected in these measure-
ments .
Comments and Remarks—
At higher voltages, the tests indicated that charging rates
due to positive and negative corona differ quite drastically
from one another. This difference is attributed to the presence
of free electrons. If free electrons are present in negative
corona discharge at high voltages, then charging would be greatly
enhanced and theories would have to account for charging by elec-
trons in addition to ions.
Data presented on charging versus time were very limited.
One set of data was presented for a particle size of 0.15 micron
and electric field strength of 2.65 kV/cm. More experimental
data is needed on this type of measurement.
Also, more tests were needed with the screen charger so
that the experimental data could be compared with theory.
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G. W. Hewitt (1957)8
Discussion—
Experimental results are given on the charging of submicron
particles in air as a function of particle size, field strength,
ion concentration, and charging time. Data are given on particle
mobilities as a function of field strength, charge, and particle
size. These data include particle sizes ranging from 0.14 ym to
1.32 ym in diameter and electric field strengths varying from 300
V/cm to 10800 V/cm.
The measurements were made with a system consisting of the
following components and capabilities.
a. Aerosol Generator, "OWL", and Concentration Meter -
Cloud-type measurements were possible.The aerosol
generator produced liquid, spherical particles of
dioctyl phthalate of controllable and very uniform
size. The size and concentration of the aerosol
particles were measured by light-scattering methods.
Particle sizes were measured with an instrument called
the "owl", which analyzes the angular intensity of
light reflected from the particles. Concentrations
were determined by a concentration meter in which
light scattered by the particles is focused on
a photomultiplier tube.
b. Particle Charger - The charging device provided inde-
pendent control of the electric field strength E,
ion concentration N, and charging time t.
c. Mobility Analyzer - Mobilities of the charged par-
ticles were obtained by measuring their velocities
in an electric field. Data were obtained in order
to plot a curve of relative particle concentration
versus mobility from which an average mobility is
found. The relation between mobility and particle
charge is determined by mobility measurements on
particles of the same size carrying very few
charges. A small amount of charge can be given
to the particles by using low values of E, N, and
t in the particle charger.
Conclusions—
The experimental results lead to the following statements.
a. The most difficult particles to precipitate are
those ranging from 0.2 ym to 0.4 ym in diameter.
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For each charging field, there is a particle size
at which the mobility reaches a minimum.
The additional mobility produced by a charging
field is approximately proportional to the
strength of the field.
The external electric field is important for
all particle sizes.
Charging curves show a greater slope at Nt=107
sec) than theory indicates.
f. Experimental curves do not flatten off as
quickly as theory predicts.
g. In the absence of an external field, the
"classical" diffusion charging theory agrees
reasonably well with experiment.
h. For large particles and high electric field
strengths, the "classical" field charging
theory is in line with experimental results.
Comments and Remarks —
This experimental work was carefully done and covers the
broadest range of particle sizes and electric field strengths
available in the literature. All results are presented in
graphical form. The results predicted by field charging and dif-
fusion charging theories are plotted with the experimental re<-
sults in certain cases to check for agreement. The charging
rates for particles of diameters 0.18 to 0.92 vim are most com-
plete. Still, more experimental charging rates are needed for
particles larger than 0.92 ym in diameter.
Vadim G. Drozin & Victor K. La Mer (1959) 22
Discussion —
As part of a method for determining the particle size dis-
tribution of aerosols, the particle charging law was determined
experimentally by measuring particle charge as a function of
particle radius. The data was obtained using monodisperse
stearic acid aerosols produced in a La Mer-Sinclair generator.
The particle size was determined from the angular position of
red bands in the higher order Tyndall spectra. Particle sizes
ranging from 0.1 ym to 0.7 ym in radius were examined.
The charging device employed a unipolar corona discharge
and satisfied the following conditions:
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a. The losses of particles, in the device due to
precipitation under the influence of the charging
field should be as small as possible.
b. The particles may obey any charging law except one
in which the/ number of acquired charges is linearly
dependent on the radius of the particle. The gen-
eral form of this dependence is
n = kra , (67)
where k and a are constants.
c. All particles of the same size should pick up the
same number of charges.
Two methods were investigated for determining the charge
acquired by a particle during the charging process.
a. Individual Particle Observation - The upward and down-
ward velocities of charged particles were measured with
a known electric field in a Millikan chamber. If the
particle sizes were determined optically, then the par-
ticle charge could be determined from the equation
neE ± mg » -. (68)
up
where n = particle charge,
e = elementary unit of charge,
E = electric field in Millikan chamber,
m = mass of particle (4/3 irr3p) ,
g = acceleration of gravity,
ri = viscosity of the carrier gas,
a = particle radius,
S = distance particle travels under the influence
of E, and
t = time it takes the particle to travel the dis-
u^ tance S upward.
As a check on how uniformly the particles were charged
in the charging device under given charging conditions,
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the particle size and charge were both determined in the
Millikan chamber for a small number of particles. Nor-
mally, a monodisperse aerosol will have some size dis-
tribution and the size of a particular particle may not
be exactly that determined from the higher order Tyndall
spectra.
The particle radius was determined from the equation
, (69)
./iT
a = k » t-, t
• down up
where
_ /Qn
-------
particles. A zero-penetration filter was weighed,
the aerosol was passed through the filter, and after
15 to 20 minutes of filtration, the filter was
weighed.
2. The penetration P through the charging device was
measured by determining the ratio between the number
of aerosol particles leaving and entering the charg-
ing device as a function of ionic current.
3. The current ip caused by total precipitation of
charged particles in the precipitator was measured
as a function of ionic current.
Using the results of the above three steps, the number
of charges n on a particle of given size could be deter-
mined from the equation
i
31 = HtJPe '
where U is the rate of aerosol flow.
Then, by following the same procedure on monodisperse
aerosols of different particle sizes, the charging law
was determined from the curve representing particle
charge as a function of particle radius.
Conclusions—
Experimental curves for particle charge as a function of
particle radius were obtained for an aerosol flow rate of 4 1/min
with a charging current of 300 uA and for an aerosol flow rate of
2 1/min with charging currents of 40 yA, 80 yA, and 120 yA. The
charging curves yielded a charging law of the form, n = kra, with
a having a value of approximately 2 for particles of radius
greater than 0.2 ym. The result that n is proportional to r2 is
in agreement with the prediction of classical field-charging the-
ory. For particles of radius less then 0.2 ym, the exponent a
must be decreased in order to fit experimental data. This indi-
cates that a mechanism other than field-charging is predominant
for these particle sizes.
Comments and Remarks—
This work indicates that experimentally, it is best to
measure macroscopic properties of a large number of monodisperse
particles rather than the properties of individual particles
when studying aerosol particle charging.
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Arthur T. Murphy, Felix T. Adler, & Gaylord W. Penney (1959)*
Discussion—
A theoretical model is developed based on the concepts of
kinetic theory in order to describe the charging of fine parti-
cles. The particle is considered to acquire charge primarily due
to the thermal motion of ions in the process known as "ion diffu-
sion" charging. It is assumed that "field" charging takes place
initially and very quickly the particle reaches a maximum charge
due to this mechanism. This maximum charge is then used as the
initial charge for calculations in this model. Previous models
for "ion diffusion" charging accounted only for electric field
effects due to the charge on the particle and neglected any
effect due to the external electric field. The model presented
accounts for both the field due to the particle and external
field. By use of the model, an attempt is made to estimate the
effects of the external field under differing conditions. In
analyzing the effects of the external field on the random-motion
charging process, two possible mechanisms for altering the charg-
ing rate are investigated in depth:
a. An ion moving in the direction of the external
field towards a particle will acquire a certain
amount of energy due to the field in addition
to its thermal energy which will enhance its
chances of overcoming the potential field due
to the charge already on the particle.
b. The external electric field will alter the
density distribution of ions in the neighbor-
hood of the particle and thus affect the
movement of ions towards the particle.
In the mathematical formulation of the charging model, the
number of ions that may reach the particle depends on the follow-
ing factors:
a. The number of ions in the neighborhood of a point
P in space.
b. The number of ions at point P headed in the cor-
rect direction.
c. The number of ions at point P with sufficient
velocity to overcome the repulsive force due
to the like-charged particle.
d. The number of ions at point P that manage to
avoid a collision on the way to the particle.
e. All points P in space.
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f. All areas on the particle that an ion may strike
from point P.
Basic Equations—
The charging rate for an infinitesimal surface area dS on
the particle is given by
fe = T! / dr / de sine^ X / d N cose e~r'/X J °-f (c)dc
Q.U. -,„ fur •'0 *'o r r •'n r 37 c A
a-£> » m
(72)
where n = number of electronic charges on particle,
dS = infinitesimal area on particle, cm2,
Xr' yr' Zr = Cartes;i-an co-ordinates with dS as origin, cm,
r, 6 , 4> = spherical co-ordinates for x , y , z system,
cm, radians,
N = ion density at point P, ions/cm3,
c = speed of ion (without regard to direction),
cm/sec,
A, = mean free path of ions colliding with molecules,
cm,
f(c)dc = probability that an ion will have a speed be-
tween c and c+dc after collision,
c = minimum speed which an ion can have at P and
m still reach dS, cm/sec, and
t = time measured from start to charging, sec.
Equation (72) accounts for the first five factors (mentioned
in the general discussion), which determine the charging rate in
this model. The sixth factor is accounted for by integrating
over the surface of the particle to find the total charging rate
which is given by
where a = particle radius, cm,
x^, y,,, z„ = Cartesian co-ordinates with center of sphere
Ti T? wf
as origin, cm, and
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r_, 0_, _ = spherical co-ordinates for x . y_, z_ system,
Ei Ei £1 -i • E ilj £1
radians.
In order to evaluate equation (73), the quantities f(c) and
N must be known.
Ideally, f(c) represents the general velocity distribution
for ions in an electric field. Once a form is chosen for f(c),
the integral
CO
f c f(c)dc (74)
cm
can be evaluated. It is noted that the minimum speed c^, that an
ion can have at point P and still reach the surface of the parti-
cle is a function of position and a criterion is established for
determining cm for each point in space.
The ion density N is a function of position and in general,
is a solution to the diffusion equation
V2N + V\() • VN = 0 (75)
where the dimensionless potential energy function is given by
and
e = electronic charge, statcoulombs,
k = Boltzmann's constant, erg/°K,
T = absolute temperature, °K,
R = distance from center of particle to P, cm,
Eo = uniform external field strength (E0 parallel to Z_), cm,
and E
K = dielectric constant of particle.
The solution to equation (75) is of the form e"1^ and must
satisfy the boundary condition that \^\ remain finite as R -*•<».
166
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Conclusions-!—
Due to the difficulties involved in solving equation (73),
it is not solved rigorously. Insight into the effects of the
external electric field is gained by other methods. In order to
determine the effect of the external field on the energy of the
ion, the dimensionless function
g = ^o - i|» (77)
is examined for certain simple cases, where IJJQ is the dimension-
less potential energy at the surface of the particle. The effect
of the external electric field on the ion density N is estimated
by solving equation (75) using finite difference approximations
along special directions in space where solutions could be ob-
tained more easily.
All ions headed towards dS from points in space such that
g £ 0 have enough velocity to reach the particle. Only a frac-
tion, (1 + g)e~g, of the ions headed towards dS from points in
space such that g > 0 have enough velocity to reach the particle.
Consideration of the function g in the case where the ions travel
along the direction of the external field shows that g = 0 at
some distance RO from the particle and all ions a distance of R0
or greater from the particle will have sufficient velocity to
reach the particle. In the absence of an external field, the
number of ions reaching RO with sufficient velocity to reach the
particle is smaller. So in the presence of an external field,
more ions arrive at RQ with sufficient velocity to reach the
particle than in the absence of an external field. Even though
the external field increases the number of ions arriving at RO
with sufficient velocity to reach the particle, these ions only
have a chance of getting to the particle because of the possibil-
ity of suffering a collision along the way. The probability of
suffering a collision over the distance R0 is ej^o/*. pOr a
mean free path typical of a molecular ion, e-K°/A is very small.
Thus, it is seen that the increased energy effect for ions mov-
ing in the direction of the field will be small for molecular
ions. Also, for ions moving in a direction opposite to the ex-
ternal field g is always positive and always larger with an ex-
ternal field present than with no external field. Thus, there
will be fewer ions capable of reaching the particle from this
direction when an external field is present.
Solution of equation (75) using finite difference approxi-
mations along special directions shows that the external field
has a large effect on the ion density N at the surface of the
particle which would lead to increased charging. The following
results are found:
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a. The ion density at the surface of the particle
is increased by a large factor over the zero
field value where the external field and par-
ticle field are directly opposite one another.
In addition, the factor by which the ion den-
sity increased depends greatly on both the
particle charge and the external field.
b. The ion density at the surface of the particle
is decreased by only a small factor from the
zero field value where the external field and
the particle field are exactly in the same
direction.
Comments and Remarks—
The model presented here is fundamentally sound and the con-
clusions drawn concerning the effects of the external field are
valid. The difficulty with the model lies in the mathematical
complexity in finding the charging rate from equation (73) . This
difficulty centers around the solution of equation (75) for the
ion density N as a function of position in the existing fields,
the many integrations that must be performed in equation (73),
and the complex relationships between certain variables in equa-
tion (73). Since equation (73) could not be solved rigorously,
the theory could not be compared with experiment for agreement
except by making rough estimates. These rough estimates showed
fair agreement with the limited experimental data of Penney and
Lynch. Also, the initial charge used in this theory should be
due to both "field" and "diffusion" charging which can occur
simultaneously instead of "field" charging alone.
Benjamin Y. H. Liu, Kenneth T. Whitby, & Henry H. S. Yu (1967)7
Discussion—
An experimental investigation was made into the pure ion
diffusion process at various pressures less than one atmosphere.
By varying the pressure, the mean free path of the ions could be
changed and its effect on the ion diffusion process could be
deduced. Theories based on kinetic theory predict that the mean
free path will have relatively little effect on the particle
charging process, whereas, those based on macroscopic diffusion
of ions indicate that it should have a considerable effect.
The experimental data were obtained by exposing a monodis-
perse aerosol to unipolar ions produced by a high-voltage posi-
tive corona discharge and measuring the electrical mobility and
charge of the aerosol. The experiment consisted of the follow-
ing techniques and apparatus:
168
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a. Aerosol Generation and Sizing - The aerosols used were
monodisperse aerosols of di-octyl phthalate (OOP) having
diameters of 1.35 ym and 0.65 ym. The aerosols were pro-
duced by a generator of the atomization-condensation
type and put through a process of charge neutralization.
The particle sizes were measured by a calibrated optical
particle counter and by direct microscopic sizing of the
collected DOP drops.
b. Aerosol Charger - The aerosol was exposed to positive
ions in the charging region which was bounded on one
side by a solid electrode and on the other by a screen
through which the positive ions produced by the corona
discharged flowed. An ac square wave voltage was
applied to the solid electrode to minimize the aerosol
loss during the charging process.
For a given particle size and pressure, charging due
to pure diffusion of ions depends on NQ, the number
concentration of ions in the charging region and t,
the time during which the particles are exposed to ions.
The charging time t was calculated from the aerosol
flow rate and the dimensions of the charging region.
In order to determine the ion concentration NO, in the
charging region, a dc voltage was substituted for the
ac square-wave voltage and the corresponding dc current,
I, which flowed through- the screen into the charging
region, was measured. The ion concentration was then
calculated using the equation
No = I/eEy,.A (78)
where e = elementary unit of charge,
E = intensity of charging field,
y. = ion mobility, and
A = area of screen through which ions flow
into the charging region.
c. Measurement of Small Ion Mobility - Since the ion mobil-
ity could be greatly affected by trace amounts of un-
known impurities, a measurement was made of this quan-
tity. In a small ion mobility analyzer, positive ions
produced by the corona wires were made to flow periodi-
cally into an ion drift space by a square-wave voltage
applied to an electronic shutter. In the ion drift
space, a high voltage dc power supply created an elec-
tric field and the time it took the ions to travel ,from
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a grounded screen to an ion collecting plate was measur-
ed on an oscilloscope screen. The ion mobility was then
calculated from the measured ion transit time, the width,
and the electric field intensity in the drift space.
Aerosol Mobility Analyzer - The charged aerosol was in-
troduced into the aerosol mobility analyzer in the form
of an annular ring around a core of particle-free, clean
air and collected at the other end by a filter. A nega-
tive voltage was applied to -a rod located at the center
of the annular ring. The negative voltage was increased
in steps and the corresponding current was measured by
an electrometer attached to the filter. The electro-
meter current represented the current due to the charged
aerosol collected by the filter and hence, not collected
by the center rod. A voltage-current curve was plotted
in order to obtain the mobility. Then, the electrical
mobility of the aerosol was obtained by using the equa-
tion
Up = C(q/V) (79)
where y = electrical mobility of the aerosol,
q = total volumetric rate of flow of air and
aerosol in the mobility analyzer,
V = value of the center rod voltage at which
the electrometer current is equal to half
of its maximum value, and
C = instrument constant depending on the dimen-
sions of the mobility analyzer.
From the measured mobility of the aerosol, the electric
charge on the particles was determined from the equation
u
np = - c
where n = number of elementary units of charge on a
p particle,
ri = viscosity of air,
c = Cunningham's correction factor, and
D = particle diameter.
170
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Conclusions—
The experimental results were obtained over a pressure range
of 0.0311 to 0.960 atm with a corresponding particle radius to
ion mean-free path ratio, a/A, ranging from 1.0 to 66. The data
led to the following results and conclusions.
a. The ion mobility varies inversely with pressure.
b. The experimental data could be fitted by the
equation
n /Do = 9.0 ln(l + 1.02 x 10~5 NQtD ) (81)
where Dp is the particle diameter in micrometers.
c. The particle charge is independent of the ratio,
a/A, and depends only on the product N0t.
d. Equation (81) agrees with the classical ion dif-
fusion equation,
n e2/akt = In [l 4- (irce2aNQt/kt)] , (82)
provided the value of c", the mean thermal- speed
of ions, is taken as 1.18 x 10** cm/sec.
e. The measured ion mobility ]ij_ at atmospheric
pressure was 1.1 cm2/V«sec.
f. The values of c" and \ij_ we£e considerably smaller
than the usual values of c = 4.72 x 10" cm/sec
and yj_ = 1.6 cm2/V-sec for positive ions pro-
duced in a corona discharge. These results
suggest a molecular weight for the ions which
is on the order of 16 times that of air. Thus,
the ions were probably clusters of molecules
produced in the corona discharge rather than
simple ionized air molecules.
Comments and Remarks—
The results of this investigation indicate a need to design
experiments to identify the ions present in the corona discharge
and determine their relative numbers. Mass spectroscopy has been
used by other investigators to identify the ions present in the
corona discharge. Several different ions were identified and
the largest mass found was 200. Liu, et al, suggest a molecular
weight for ions of 460 in order to obtain agreement between their
experimental data and classical charging by pure ion diffusion.
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Since theories based on kinetic theory depend on the mass of the
ions, it is necessary to have some average ionic mass representa-
tive of that found in the corona discharge.
Benjamin Y. H. Liu, Kenneth T. Whitby, & Henry H. S. Yu (1967)23
Discussion—
An analysis of the particle charging process in the absence
of an applied electric field is presented. An order of magnitude
calculation is made in order to show that under practical charg-
ing conditions, the charging process for micron and submicron
particles cannot be described as a macroscopic diffusion process
in which ions are assumed to diffuse continuously in a quasi-
steady state toward the particle under the action of a concentra-
tion gradient because, in fact, the charging process is essen-
tially discontinuous. A theory is developed based upon the clas-
sical kinetic theory of gases and its predictions are compared
with available experimental data and other existing theories.
This theory predicts that the particle charging rate will be un-
affected by the mean free path of the ions.
Basic Equations—
For a neutral particle of radius, a, in a gaseous medium
containing No ions/cm3, the average time t, needed for the parti-
cle to capture an ion is
ti = l/Tra2cN0 , (83)
where c is the mean thermal speed of the ions.
The average diffusion time ta is on the order of
tz = a2/D , (84)
where D is the diffusion coefficient of the ions. If ti « ta/
then many ions will be captured within the time interval ta and
the charging process may be considered a continuous diffusion
process. From equations (83) and (84) and the condition ti «t2/
it is found that
No » ^— . (85)
ira^c
If the diffusion coefficient D is taken to be
^/o ' (86>
16/1
where X is the mean free path of the ions, then equation (85)
172
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requires that
No » — (87)
16/2 a*
in order that the particle charging process may be considered as
a continuous diffusion process. Taking a = l.Oy and A = 10~6 cm,
NO must be much greater than 109 ions/cc for the process to be
considered as continuous. In practical charging devices, the
maximum N0 is on the order of 108 ions/cm3 which is sufficient to
produce a continuous charging process.
An alternate approach, based on kinetic theory, is developed
in order to describe the particle charging process. The develop-
ment employs the same line of reasoning as that used by Murphy
et al, in an earlier publication and, as before, the charging
rate is found to be
dnp [ / / / / dScos 6 (r2sin9drdedc())N I
-at = W *.o £o fa —*— /
).
(88)
where n = particle charge,
P
t = time,
dS = element of surface area on the particle,
S = surface of the particle,
r, 6,
-------
X = mean free path, of ions.
In order to perform the integrations in equation (88) , the
value of c , the spatial dependence of N, and the dependence of
f (c) on c must be known.
The value of cm is determined by using the results of clas-
sical scattering theory and accounting for the deflection of the
ion due to the charge on the particle. An ion has a chance of
making a grazing collision with a particle provided that it has
a minimum initial speed cm which satisfies the condition
sin29 = 1-1 +1 , (89)
n e2 -, m c2
- J. . ul / nn\
' ? = —- ' (90)
where
and
6 = spherical coordinate of a point P in space with dS as
origin,
n = number of electrons on particle,
e = elementary unit of charge,
a = particle radius,
k = Boltzmann's constant,
T = absolute temperature,
m = ionic mass , and
R = radial distance from the center of the particle to a
point P in space.
The local concentration N of ions at a point P in the vicin-
ity of a charged particle is obtained using the Boltzmann distri-
bution,
N = N0e~Ya/R (91)
In using equation (91) , it is assumed that the average time
interval needed by the particle to capture an ion is long com-
pared to the time needed for the equilibrium distribution of
ions to be established around the particle.
Assuming that the presence of the charged particle does not
disturb the distribution function f (c) too greatly, tfien f(c)
174
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may be taken as the equilibrium distribution function and will
be Maxwellian. Then,
cf(c)dc = c £e~^d£ , (92)
where
and
c = —|— l^-J . (94)
/fr
Due to symmetry considerations, equation (89) can be readily
integrated with respect to dS and d. The remaining integrals
can be written in a simpler form by using relations (90), (91),
(92), and defining new variables T and x given by
trace2 N0t r ._._.
T = E-J- ; x = - . (95)
Then, equation (88) can be rewritten in the form
°°f ^fe --via/Hi
dr _ a / -x(a/A) , / 2 sin6cos6e Tia/K'd6
d? - I J0 e dx ^o
7
£e "d£ . (96)
Since
I
(97)
and according to equation (89) ,
1
m cos2e
we have
Yd - ) , (98)
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IT/2
//•
-x(a/A), / 2 sin9cos6
e dx /
... »/
.x=0 6=0
X i + -J:—Y(l - I) exp I -Y | + (1 - f) ( d0. (99)
|_ cos26 J (L cos20 JJ
In equation (98) , the ratio (a/R) is a function of 6 where
it can be shown from geometrical considerations that
(R/a)2 = 1 -I- x2 + 2 x cos 0 . (100)
i
Since the ratio (a/R) does not vary greatly over the interval of
integration, it is replaced by an appropriate mean value (a/R) so
that the integral over 0 can be performed in closed form. After
integrating equation (99), the charging rate is given by
37 = e~Y . (101)
Conclusions—
The charging rate derived by Murphy is
(102)
where 5 is a function of the ratio a/X.
Murphy's equation differs from equation (101) in that the charg-
ing rate depends on the mean free path of the ions. Experiments
performed by Liu et al, in which charging rates were found for
different mean free paths, indicate that equation (101) is valid.
In equation (101), the charging rate is independent of the mean
free path and this is a consequence of considering the deflec-
tion of an ion as it approaches a charged particle. Murphy did
not consider the deflection of the ions in his development.
Equation (101) is identical with the classical diffusion
equation derived by White. White derived his equation under the
assumption that the particle radius is large compared to the
mean free path of the ions. This analysis shows that the equa-
tion will be valid even when the radius of the particle may not
be considered large compared to the mean free path of the ions.
The theory developed shows good agreement with experimental
charging curves when the mean thermal speed of the ions is taken
176
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to be 1.18 x 10** cm/sec. This is equivalent to an ionic molec-
ular weight of 460.
Theories based upon the microscopic diffusion of ions pre-
dict a dependence of the charging rate on the mean free path.
The steady-state diffusion equation can not properly describe
the particle charging process because of the low concentration of
ions present in the charging process and the essentially discon-
tinuous nature of the charging process.
Comments and Remarks—
The experimental data is plotted, and it is stated that the
classical diffusion equation gives reasonable agreement with the
data if the mean thermal speed c is taken to be 1.18 x 101* cm/sec.
It would be of interest to see the results given by the classical
diffusion equation when the usual value of 4.63 x 10** cm/sec is
used and see how this compares with the experimental data. This
would give some idea into how sensitive the diffusion charging
process is to the choice of c. If it is highly sensitive to the
value of c, then a determination of the ionic masses must be made
in order to have a reliable value of c to use in the theories.
Benjamin Y. H. Liu and Hsu-Chi Yeh (1968)5
Discussion—
An approximate theory is developed in an attempt to describe
particle charging over a broad range of particle sizes and
applied electric fields. Due to the approximations introduced
in the theory, the resulting mathematical equations can be
readily solved by numerical methods. The theory is constructed
so that it will account for the following experimentally observed
facts.
1. For high electric-field intensities and large
particles, the field-charging equation
n = n irN0eu.t/(TrNoeia.t + 1) (103)
5 J_ JL
is in reasonable agreement with experimental
results, where
n = charge on particle, elementary units,
n = saturation charge on particle, elemen-
tary units,
No = concentration of ions at a great distance
from particle, ions/cm3,
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SOUTHERN RESEARCH INSTITUTE
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e = elementary unit of charge/ 4.8 x 10 10 esu,
y. = electric mobility of ions, cm2/stat V-sec,
1 and
t = time, sec.
2. In the absence of an external electric field,
the diffusion-charging equation
n= (akT/e2)ln (1 + TTe2caN0t/kT ) (104)
yields results in line with experimental data,
where
a = particle radius, cm,
k = Boltzmann's constant, cgs,
t
T = absolute temperature, degrees K,
and
c = mean thermal speed of ions, cm/sec.
3. The applied electric field has a large effect on
the charging rate for submicron particles.
The theory approaches equation (103) in the limit of large
particles and high external fields, reduces to equation (104) with
no external field, and allows the external field to have an ap-
preciable effect in charging submicron particles.
The theory divides the charging process into two regimes
depending on the amount of charge on the particle. If the
charge n on the particle is less than the saturation charge n ,
then charging takes place in Regime II. Charging in Regime Is
is considered as due to both field charging and diffusion occur-
ring simultaneously. Thus, in Regime I the ions are driven onto
the particle by the electric field and also reach the particle
due to their thermal motion. In Regime II, since no electric
field lines can enter the particle, the mechanism by which ions
reach the particle is deduced by analyzing their motion along
the special direction where the electric field due to the parti-
cle and the external electric field are exactly opposite one
another. An ion is visualized as drifting towards the particle
along the direction of the total electric field until it reaches
a certain distance ro from the particle where the potential
energy is a minimum. From ro to the surface of the particle,
the ion must move against the total electric field and can
accomplish this by means of the diffusion process and a concen-
tration gradient. Thus, diffusion is the sole charging mechanism
in Regime II.
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Basic Equations—
The ions experience an electric potential given by
V = + EOCOS 9
{r-(.Vr'> [(££)]} (105)
where EO = the external electric field, and
K = the dielectric constant of the particle.
In Regime I, ions are driven onto the particle along elec
tric field lines between the angles 9 = 0 and 9 = 8 o , where 9 o
is determined from the condition that
• (106)
The charging rate in Regime I is given by
>] I107)
where the first term is the "classical" field-charging rate and
the second term is a correction to the charging rate which allows
for diffusion of ions to the particle. The factor 2 a (1+ n/ns)
is the surface area of the particle containing all electric
field lines that leave the particle.
In Regime II, the diffusional charging rate is given by
(•&) = felic)(4Tra2) (108)
var/
where "N = the average concentration of ions over the entire par-
ticle surface.
In general, the local ion concentration N must be found by
solving the steady state diffusion equation for ions in an elec-
tric field given by
V2N +V(eV/kT) . VN = 0 . (109)
A solution to equation (109) is constructed and is given by
"N = No for r>r0
N- Mbe-(e/KP)(V-V«) for r
-------
where VQ = the electric potential at r0.
Solution (110) satisfied the boundary condition that as r-*»,
To find r0 along the line 9=0, the condition
3V
3r
= 0
9=0
is used so that
-(ne/ro2) + E0 |l + 2 |(g£)|(2_.)t = 0 (111)
determines ro.
The concentration of ions at the particle surface at 6 = 0
is
N = N0e
where V = the electric potential on the particle's surface at
a 9 = 0.
It is argued that the average ion concentration of ions over
the entire particle surface should be of the same order of mag-
nitude as Na and as a first approximation Na is used in place of
N in equation (108). Thus, the charging rate in Regime II can
be calculated from
(|£) = ™2N0ce-e/kT(AV) (113)
used in conjunction with equations (105) and (111).
Conclusions—
The predictions of the theory are compared with the experi-
mental particle charging data of Hewitt for particles of radius
0.09 urn to 0.46 urn and with external field strengths ranging from.
300 V/cm to 10,800 V/cm. The agreement of the theory with exper-
iment is excellent for the 0.09 ym particle for all electric field
intensities available. The agreement of the theory with experi-
ment for the 0.46 ym particle is less desirable and overestimates
the charge by about 30% for all electric field intensities. It
is concluded that the theory gives a reasonable explanation of
the charging process because it agrees fairly well with experi-
ment over a wide range of conditions.
180
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Comments and Remarks—
The following observations are made concerning the theory.
1. In the physical picture of the theory, N=N0 for
r>r0 where r0 corresponds to the radial distance
from the particle along 9 = 0 at which the poten-
tial is a minimum. Since at r0, the electric
field due to the particle is exactly equal in
magnitude to the external electric field, it
appears that the electric field due to the par-
ticle will have an appreciable effect on the
ion concentration out to a much larger distance
than r0 so that N is approximately equal to NO
at some greater distance from the particle than
r0.
2. In finding the average ion concentration at the
particle surface, it is assumed that the average
is equal to the concentration of ions at the
particle surface at 9 = 0. This should lead to
charging rates that are too large since the con-
centration of ions at the particle surface will
be largest at 9 = 0. Some type of averaging of
the ion concentration over the entire particle
surface is needed.
3. The theory agrees well with Hewitt's experimental
data for small particles but the agreement appears
to worsen as the particle size is increased.
Since the largest particle size given in Hewitt's
data is 0.46 ym, the theory is untested for particle
sizes of one micron and larger.
G. Z. Mirzabekyan (1969)2
Discussion—
Existing theories concerned with particle charging by uni-
polar ions are discussed and commented upon. The charging pro-
cess is discussed in light of two possible charging mechanisms,
field charging and diffusion charging. The relative effects of
the two mechanisms are classified according to the following
ranges of particle size:
1. For particles of radius p >_ 2-3 ym, field charging
predominates and the effects of ion diffusion may
be neglected.
2. For particles of radius 0.8 ym £ p < 2 ym, field
charging and diffusion charging are both important
and should be considered simultaneously.
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SOUTHERN RESEARCH INSTITUTE
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3. For particles of radius p <_ 0.08-0.1 ym, diffusion
charging is the dominant effect and the contribu-
tion due to field charging may be disregarded.
A new theory which includes both charging mechanisms is de-
veloped based on the general diffusion equation. The results
are compared with the best experimental data available and the
differences do not exceed 3-8 percent.
Basic Equations—
The mechanism of field charging, which is valid for parti-
cles of radius p >^ 2-3 ym, was described by Pauthenier and Moreau-
Hanot. The particle charge as a function of time was given by
these authors as
- , (114)
where Q = particle charge,
GO = permittivity of free space,
e = relative dielectric constant of the particle,
E0 = external field strength,
p = particle radius,
y = ionic mobility,
e = ionic charge,
no = undisturbed ion concentration, and
t = time.
The diffusion process, which predominates for particles of
radius p < 0.08-0.1 ym, was investigated by several authors,
using different methods. Deutsch and Koptsov employed general
energetic relationships to describe the process and it is pointed
out that this approach produces some error, since the energy of
the ions does not remain unchanged after its collisions with air
molecules. Fuchs and Arendt, Kallman considered the diffusion
of the ions in the electric field of the particle and it is
pointed out that this approach is better justified physically.
The ion current to the particle was found by solving the diffu-
sion equation in the form
4iTR p^ - nyER |= $ = constant, (115)
182
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where R = distance from the center of the particle to the
point in space under consideration,
D = diffusion coefficient,
n = ion concentration,
ER = magnitude of the electric field of the particle,
which consists of the coulomb repulsion field of the
ion and the polarization field of the particle in
the field of the ion impinging on it, and
$ = ion current to the particle.
The first term on the left-hand side of equation (89) gives
the component of the current $ due to the nonuniform distribution
of ions around the particle; the second term represents the
movement of the ions under the influence of the electric field
ER-
In order to solve equation (115) , it is necessary to impose
two boundary conditions. The first condition was
lim n = n0 . (116)
R •*• oo
The second boundary condition employed by Fuchs was
lim n = 0 . (117)
R -»• p
The solution to equation (115), with boundary conditions,
(116) and (117) was given by
dN ,, 2n dni ^ _ 4irD
_._= 47rp D m\ =n0 fi4)/kT
R~p /S - dR
where <|> = potential due to the electric field of the particle,
N = number of ions impinging on the particle,
k = Boltzmann's constant, and
T = absolute temperature.
The second boundary condition employed by Arendt gave the
ion current at the particle surface as
183
SOUTHERN RESEARCH INSTITUTE
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$ = 4irp2 ±|^ nR = p + X , (119)
where = mean thermal velocity of the ions, and
X = mean free path of the ions.
The solution to (115), with boundary conditions (116) and
(119), was given by
A dN A 2
$ = _ = 47TP2-T-
1 + ^- V-p ^pin "^1 5 dR. (120)
The charging curves given by equations (118) and (120) agree
well with each other. The agreement is due to the fact that
boundary conditions (117) and (119) are approximately equivalent.
Equation (118) can be written in final form, neglecting the polar
ization field, as
!£[£.._ (A) -In (A) - 0.5772J = n0t , (121)
where E . is an integral exponential function and
A(not) "
The graph of the function A can be constructed and then the
particle charge can be determined from the relationship
kT
Q = 4Tre0p — A(n0t) . (123)
From equation (123) , it is seen that in purely dif fusional charg-
ing, the particle charge is proportional to the particle radius.
In the transition region where particle radii lie in the
range 0.8 pm < p < 2 ym, it is necessary to consider simultane-j
ously dif fusional and field charging. Kapotev, Murphy, and
Cochet proposed models to account for both mechanisms. These
models are discussed and their weaknesses are pointed out. It is
concluded that a rigorous solution of the problem can be achieved
184
-------
only by a solution of the of the general diffusion equation in
which account is taken of both field and diffusional charging.
A differential equation is developed based on both charging
mechanisms. The following assumptions are made in the derivation:
1. The charging process is considered to be quasi-
stationary;
2. The effect of the space charge due to the ions
on the resultant field near the particle is
neglected.
The condition of continuity of the ion current vector v is
given by
v = nyE - DVn . (124)
The first term on the right-hand side of equation (124) is
the component of the current produce^ by movement of ions under
the influence of the electric field E, the sum of the external
field E0/ the polarization field of the particle in the field
EO, and the coulomb field of the particle; the second term is the
component of the current produced by diffusion of the ions under
the influence of the concentration of the ions.
Under assumption (1),
Vv = 0 (125)
and from the assumption (2),
VE = 0 . (126)
Substituting equation (124) into equation (125 and using (126)
gives
Vn + ji V-Vn = 0 . (127)
The electric potential <|> in equation (127) is given by
* - Q=— -I- E0R(1 - f£i- £-) cose. (128)
A solution to equation (127) was sought with the boundary condi-
tions
185
SOUTHERN RESEARCH INSTITUTE
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lira n = n0
R •> <»
lim n = 0
R -*• p
(129)
Initially, analytical solutions were investigated but a
solution of this type could not be found. Next, numerical solu-
tions were examined. Using the method of finite differences, it
was found that a very large number of increments were necessary
in order to obtain a system of algebraic differential equations
that were solvable.
In order to facilitate the numerical solution of equation
(127) on a computer, a change of variable was made by letting
U = (n0-n)e . (130)
Using relation (130) , equation (127) can be written in terms of
the variable U as
VU - % (£)2 (V<|))2U = 0 . (131)
The boundary conditions that U must satisfy are
lim U = n0e^/2D
R •> p
lim U = 0 ( (132)
R -9- oo
lim
Using spherical coordinates and introducing the variable
X = cos 9 in equation (131) leads to the equation
Equation (133) is solvable, hence the ion current to the particle
is determined by
D . (134)
S particle R~p
186
-------
Conclusions—
The charging curves obtained using this theory showed the
following agreement with existing theories and experimental data:
1. For p j> 1-6 urn, the curves practically coincided
with those obtained by using Pauthenier's theory.
2. The curves were in agreement with Hewitt's experi-
mental data to within 3-8% and this agreement was
over a wide range of particle sizes and electric
field strengths.
3. Charging curves were calculated for a wide range
of values of E0(100-500 kV/m) and p(0.2-2 ym) and
compared with the results obtained by taking the
sum of the charge calculated by Pauthenier's
field charging (equation (114) and that calcu-
lated by Fuch's diffusion charging (equation
(123)). The comparison showed that the differ-
ence in the curves did not exceed 20%.
The following conclusions were made:
1. The general diffusion equation describes the
particle charging process over a wide range
of values of p and EQ.
2. The magnitude of the charge on the particle
may be approximately determined as the sum
of the charges calculated by the theories
of field and diffusion charging.
Comments and Remarks—
The authors approach of combining field and diffusional
charging mechanisms into their formalism is physically sound.
Murphy et al, and Liu and Yeh both suggest this approach. Al-
though agreement with Hewitt's data to within 3 to 8 percent is
claimed, those results are not shown here. A quantitative eval-
uation of the theory can only proceed by solving equation (133)
for a variety of particle sizes and electric fields. Since, as
Mirzabekyan points out, solutions of this equation involve a
complicated numerical procedure and unusually long computer run-
ning times, his formalism does not seem practical for our pur-
poses.
Arendt and Kallmann (1926)18
Discussion—
The mechanism of diffusional charging of aerosol particles
was studied theoretically and experimentally. The particles
187 SOUTHERN RESEARCH INSTITUTE
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ranged in size from 0.5 ym to 2.2 i_im diameter. Theoretically,
the desired result is to calculate the charge taken up by a par-
ticle in a given time and the dependence of this charge on parti-
cle radius and ion density in air. To do this, the classical
diffusion equation is solved with the assumption of no external
field and large initial charge on the particle. Boundary condi-
tions are constructed so that simple forms are obtained for the
potential energy $ and boundary surface current i0. Due to the
initial basic assumptions, the charging equation obtained is only
valid for large times. The theory is compared with charging mea-
surements made on a Millikan Oil-Drop Apparatus modified to pro-
duce large numbers of ions. Individual particles were observed
for hours at a time and their accumulated charge was recorded to
obtain the charging curves. At high ion densities, spontaneous
discharges occurred from the particles, but these discharges did
not grossly affect the shape of the charge curve or the limit
charge.
Basic Equations—
When an uncharged particle of radius a, is brought into an
ionized space, ions will impinge on the particle surface due to
thermal motion and the particle will acquire an electric charge.
As the charge increases, the ionic current must decrease due to
coulomb repulsion and eventually a limit charge is reached. In
a calculation to determine an expression for this current, one
must account for the separate effects of an external electric
field, image forces, ionic diffusion and coulomb repulsion. If
the density distribution of ions in the vicinity of the ion can
be determined with these effects accounted for, then the charg-
ing rate can be determined.
The change in ion density f, with time is controlled by the
general diffusion equation
||- = V- (yfVcf) + DVf) (135)
where y = ionic mobility,
D = diffusion constant, and
<}> = electric potential energy.
A solution of (135) requires specification of a uniformly con-
stant ion current at t=0, f, at the particle surface, fa, and at
infinity, f^.
The following simplifications are introduced:
1. The effect of any external field is neglected.
188
-------
At a distance on the order of a mean free path,
A, from the surface of the particle, the simple
diffusion equation fails. Therefore, the assump-
tion is made that for a + X <_ r <_ °° the ion cur-
rent i through a surface element ds given from
diffusion theory by
i = (yEf - D||)ds
where E = electric field strength, and
z j normal to ds.
For a _< r <_ a+A, the ion current is given from
kinetic theory by
(136)
i = xcfds
with
c =
where x = fraction of ions retained after
striking a unit surface of the
particle,
c = a constant which comes from kinetic
theory and is proportional to the
number of ions striking a unit
surface of the particle per unit
time, here with no field effects
considered,
(137)
(138)
k = Boltzmann's constant,
T
m
Kelvin temperature of the ions, and
mass of the ions.
Consider only the case in which the ion current
to the particle has decreased so that 3f/9t£>0.
Thus, we obtain a "stationary" diffusion equation
V- (yfV$ + DVf) = 0
with a boundary condition given by integrating
(136) and (137) over a surface area enclosing
the particle to obtain the total current to
the particle io-
189
(139)
SOUTHERN RESEARCH INSTITUTE
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' /xcfads (140)
where the subscript indicates where the var-
iable is to be evaluated. It is assumed
that negligible error is introduced by
evaluating the right hand side of (140) at
a instead of a+\.
Equation (139) is rewritten as
DV2f + yVf-V(J> = 0 (141)
where the effect of the ions in the calcu-
lation of 4> is neglected; therefore,
V2c|> = 0. Approximating the spherical sur-
face by an infinite plane gives the image
contribution to the electrical potential
energy of the particle of charge ne,
, ne e e— 1 /n * 0 \
* ' -r - (r-a) e+T (142)
where e = dielectric constant of the particle.
Equation (139) is now solved to obtain an
expression for f. This solution contains
two arbitrary constants. One is determined
from the known ion density at infinity, f^.
The other is expressed with the help of the
first part of (140) . f is thus obtained as
a function of i0. This expression for f is
introduced into the right side of (140) from
which io is calculated as a function of n,
the number of ions captured by the particle
f , and a. The result is
00'
/kT
The calculation of i0r the current flowing
to the particle follows from (140) .
io = eg. = 4Traxcf (144)
a
where
190
-------
- e/kT
f=Ce a + a {/-°r dr} (145)
Substituting (142) in (144) and (145) gives an
expression which can be integrated with respect
to time to obtain the relationship between cur-
rent and particle charge. When this is done,
the effect of the image force is seen to be
important only if it is appreciable at a dis-
tance of one mean free path, X, away from the
particle. Separate calculations show that the
image force is large at X/2, but small compared
to coulomb repulsion at X; therefore, all image
effects are disregarded. Expressing C through
the constant ion density at infinity foo, one
obtains °°
which is valid only for n initially larger (at
t=0) .
Equation (146) exhibits the following behavior:
a. With increasing particle charge,
the charging rate decreases rapidly.
b. The limit charge increases almost
linearly with particle radius.
c. The limit charge grows very slowly
with increasing ion density. The
limit charge doubles if the ion
density increases by one hundred
fold.
Experiments, Results and Conclusions —
The aerosol particles of paraffin oil were studied in a
modified Millikan Oil-Drop Apparatus. Aluminum foil coated with
varying amounts of Polonium was used to produce ions which were
brought into the charging region by the action of an applied elec-
tric field. The number of ions per cubic centimeter varied from
515 to 67,000. In the charging region, a separate electric field
was used to manipulate the particle under observation and keep it
located at roughly the same place for all observations. The
growth of charge with time was measured for more than 300 drop-
191
SOUTHERN RESEARCH INSTITUTE
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lets with sizes ranging from 0.5 urn to 2.2 ym. The charging rate
was obtained from the slope of the charging curve.
Occasional discharges were obtained at high ion densities.
Investigation shows that this is a transient phenomena with no
lasting effect on either the limit charge of the charging rate.
When a discharge occurs, only several elementary charges are lost
and these are replaced rapidly.
The following experimental results are noted:
a. The limit charge does not noticeably depend
on charge polarity.
b. The limit charge increases almost linearly
with particle radius in good agreement with
equation (146). This measurement was some-
what difficult because of changing fields
and ionization rates, but the overall be-
havior was clear.
c. The dependence of limit charge on ion density
was again in agreement with equation (146) .
d. Experimental and theoretical agreement on ion
density versus particle radius and total charge
allow estimation of the fraction of particles
adhering after collision, x. Within experi-
mental uncertainty all the ions adhere.
It is therefore concluded that the theory developed above
is sufficient to describe the charging of small particles with
time, as well as their limit charge.
The close agreement of theory and experiment indicate that
a diffusion-like charging mechanism is probable for particles in
the size range investigated.
Comments and Remarks—
In order to solve the diffusion equation, a number of simpli-
fying assumptions were made. The net effect of these assumptions
is to limit the applicability of the results to diffusional or
thermal charging; i.e., charging in the absence of an applied
field.
The experiments are described in detail and the discontinu-
ous nature of the diffusional charging process is clearly demon-
strated. The agreement between theory and experiment is good
enough to verify the validity of the "classical" diffusional
charging equation. Although a broad range of ion densities was
192
-------
used in the experiments, the values were far lower than ordinar-
ily encountered in conventional electrostatic precipitators .
Robert Cochet (1961) 2I>
Discussion —
A correction is made to the classical law of field charging,
due to Pauthen^er and Moreau-Hanot . 3 The nature of this cor-
rection is to extend field charging equations to particles of
submicron size. To test the corrected theory, small shellac
particles with radii from 0.02 ym to 0.5 ym were precipitated in
a planar precipitator . The relationship of particle size to pre-
cipitation rate was measured and was found to be adequately de-
scribed by the corrected theory.
Basic Equations —
It is assumed that an exact solution to the problem of
charging micron and submicron sized particles which takes into
account both field and diffusional effects is impossible to
obtain, and that despite thermal motion of the ions, it is almost
always the ion flow due to the electric field which controls the
charging mechanism for electrostatic precipitator applications.
Therefore , the author ' s approach to this problem is to introduce
a correction to the classical field charging theory as developed
by Pauthenier and others. This correction combines both the
charging due to thermal agitation of the ions and the electric
field into a single generalized law of charging.
From classical field charging theory, the number n of
charges captured in a time t by a spherical particle of radius
a in an electric field of strength E0 is
n = ° (147)
n e t+9 l /;
with
(e-e1)
= 1 + 2
e+2e'
and
9 = i (149)
TryNQe
where e and e' are the dielectric constants of the particle and
the surrounding medium respectively, y is the ionic mobility,
and Noe is the charge density.
193
SOUTHERN RESEARCH INSTITUTE
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These formulas are valid in air at STP for a > 1 JBO. When
a < 1 vim, the capture of ions by the particle is enhanced by the
image force and thermal diffusion. Previous authors have usually
accounted for one effect or another but not both.
The ions are imagined to be entrained in a cylindrical vol-
ume so that all ions which pass within one ionic mean free path,
Aj_ of the particle are captured. This is a reasonable assumption
because the image force is not small in this region.
The region in which ions may be captured is defined by the
condition that at the boundary p = a-fA^, the radial component of
the electric field is zero.
The ion flow is thus :
an = Notnr(aE0a2- ne) * (15Q)
dt
where
.a
If E0, NO, and \i are constant along the particle trajectory,
then integration of (150) yields n as a function of time:
=
e t+9
giving a limit charge
Qo = aE0a2 (153)
when X^/a. is small, a approaches p and the classical field charg-
ing analogs of equations (152) and (153) are regained.
If the charge on a particle is known, then the precipitation
rate u> of the particle in an electric field E can be calculated
by the use of Stokes1 Law as corrected by Millikan.25
where A1 = Millikan correction coefficient,
A = mean free path of the surrounding gas molecules, and
n = the absolute viscosity of the surrounding medium.
194
-------
Curves of u> versus a exhibit minima such as that found by Pau-
thenier.
Experimental Results and Conclusions—
An aerosol made of shellac particles was entrained in an
electric field EO, and exposed to positive ions for varying
lengths of time. After charging, the particles were passed
through a parallel plate capacitor where the field E0 was main-
tained. The capacitor thus acted as a precipitator for these
particles. An experimental study was made using an electron mi-
croscope to study the particles' size as a function of the posi-
tion where they were precipitated on the capacitor/precipitator
plate.
As Pauthenier had seen earlier, the size spectrum of preci-
pitated particles is not single valued. At the beginning of the
deposit, one finds both large (a=0.5 ym) and small (a=0.05 ym)
particles and at the end, only very small (a=0.01 ym) particles.
In addition to parallel plate capacitors, cylindrical capa-
citors were also used for precipitating the shellac aerosol.
Essentially the same particle size spectrum was observed here
as was seen above. The principal difference was that initially
particles of all sizes were observed. At the end, only spheres
with a^O.Ol ym were seen. In the cylindrical capacitor, the
ionization current from the axial electrode produces flow
turbulence in the aerosol. Thus, one might expect some mixing
of particle sizes with this device.
It is observed that in equation (154), taking AI = Xg does
not give a high enough precipitation rate. However, by taking
Xi = /2 Xg, good agreement is found between theory and experi-
ment. The author therefore concludes that the correction to the
classical theory made here is sufficient to extend the theory to
submicron sized particle charging.
Comments and Remarks—
This paper is a combination of two earlier papers,2 6'2 7 by
the same author. The idea of extending the particle radius by
one mean free path in the field charging equation was first
suggested here, and does lead to better agreement with experi-
ment.
The experiments confirm the existence of a minimum in the
mobility of charged particles according to size as previously
observed by Pauthenier. For satisfactory agreement between
theory and experiment, the ionic mean free path is^treated as an
adjustable parameter. No justification is given for the value
finally used; i.e., X^ = /2 X.
195
SOUTHERN RESEARCH INSTITUTE
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APPENDIX B
LITERATURE REVIEW - PARTICLE CHARGING DATA
The literature was reviewed for information pertinent to
experimental charging studies. Four papers8'27 •l 7>z l contain ex-
perimental results and/or techniques which were of use in valida-
ting our experimental results. Table 7 summarizes the available
experimental data.
Cochet2 7 presents curves for the speed of precipitation
versus particle radius. Using the relationship between electri-
cal mobility and the speed of precipitation, it is possible to
obtain the electrical mobility as a function of particle size.
This was done and the results are plotted in Figure 86. Cochet
used a shellac aerosol having a dielectric constant of 3.2 (as
measured by Pauthenier. **)
Fuchs et al17 determined the charge on mineral oil droplets
as a function of their size for a given Nt and electric field
strength. Figures 87, 88, and 89 give his results. There is
a large amount of scatter in these data but the dearth of experi-
mental information with the charging conditions specified makes
these figures worth noting. Knudsen28 has observed that the
scatter in some early experimental data may be introduced by the
charging device used. This may also be the case here.
Hewitt8 has performed an exhaustive experimental charging
study, and the majority of the experimental information presented
in this section has been drawn from his paper. Figures 90
through 98 give the pertinent results. Figure 92 is not a
reproduction of any of Hewitt's graphs but is plotted so that
some of the results obtained by Hewitt may be compared with
other results from Penny and Lynch.21 Figure 98 does not strict-
ly pertain to aerosol particle charging but gives information on
the performance of Hewitt's Mobility Analyzer. Since the SRI
Mobility Analyzer is patterned after Hewitt's device, Hewitt's
data has been used for characterizing the performance of the SRI
Mobility Analyzer.
Penney and Lynch2l made a charging study which was contem-
porary with Hewitt. The same type of aerosol was used and there
is enough overlap in the data so that some comparisons can be
made. Figures 99 through 102 give these authors' results. Note
that both positive and negative corona charging has been used.
Figures 100 and 101 show the effect of changing the potential on
the corona wires while particle size and air flow are held
constant. Thus, the particle charge is found for a particular
value of E and Nt.
196
-------
TABLE 7. SUMMARY OF THE PUBLISHED EXPERIMENTAL DATA ON PARTICLE CHARGING
vo
o
c
X
pi
a
z
nr
81
PI
a
n
1
-i
H
PI
Author
Cochet
Fuohs et al
Hewitt
Hewitt
Hewitt
Hewitt
Hewitt
Hewitt
Hewitt
Hewitt
Hewitt
Penney & Lynch
Penney & Lynch
Penney i Lynch
Penney & Lynch
Aerosol
Shellac
K
3.2
Corona
Positive
d, diameter p, mobility
(ym)
-------
10
,-6
o
0>
0>
CM
_J
CO
o
UJ 10"
o
10"
.0 O
O E = 5.0xl05 V/m
Nt=8.0x I011 sec/m3
DE = l.5xl05 V/m
Nt = 3.2 xlO12 sec/m3
SHELLAC AEROSOL K^
0.0
0.2
1.2
1.4
0.4 0.6 0.8 1.0
PARTICLE DIAMETER,/im
Figure 86. Particle mobility as a function of diameter for shellac
aerosol particles charged in a positive ion field
(after Cochet and Trillat18). K is the dielectric
constant of the aerosol.
198
-------
CO
150
= 5.56xl04V/m
Nt = 3.27 xlO11 sec/m3
K=2.56
Figure 87.
Figure 88
2.0 3.0 4.0 5.0 6.0
PARTICLE DIAMETER.Mm
Charge per particle for a mineral oil aerosol charged
in a negative ion field (after Fuchs et al2). Nt =
3.27x10 x sec/m3. K is the aerosol dielectric con-
stant.
CO
= 7.32xl04v/m
Nt = 4.64 xlO11 sec/m3
K = 2.56
1.0 2.0 3.0 4.0 5.0
PARTICLE DIAMETER,ptm
Charge per particle for a mineral oil aerosol charged
in a negative ion field (after Fuchs et al2). Nt =
4.64x10 sec/m3. K is the aerosol dielectric con-
199
SOUTHERN RESEARCH INSTITUTE
-------
tn
E=9.40xl04 V/m
= 5.IOxlo" sec/m3
K=2.56
1.0 2.0 3.0 4.0
PARTICLE DIAMETER,
Figure 89. Charge per particle for a mineral oil aerosol charged
by negative ions (after Fuchs et al2). Nt = 5.10x10:
sec/m . K is the aerosol dielectric constant.
200
-------
l\J ~
o
tVI
E
d 10-7
m
o
PARTICLE
I0~8
0
1 1 1 •— 1 1
V
V o
v o o o o
o
V °°
0 D °
CD D D
0
^00 OOM6 000 4 0^00
VE = 1.08 xlO6 V/m
OE=7.2xl05 V/m
D E = 3.6 x IO5 V/m
OE= 6.0 xlO4 V/m
IMt= .OxIO13 sec/M3
— DIOCTYL PHTHALATE AEROSOL —
K=5.l
1 1 1 1 1 1
.0 0.2 0.4 0.6 0.8 1.0 1.2 l.<
PARTICLE DIAMETER, fim
Figure 90. Electrical mobility of dioctyl phthalate droplets as
a function of particle diameter (after Hewitt8). Pos-
itive corona charging.
constant.
K is the aerosol dielectric
201
SOUTHERN RESEARCH INSTITUTE
-------
4.0
ro
o
to
A PARTICLE DIAMETER = 1.20
• PARTICLE DIAMETER = 0.84
D PARTICLE DIAMETER =0.60
0 PARTICLE DIAMETER = 0.38 (im
• PARTICLE DIAMETER = 0.28 jim
O PARTICLE DIAMETER =0.14
= l.0xl0l3sec/m3
DIOCTYL PHTHALATE AERO
K = 5.
0.5
Figure 91.
2.0 4.0 6.0 8.0 10.0
CHARGING FIELD STRENGTH x IO"5 , V/m
Particle mobility as a function of charging field
strength for a dioctyl phthalate aerosol under posi-
tive corona charging (after Hewitt8). K is the
aerosol dielectric constant.
-------
103
102
m
c
>\
k.
o
s.
o>
LU
QC
O
LU
O
ID'
— O
— aa
a a
OE= 1.08 x !06V/m
AE= 3.60xl05V/m _
DE= 6.0 x I04 Vm
Nt=IOl3sec/m3
DIOCTYL PHTHALATE AEROSOL
K = 5.l -
0.4
0.8
1.2
PARTICLE DIAMETER
Figure 92. charge per particle as a function of particle diameter
for a dioctyl phthalate aerosol under positive corona
charging (after Hewitt8). K is the aerosol dielectric
constant.
203
SOUTHERN RESEARCH INSTITUTE
-------
35
30
tn
25
20
LU
e>
QC
s
o
LU
O
15
10
d = O.I8um
DIOCTYL PHTHALATE AEROSOL
POSITIVE CORONA CHARGING
£E=l.08xl06V/m
OE=3.6xl05 V/m
OE = 3.0xl04V/m
0.0
1.0
2.0
3.0
4.0
5.0
Nt
Figure 93.
Charge per particle as a function of ion density-resi-
dence time product, Nt in a positive corona (after
Hewitt ) for 0.18 pm diameter dioctyl phthalate parti-
cles. K is the aerosol dielectric constant.
204
-------
70
60
50
in
c
s.
Ill
< 30
5
Id
_1
O
I20
10
d = 0.28um
DIOCTYL PHTHALATE AEROSOL
POSITIVE CORONA CHARGING
0.0
D-
V/m
D E = 3.6 x I05 V/m
OE = 3.0xl04V/m
2.0 3.0 4.0
NtxlO~'3,sec/m3
5.0
6.0
Figure 94. Charge per particle as a function of ion density-resi-
dence time product, Nt in a positive corona for 0.28 ym
diameter dioctyl phthalate particles (after Hewitt8).
K is the aerosol dielectric constant.
205
SOUTHERN RESEARCH INSTITUTE
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60
50
10
>• 40
o
"c
o>
E
o>
o>
u
30
o
a
o 20
l-
cr
10
0.0
d=0.28um
DIOCTYL PHTHALATE AEROSOL
POSITIVE CORONA CHARGING
K =
O Nt = 5xlOl3sec/m3
ANt = 4xlOl3sec/m3
DNt = 3xlO|3sec/m3
Nt =2x I0|3sec/m3
2.0 4.0 6.0 8.0
CHARGING FIELD STRENGTH x!0~5,v/m
10.0
Figure 95.
Particle charge as a function of charging field
strength for 0.28 ym diameter dioctyl phthalate
particles (after Hewitt8). K is the aerosol dielec-
tric constant.
206
-------
d= 0.56 urn
= 3.6xl05 V/m
DIOCTYL PHTHALATE AEROSOL
POSITIVE CORONA CHARGING
K =
0.0 1.0 2.0 3.0 4.0
Nt x I0~l3,sec/m3
Figure 96. Particle charge as a function of ion density-residence
time product for 0.56 um diameter dioctyl phthalate
particles (after Hewitt8). K is the aerosol dielec-
tric constant.
207
SOUTHERN RESEARCH INSTITUTE
-------
350
300 —
CO
>>
k.
o
c
i
250 —
UJ
tr
o
UJ
o
QC
7 200
Figure 97.
DIOCTYL PHTHALATE
AEROSOL
POSITIVE CORONA CHARGING
0.0
2.0 3.0
NtxlO~l3,sec/m3
Particle charge as a function of ion density-residence
time product for 0.92 ym diameter dioctyl phthalate
aerosol particles (after Hewitt8). K is the aerosol
dielectric constant.
208
-------
= 3.6xl05V/m
DIOCTYL PHTHALATE AEROSOL
K=5.l
0.0
0.0
2.0 3.0 4.0
NtxlO~l3,sec/m3
5.0
6.0
Figure 98. The spread of the mobility analyzer response curve
for fixed values of Nt, particle size and charging
field strength (after Hewitt8).
209
SOUTHERN RESEARCH INSTITUTE
-------
I03
I
Si
iioz
<
o
o
fe
10
E = 2.3 x!05V/m
Nt=6.4xl013 sec/m3
DIOCTYL PHTHALATE AEROSOL
K = 5.l
1
0
0.2
0.4
0.6
Figure 99,
PARTICLE DIAMETER,
Particle charge as a function of particle diameter
for a dioctyl phthalate aerosol (after Penney and
Lynch7). K is the aerosol dielectric constant.
210
-------
60
50
40
c
a>
E
"5
ciT 30
(•>
a:
©MEASURED CHARGE
ANt
I
I
1.0 2.0 3.0 4.0
CHARGING FIELD STRENGTH x IO"5,V/m
10.0
8.0 IE
x
u
-------
40
35
30
3
§ 25
E
—
<0
UJ
cc
X
o
a
o
h-
oc
20
15
10
DIOCTYL PHTHALATE AEROSOL
SCREEN CHARGER NEGATIVE
CORONA
K = 5.l
O MEASURED CHARGE
ANt
I
0.0 1.0 2.0 3.0 4.0 5.0
CHARGING FIELD STRENGTH x 10~5,V/m
5.0
4.0 e
o
m
ro"
3.0 b
2.0
6.0
1.0
Figure 101.
Particle charge as a function of charging field
strength and ion density-time product for a 0.30 jim
diameter dioctyl phthalate aerosol in a negative ion
field (after Penney and Lynch7). K is the aerosol
dielectric constant.
212
-------
60
55
2. 50
c
3
O
Si
* 45
•• to
LU
O
o:
<
5
3
H 40
cc
35
30 —
d = 0.30jum
E = 2.7xl05V/m
DIOCTYL PHTHALATE AEROSOL
K=5.l
A NEGATIVE CORONA
O POSITIVE CORONA
4.0
6.0 8.0 10.0
NtxIO"13 ,sec
12.0
14.0
Figure 102.
Comparison of particle charging for negative and posi-
tive corona acting on 0.30 ym diameter dioctyl
phthalate particles (after Penney and Lynch7). K is
the aerosol dielectric constant.
213
SOUTHERN RESEARCH INSTITUTE
-------
Figures 101 and 102 for a field strength of 2.7 x 105 V/ra and
positive corona charging, allow one to compare, with some extra-
polation, the charges acquired for different Nt values for DOP
droplets of approximately the same size. Table 8 shows that the
agreement between Hewitt, Penney and Lynch over a range of Nt
values is quite good.
214
-------
o
c
X
m
31
Z
m
a
o
(0
-i
«p*
-i
c
TABLE 8. COMPARISON OF EXPERIMENTAL DATA
Number of Elementary Charges as a Function of Nt
to
Nt
(sec/m3)
2
3
4
5
x 1013
x 1013
x 10 13
13
Hewitt8
(d=0.28 ym)
25.5 elementary charge units
27.0
28.5
29.5
x 10
OOP Aerosol, E = 2.7 x 105 V/mf positive corona charging
Penney & Lynch22
(d=0.30 ym)
25.0 elementary charge units
27.2
29.5
31.5
-------
APPENDIX C
PARTICLE CHARGING PROGRAMS FOR PORTABLE CALCULATORS
An approximate calculation of the total charge accumulated by
an aerosol particle of radius a in an electric field E, where
there exists a unipolar ion density N, may be derived from the
sum of diffusion charging and field charging effects:
where
np = (np)field + (np} cliff
(n ) = 47r£oa2E Fl
1V field e L
: + to
and
,ae*vNt
f« <» - ,
{V ciiff = —-r~ ln
w
In these expressions
t = particle residence time (sec),
to = 4eo/Ney,
k = particle dielectric constant,
e = electron charge (coul),
EO = permittivity of free space (fd/m),
y = ion mobility (m2/V'sec),
T = temperature (°K),
K = Boltzmann's constant (j/°K), and
v = mean thermal ion speed (m/sec).
The sum of (np)field and (np)diff may therefore be written
n = iraCi
(155)
*. »----•—* »»-~. X^^N^^J. |
where
Ci =
and
4£o
c,-f
216
-------
Texas inten Hewlett-**ckard model HP-65 and the
included in^his Ar^enJ- I Programmable pocket calculators are
a calculation lor nP? ES°h °f these P*°<3*™s will carry out
a calculation for np in accordance with the above expression!
HP-65 Program
User Instructions
STEP
1
2
3
4
5
6
7
8
9
10
1 ex
2 ex
3 ex
4 ex
INSTRUCTIONS
Clear programs (W/PRGM mode)
Enter card (RUN mode)
Enter particle diameter
Enter Nt product
Enter average electric field
Enter temperature
Enter relative dielectric
constant, particle
i Enter ion mean thermal speed
1 Press A
Read particle charge
To rerun for different chargin
i conditions it is neees.Qarv to
enter in the appropriate regi-
sters only the oharg^ para-
meters, and then press key A,
as in the following example
j where only the particle dia-
KA-t-Av r=»v»/3 4- Vn=» ^•£*mriAY*9 +-n *»^ 2aT~o
iQ U-Sja- CmO ^Il-fei — TgfcgltiJLL/fcS J- Cl Li U.X. O CiJ. C5
; changed:
! Enter new particle diameter
Enter new temperature
Press A
Read charge
INPUT
DATA/UNITS
Urn
sec/m3
V/m
°K
m/sec
np
g
ym
°K
KEYS
1 f 1
PRGM
STO || 1
STO
2
STO H 3
STO || 4
STO || 5
STO || 6
A
II
I
I
| STO || 1
STO
4
A
OUTPUT
DATA/UNITS
electroni
charges
'
electroni
charaes
217
SOUTHERN RESEARCH INSTITUTE
-------
Example
Store the following parameters as indicated in the instruc-
tions :
d = 2a = 1.0 ym
Nt = 1.0 x 1013 sec/m3
E = 6.0 x 10" V/m
T = 295 K
k = 5.0
v = 500 m/sec
Initiate program, key A to find np = 74.5 elementary charges
Program Listing
CODE
23
II
34 01
05
43
42
07
71
33 01
34 06
71
34 02
71
34 04
81
01
09
00
05
02
33 07
81
01
61
31
07
34 04
71
KEYS
LBL
A
RCL 1
5
EEX
CHS
7
x
STO 1
RCL 6
x
RCL 2
x
RCL 4
•*
1
9
0
5
2
STO 7
-5"
1
+
f
In
RCL 4
x
CODE
34 07
71
33 07
03
05
07
01
34 02
81
04
83
05
02
03
43
42
09
61
35
04
34 03
71
34 01
71
33 08
34 05
01
KEYS
RCL 7
x
STO 7
3
5
7
1
RCL 2
•%•
4
m
5
2
3
EEX
CHS
9
+
g
1/x
RCL 3
x
RCL 1
x
STO 8
RCL 5
1
CODE
] 51
34 05
02
61
81
02
71
01
61
34 08
71
34 07
61
35
02
71
34 01
71
33 07
34 01
02
43
06
71
33 01
34 07
24
KEYS
-
RCL5
2
+
•s-
2
x
1
+
RCL8
x
RCL7
+
g
7T
X
RCL 1
x
ST07
RCL 1
2
EEX
6
x
STO 1
RCL 7
RTN
R1
R2
R3
d
Nt
E
R4
R5
R6
T
k
V
R7
R8
R9
218
-------
SR-52 Program
Two different programming formats are in general use in
T3CaiCUlators* The "reverse polish" format, employed in
i ^-Packard systems, was used in the above development. A
calculation for np, based on Equation 155 is presented on the
following pages in the algebraic format used in the Texas Instru-
ments SR-52 calculator.
User Instructions
STEP
1
2
3
4
5
6
7
8
Store particle diameter
Store Nt
Store electric field
strength
Store Temperature
Store ion speed
Store dielectric constant
Store ion mobility
Calculate particle charge
For new parameters, repeat
only those steps of 1
through 7 for which a
change is required, then
go to step 8 .
INTER
d,ym
Nt,sec/m3
E,V/m
T,°K
v,m/sec
K
y ,m2/Vsec
PRESS
A
B
C
D
E
2nd
2nd
2nd
A
B
C
DISPLAY
d,ym
Nt, sec/m8
E,V/m
T,°K
v,m/sec
K
y,m2/Vsec
nP
The previously mentioned example may be used to test this
program. A complete program listing follows:
SOUTHERN RESEARCH INSTITUTE
219
-------
LOG
000
005
010
015
020
025
030
CODE
46
18
43
00
01
55
02
52
06
95
42
00
08
65
59
65
02
93
02
02
04
52
08
42
00
09
65
53
19
85
10
54
95
KEY
LBL
C'
RCL
0
1
•*-
2
EE
6
=
STO
0
8
X
7T
X
2
•
2
2
4
EE
8
STO
0
9
X
(
D'
+
E'
)
=
LOG
035
040
045
050
055
060
065
CODE
81
46
19
53
53
53
43
00
07
65
43
00
08
65
43
00
02
65
43
00
03
54
55
53
53
43
00
07
65
43
00
02
85
KEY
HLT
LBL
D'
(
(
(
RCL
0
7
X
RCL
0
8
X
RCL
0
2
X
RCL
0
3
)
•*•
(
(
RCL
0
7
X
RCL
0
2
+
(continued)
220
-------
LOC
070
075
080
085
090
095
CODE
43
00
09
54
54
54
65
53
01
85
02
65
53
53
43
00
06
75
01
54
55
53
43
00
06
85
02
54
54
54
54
56
46
KEY
RCL
0
9
)
)
)
X
(
1
+
2
X
(
(
RCL
0
6
_
1
)
^P
(
RCL
0
6
+
2
)
)
)
)
RTN
LBL
LOC
100
105
110
115
120
125
130
CODE
10
53
08
93
06
07
01
52
94
05
42
01
00
65
43
00
04
65
53
53
43
00
08
65
43
00
05
65
43
00
02
55
53
KEY
E'
(
8
•
6
7
1
EE
+/-
5
STO
1
0
X
RCL
0
4
X
( ;
(
RCL
0
8
X
RCL
0
5
X
RCL
0
2
-s-
(
(continued)
SOUTHERN RESEARCH INSTITUTE
221
-------
LOG
135:
140
145
150
155
160
CODE
43
00
09
65
43
01
00
65
43
00
04
54
54
85
01
54
23
54
56
46
11
42
00
01
56
46
12
42
00
02
56
46
13
KEY
RCL
0
9
X
RCL
1
0
X
RCL
0
4
)
)
+
1
)
In
)
RTN
LBL
A
STO
0
1
RTN
LBL
B
STO
0
2
RTN
LBL
C
LOG
165
170
175
180
185
190
CODE
42
00
03
56
46
14
42
00
04
56
46
15
42
00
05
56
46
16
42
00
06
56
46
17
42
00
07
56
KEY
STO
0
3
RTN
LBL
D
STO
0
4
RTN
LBL
E
STO
0
5
RTN
LBL
A'
STO
0
6
RTN
LBL
B'
STO
0
7
RTN
Comparison With Other Particle Charging Calculations
The calculator program results, derived from Equation
provide a good approximation, in most cases, to the computer
results obtained from the more complete charging theory described
in Section 3 of this report. In Figure 103 there is presented a
set of curves representing simple diffusion charging theory,
simple field charging, the sum of diffusion and field charging
(Equation 155), and the S.R.I theory, all calculated from the
same charging data.
222
-------
= 6.0xi04 V/m
Nt=l.0xi013 sec/m3
DIFFUSION CHARGING
FIELD CHARGING
S.R.I. THEORY
CALCULATOR PROGRAM
0.2 0.4 0.6 0.8 1.0
PARTICLE DIAMETER,
1.2
1.4
Figure 103. Average charge per particle as a function of
particle diameter. The curve derived from the
calculator program is the simple sum of the
field charging and diffusion charging results.
223
SOUTHERN RESEARCH INSTITUTE
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/2-77-173
2.
4. TITLE AND SUBTITLE
Fine Particle Charging Development
7. AUTHOR(S)
D.H. Pontius, L. G. Felix,
W.B. Smith
J.R. McDonald, and
9. PiRFORMING ORGANIZATION NAME AND ADDRESS
Southern Research Institute
2000 Ninth Avenue, South
Birmingham, Alabama 35205
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
3. RECIPIENT'S ACCESSION-NO.
5. REPORT DATE
August 1977
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
SORI-EAS-77-039
Project No. 3345F
10. PROGRAM ELEMENT NO.
1AB012; ROAP 21ADL-036
11. CONTRACT/GRANT NO.
68-02-1490
13. TYPE OF REPORT AND PERIOD COVERED
Final; '7/74-2/77
14. SPONSORING AGENCY CODE
EPA/600/13
15. SUPPLEMENTARY NOTES IERL-RTP project officer for this report is Leslie
Mail Drop 61, 919/541-2925.
E. Sparks,
ie. ABSTRACT ^g repOrt gives results of theoretical and experimental investigations into
the charging of fine particles by unipolar ions in an electric field, and evaluation of a
specially designed small pilot-scale (600-1000 acfm) precharging device. Following
an extensive review of the literature, a new theory was developed, predicting statis-
tically the average charge per particle in a large collection of particles. The electri-
cal mobility of particles charged under controlled conditions of ion density, charging
time, electric field strength, and ion polarity was measured to determine the
average charge per particle for comparison with the theory. Agreement between
experimental results and theory was generally within 20%. The precharger evaluation,
based on direct particle charge measurements and the effects on performance of a
pilot-scale electrostatic precipitator of conventional design located downstream from
the precharger, indicated that effective particle charging was achieved in accordance
with the theoretical predictions. Particle migration velocities in the precipitator,
with the precharger on, were up to 60% greater than with the precharger off.
,1
17.
a. DESCRIPTORS
Air Pollution
Dust
Electrostatics
Charged Particles
Charging
Electrostatic Precipitators
13. DISTRIBUTION STATEMENT
Unlimited
KEY WORDS AND DOCUMENT ANALYSIS
b.lOENTIFIERS/OPEN ENDED TERMS
Air Pollution Control
Stationary Sources
Particulate
Particle Charging
Precharging
Unipolar Ions
19. SECURITY CLASS (This Report)'
Unclassified
20. SECURITY CLASS (This page)
Unclassified
EPA Form 2220-1 (9-73)
c. COS ATI Field/Group
13B
11G
20C
20H
21. NO. OF PAGES
240
22. PRICE
224
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