EPA-650/2-74-075
August 1974
Environmental Protection Technology Series
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EPA-650/2-74-075
CHARGED DROPLET SCRUBBING
OF SUBMICRON PARTICULATE
by
J. R. Melcher and K. S. Sachar
Massachusetts Institute of Technology
Department of Electrical Engineering
Cambridge, Massachusetts 02139
Contract No. 68-02-0250
ROAP No. 21ADL-003
Program Element No. 1AB012
EPA Project Officer: B.C. Drehmel
Control Systems Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
August 1974
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This report has been reviewed by the Environmental Protection Agency
and approved for publication. Approval does ntft signify that the
contents necessarily reflect the views and policies of the Agency,
nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
ii
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ABSTRACT
The report gives results of an investigation of the collection of charged
submicron particles, through a sequence of interrelated experiments and
theoretical models; by oppositely charged supermicron drops; by bicharged drops;
and by drops charged to the same polarity as the particles. It provides
experimentally verified laws of collection for a system with different
effective drop and gas residence times. The report shows, experimentally and
through theoretical models, that all three of the above configurations have
the same collection characteristics. Charging of the drops in any of these
cases: results in dramatically improved efficiency, compared to inertial
scrubbers; and approaches the efficiency of high-efficiency electrostatic
precipitators. For example, in experiments typical of each configuration,
inertial scrubbing by 50 pm water drops of 0.6 Vim DOP aerosol particles gives
25% efficiency; self-precipitation of the particles with charging (but without
charging of the drops) results in 85-87% efficiency; and drop and particle
charging (regardless of configuration) results in 92-95% efficiency. Charged-
drop scrubbers and precipitators have the operating costs and capital investment
profiles of wet scrubbers, and submicron particle removal efficiencies
approaching those of high-efficiency electrostatic precipitators.
iii
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TABLE OF CONTENTS
Abstract ill
Table of Contents iv
Figures vlli
Tables xvi
Acknowledgement xvii
Conclusions i
Recommendations 4
1 Introduction g
1.1 Submicron Particulate as an Environmental Control Problem g
1.2 Incentives for Developing Charged Droplet Scrubbers 7
1.3 Scope and Objectives IQ
2 Conventional and Charged-Drop Submicron Particle Control in
Perspective 13
2.1 Residence Time as a Basis for Comparisons 13
2.2 The Inertial Impact Wet Scrubber 14
2.3 The Electrostatic Precipitator 19
2.4 Hierarchy of Characteristic Times for Systems of Charged
Particles and Drops 23
2.5 Classification and Comparison of Basic Collection
Configurations 32
3 Survey of Devices and Studies 45
3.1 Charged Drop Control Systems 45
3.2 Patents 50
3.3 Literature 57
4 Electrically Induced Self-Precipitation and Self-Discharge 64
iv
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4.1 Objectives 64
4.2 Theory of Self-Precipitation Systems 65
4.2.1 General Equations 65
4.2.2 Laminar Flow Systems 68
4.2.3 Turbulent Flow Systems 72
4.3 Analysis of Self-Discharge Systems (SAG) 74
4.3.1 Mechanisms for Self-Discharge 74
4.3.2 Self-Discharge Dynamics 80
4.4 Generation of Monodlsperse Submicron Aerosols 84
4.4.1 Classification of Techniques 84
4.4.2 Liu-Whitby Generator 85
4.5.1 Light Scattering by Small Particles 89
4.5.2 Higher Order Tyndall Spectra 91
4.5.3 90° Scattering Ratio 94
4.5.4 Extinction 96
4.6 Ionic Charging of Submicron Aerosols 100
4.6.1 Diffusion and Impact Charging 100
4.6.2 Higi Efficiency Charger for Submicron Aerosols 102
4.7 Analysis of Submicron Aerosols for Charge Density and
Mobility 105
4.7.1 Imposed Field Analyzers 105
4.7.2 Space-Charge Effects 109
4.8 Self-Precipitation Experiments (SCP) 113
4.8.1 Laminar Flow Experiment 113
4.8.2 Turbulent Flow Experiment 116
4.9 Self-Discharge Experiments (SAG) 117
Electrically Induced Self-Discharge and Self-Precipitation of
Supermicron Drops 124
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5.1 Objectives 124
5.2 Self-Precipitation in Systems of Unipolar Drops 125
5.2.1 Mechanisms for Deposition 125
5.2.2 Self-Precipitation Model for a Channel Flow 129
5.3 Analysis of Self-Discharge Systems 131
5.3.1 Mechanisms for Discharge 131
5.3.2 Self-Discharge Model for a Turbulent (Slug-Flow)
Channel Flow 139
5.4 Techniques for Generation of Charged Drops 141
5.4.1 Fundamental Limits on Charging and Polarization of
Isolated Drops 142
5.4.2 Pressure Nozzles and Orifice Plate Generators
With Charge Induction 144
5.4.3 Pneumatic Atomization With Induction Charging 149
5.4.4 Ion-Impact Charging 153
5.5 Charged Drop Self-Precipitation Experiments 156
5.5.1 Experimental System 158
5.5.2 Drop Velocity Measurements 158
5.5.3 Measurements of Self-Precipitation of Charged Drops 165
5.6 Experimental Investigation of Self-Discharge of
Bicharged Drops 170
5.6.1 Experimental Apparatus 172
5.6.2 Measurement of Drop Velocity 172
5.6.3 Drop Discharge Process 175
Scrubbing and Precipitation of Charged Submicron Aerosols by
Charged Supermicron Drops 178
6.1 Objectives 178
6.2 Models for Particle Collection on Isolated Drops 179
vi
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6.2.1 Laminar Theory of Whipple and Chalmers 179
6.2.2 Collection With Complete Turbulent Mixing 193
6.3 Multipass System 198
6.4 Model for Scrubbing With Unipolar Drops and Particles
of Opposite Sign (CDS-I) 201
6.5 Model for Scrubbing With Bicharged Drops and Charged
Particles (CDS-II) 207
6.6 Model for Precipitation by Unipolar Drops and Particles
of the Same Polarity (CDP) 209
6.7 Experiments With Unipolar Drops and Particles of
Opposite Sign 210
6.7.1 Experimental System 210
6.7.2 Experimental Diagnostics 211
6.7.3 Scrubbing Efficiency 214
6.8 Experiments With Bicharged Drops and Charged Particles 215
6.9 Experiments With Unipolar Drops and Particles of the
Same Polarity 217
6.10 Summary of Measured Efficiencies 217
7 Summary
7.1 State of Fundamentals 221
7.2 Charged Drop Devices Compared to Conventional Devices 222
7.3 Practical Application 225
7.4 Summary of Calculations Estimating CDS-I, CDS-II and
CDP Performance 227
References 229
Glossary of Symbols 234
vii
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FIGURES
No. Page
2.2.1 Inertial impact scrubbing viewed from drop frame of
reference. Gas entrained particles approaching the
2
drop within the cross-section Try impact the drop. 15
2.3.1 A conventional (imposed-field) electrostatic
precipitator configurations, a) plane parallel
geometry b) generalized geometry 21
2.A.I Two-"particle" model for electrical discharge
and possible agglomeration due to micro-fields 26
2.4.2 Limits of collection time for two particle model
that give the three time constants when these are
interpreted as self-discharge and drop-particle
agglomeration times. 28
2.4.3 Simple model used to illustrate roles of T and TD
a K
as self-precipitation times for like-charged
particles and like-charged drops respectively 29
2.5.1 Collection particles polarized by means of ambient
electric field imposed by means of external electrodes. 43
3.1 Overall charged drop scrubbing system 48
4.2.1 Self-precipitation in a cylindrical channel with
radius 0.95cm carrying a flow with F « 1.08 x
10~4m3/sec. 71
viii
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4.2.2 Comparison of typical decay laws for self-precipitation
and "imposed"field types of devices. 72
4.3.1 Self-discharge model consisting of a pair of
oppositely charged particles. 75
4.4.1 Monodispersed aerosol generating system (Liu,
Whitby and Yu, 1966). 86
4.4.2 Collision atomizer (Liu, Whitby and Yu, 1966) 87
4.4.3 Calibration curve showing the variation of the
number median diameter of the aerosol with the
volumetric concentration of DOP in the atomizer. 88
4.5.1 Light scattering from a single sphere. 90
4.5.2 Tyndall red angular positions for DOP. Each point
is numerically calculated. Circled points indicate
a peak, but for which the ratio of red to green is
less than unity. 92
4.5.3 Tyndall spectra observation device ("Owl"). 93
4.5.4. 90° scattering ratio for DOP. 95
4.5.5 90° scattering apparatus 97
4.5.6 Extinction coefficient for DOP spheres as a function
of oi£. 98
4.5.7 Light extinction system for a divergent light source 99
4.5.8 Light extinction system for a laser light source and
a detector aperture determined by cell dimensions. 101
ix
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4.6.1 Aerosol charger showing alternative resistors for
positive and negative charging. 104
4.7.1 Analyzer configurations (a) plane flow with multiple
parallel electrodes (b) radial flow with air In-
jection to prevent leakage current. 107
4.7.2 Ideal imposed-field analyzer volt-ampere characteristic
for either of configurations in Fig. 4.7.1. 108
4.7.3 Typical analyzer V-I characteristic determined using
the radial flow air injection configuration of Fig.
4.7.1b. F » 1.08 x 10 m /sec. Hence from data
b - 1.45 x 10~7m/sec/V/m, nq - 4.63 x 10~5coul/m3. 110
4.7.4 Self-precipitation for a radial flow: comparison of
exact solution for Poiseuille flow with one from slug
model. 112
4.8.1 Laminar flow self-precipitation experiment.
Aerosol generator, charger and analyzer respectively
described in Sees. 4.4, 4.6 and 4.7. 114
4.8.2 Self-precipitation of aerosol from experiment of Fig.
4.8.1. Broken curve is based on slug flow model, Eq.
(4.2.12), while solid curve is result of theory including
effect of parabolic velocity profile (Sec. 4.2). 115
4.8.3 Self-precipitation experiment with mixing. Aerosol
generator, charger and analyzer respectively described
in Sees. 4.4, 4.6 and 4.7. 116
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4.8.4 Self-precipitation with mixing. Solid curve is
predicted by Eq. (4.2.20). Data points are
experiments performed using three different
flasks having different volumes V so that
residence time T is varied while holding T fixed. 118
res a
4.9.1 Charged aerosol experimental system 119
4.9.2 Analyzer curves for self-discharge experiments with
-4 3
bicharged aerosols F « 1.1 x 10 m /sec... 120
4.9.3 Experimental self-discharge of bicharged aerosol
in laminar flow as a function of distance down the duct.
Solid curve is theory based on Eq. (4.3.22) with the initial
condition found by extrpolation back from the first data
point. Inset defines analyzer currents. 121
5.3.1 Geometry for two-particle model of discharge process
between two drops. 135
5.3.2 Maximum discharge velocity occurring at instant of
impact. 137
5.3.3 Normalized discharge time T... 140
5.4.1 Cross-sectional view of acoustically excited pressure
nozzle with induction type charging electrodes. 144
5.4.2 Growth rates of instabilities on convecting liquid
streams. 145
5.4.3 Coefficient of discharge for a circular orifice as a
function of Reynolds number. 147
xi
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5.4.4 Geometry of Inducer bar relative to one of the two
sheets of drops. 150
5.4.5 Drops charge and mobility as a function of Inducer bar
-14
voltage. V_ - v - v, , Q in units of 10 coul, B In
Dab
units of 10~6m/sec/V/m. 151
5.4.6 Pneumatic nozzles with induction chargers (a) commercial
nozzle with inducer electrode added (b) multi-nozzle
unit with built in chargers. 152
5.4.7 Current carried by drops generated using 60Hz inducer
voltage. Solid curve is multi-nozzle unit with 40 psi
air pressure while broken line is single commercial
nozzle. 154
5.5.1 Jet of 50ym diameter drops ejected into open volume
between plane parallel electrodes with 10cm spacing.
Residence time for a drop in 40cm length of system is
_2
about 5 x 10 sec. 157
5.5.2 Schematic of experimental system used to study dynamics
of unipolar drops and CDS-I, CDS-II and CDP collection
of aerosol. All dimensions in cm.
5.5.3 Current probe used to measure unipolar drop current
impinging from above. 161
5.5.4 Delay time as a function of distance downstream of
charging bars. 161
5.5.5 Positions 90* out of phase with voltage applied to
charging bars for f - 20Hz and the implied velocities. 162
xii
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5.5.6 Spatial decay of probe current normalized to value
at z - z « llcm, where z is the position of the
probe relative to charging bars. 167
5.5.7 Decay of current to probe normalized to value
zr - 16cm downstream of charging bars, beyond which
drop velocity is constant (4m/sec). Downstream
position z is normalized to decay length appropriate to
particular charging voltage. Note that as voltage is
raised decay rate approaches that predicted by theory
assuming dominance of electric self-precipitation. 169
5.5.8 Measured drop-probe current as function of V (which
is proportional to the drop charge Q) at four
different positions z from charging bars. 171
5.6.1 Bicharged drop stream with variable position
analyzer to deflect drops that remain charged at a
given position z. Dimensions in cm. 173
5.6.2 Bicharged drop jet in configuration of Fig. 5.6.1.
Note increase in discharged drops as analyzer field
is imposed increasingly further downstream. 174
6.2.1 Spherical conducting drop in imposed electric field
£ and relative flow w that are uniform at infinity.
o o
EQ and WQ are positive if directed as shown; in general,
the electric field intensity E can be either positive
or negative. 180
xiii
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6.2.2 Positive particle charging diagram. 185
6.2.3 Negative particle charging diagram. 186
6.2.4 Force lines in detail for regimes (e) for the
positive ions and (h) for the negative ions.
Here, all of the force lines terminating on the
particle, also originate on the particle; hence,
there is no charging. For the case shown,
w - ±2bE , Q - ±Q /2. 192
o o c
6.2.5 Regimes (h) for the positive ion and (e) for the
negative. Some of the force*lines extend to where
the charge enters, w - ±2b.E , Q - ±Q /2. 194
o ± o c
6.2.6 Charging trajectories for a drop having total charge
Q in an ambient field E as it collects positive and
o
negative particles with complete mixing... 197
t
6.3.1 Schematic cross-sectional view of cleaning volume.
Drops are injected at top to form turbulent jet that
drives gas downward in the central interaction region.
Drops are removed by impaction at the bottom, while the
baffles provide a controlled recirculation of gas and
particles. 200
6.7.1 Drop-particle interaction experiment showing system for
controlled generation of charged particles and measure-
ment of esential parameters. 211
6.7.2 Calculated and measured collection of positively charged
aerosol particles upon negatively charged drops as a function
• of drop charging voltage. 214
xiv
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6.8.1 For bi-charged drops, calculated and measured
efficiencies for collection of positively
charged aerosol particles. 216
6.9.1 Theoretical and measured particle collection for
drop-precipitation of positively charged aerosol
particles by positively charged drops as a function
of drop charging voltage. 218
6.10.1 Stages of concentration attenuation through system
as a whole. 220
XV
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TABLES
No. Page
2.4.1 Summary of times characterizing systems of charged
drops and particles. 24
2.5.1 Summary of basic configurations for collecting sub-
micron particles. Characteristic times T ,T ,T_ are
cl C Jx
summarized in Table 2.4.1 33
3.2.1 Summary of patents relating directly to electrically-
induced collection of particles on drops... 51-53
3.2.2 Certain patents relating to the use of electrically
induced agglomeration in the control of particle
pollutants. 55-56
5.4.1 Rayleigh's limiting chargeQ , Taylor's limiting
electric field intensity £__„ and the saturation
lay
charge as a function of drop radius R. 143
5.6.1 Typical drop velocity as a function of z as measured
by observing phase of traveling charge wave. 175
6.10.1 Efficiency of system as a whole. 219
7.2.1 Estimates of average parameters in Pilat's CDS- I
experiments. 223
xvi
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Acknowledgements
Our initial interest in the use of charged collection sites in the
control of submicron particles resulted from discussions with Bob
Lorentz of the Environmental Protection Agency in 1970. Three related
programs, sponsored by EPA, have contributed to what is summarized in the
following chapters. The first, on self-agglomeration processes in oil ash,
and the second, a general study of the charged drop approach to collecting
particulate, led to a third, which is the development of models and experiments
for the charged drop family of devices, for which this is a final report.
This most recent project has been overseen by Dennis Drehmel on behalf
of EPA, and for his active participation, encouragement and patience, we are
indebted. Contributions to the laboratory tests were made by Messrs.
E. Paul Warren and Karim Zahedl. Portions of the work constituted a Ph.D. Thesis
for one of the authors (K.S.S.) in the Department of Electrical Engineering at
M.I.T. Members of his committee were Ain A. Sonin and David H. Staelin.
Valuable conversations with M.J. Pilat and L.E. Sparks helped to mature
our thinking on the relative merits of charged drop scrubbers.
xvii
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CONCLUSIONS
Although primarily concerned with systems in which charged droplets are
used to promote the collection of submicron charged particles, because they
are inherent to these systems and to place matters in perspective, this report
also considers collection processes based on the charging of the particulate
alone. Collection mechanisms considered are space charge precipitation (SCP)
(where the electric precipitation field is generated by the particles to be
collected), self-agglomeration (SAG) (where oppositely charged particles are
induced to agglomerate by an electrical force of attraction), charged-droplet
scrubbers (CDS-I) (where drops charged to one polarity collect particulate
charged to the opposite polarity), charged droplet scrubbers (CDS-II) (where
bi-charged drops collect oppositely charged particulate) and charged drop
precipitators (CDP) where the fields generated by charged drops are used to
precipitate particles charged to the same polarity as the drops.
Experiments and correlated theoretical models support the contentions that:
(1) Both SCP and SAG interactions among submicron particles (0.6ym) are
—12
governed by the characteristic time T - e /nqb (e - 8.854 x 10 farads/m)
For SCP interactions, n,q, and b are respectively the particle number
density, charge and raoblity (in MRS units). For SAG, these quantities
are based on one or the other of the two families of charged particles.
(2) Unipolar drops self-precipitate with the characteristic time TR -e /NQB.
Here N is the droplet number density, Q is the droplet charge and B is
the droplet mobility. Hence, this time characterizes the effective life-
time of a drop in the CDS-I configuration.
(3) Bi-charged drops tend to self-discharge in the characteristic time T0,
R
where N,Q and B are based on one or the other of the drop families. Hence,
this time characterizes the effective lifetime of drops in the CDS-II system.
1
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(4) A simple model for the electrically induced collection of submicron
particles on charged drops, based on complete mixing in the air surrounding
the drops, appears to give a meaningful estimate of the collection process.
This model is consistent with the notion that TC - eQ/NQb characterizes
the time required for removal of charged particles by charged drops.
(5) In terms of residence time required for achieving a given efficiency,
systems based on the CDS-I, CDS-II and CDP interactions have essentially
the same performance characteristics. Of course, in the CDP interactions,
the particles immediately agglomerate with the drops while in the CDS
interaction, the particles are precipitated on the walls. However,
because the drops are also precipitated on the walls in either the CDS-I
or CDP interactions, the entrainment of the particles in the liquid is
the end result in either of these cases.
(6) Because of the dominant role of self-discharge and self-precipitation of
the drops in the CDS-I, CDS-II and CDP interactions, there is an
optimum droplet charge for achieving the best efficiency. This charge
is given by QQ * [2ATrr)Re0(U/AyN(0)]1/2 where n is the gas viscosity,
R is the droplet radius, (U/A) is the droplet residence time in the
absence of charging and N(0) is the inlet droplet number density. This
optimum would be somewhat increased by effects of droplet inertia
which come into play for drops exceeding about 100pm diameter.
It is evident from both the theoretical models and experimental results
that regardless of which of the three types of interactions is used in the
submicron range, charging of drops and particulate (CDS-I, CDS-II and CDP)
dramatically improve the performance relative to that of an inertial scrubber.
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That it makes little difference whether the drops and particles have opposite
signs, the same signs or there is a mixture of both positive and negative
drops, points to the fact that the charged droplet devices are more nearly
typified as being precipitators than as being scrubbers. This is most obvious
for the charged droplet precipitator (CDP) which is essentially an electrostatic
precipitator with half of the electrodes replaced by the mobile drops. Thus
it is clear that, in terms of residence time required for gas cleaning, the
charged drop devices are not likely to outperform the electrostatic precipitator.
They are in fact similar in nature to the wet-wall precipitator. By contrast
with these wet-wall precipitators, however, they are akin to the wet-
scrubber in terms of capital investment and operating cost. For this reason
the charged drop devices are most viable in applications where wet-scrubbers
are attractive. If a wet-scrubber is marginally competitive because it lacks
desired performance in the submicron range, the use of charged drops in the
CDS-I, CDS-II or CDP configurations is highly attractive.
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RECOMMENDATIONS
Further development of the charged droplet system is recommended provided
that it is recognized that such an effort is justified only because of operational
advantages of using a scrubber-like system instead of an ESP. Whether the
configuration is CDS-I, CDS-II or CDP, the residence time for removal of
submicron particulate at best only approaches that of the wet-wall ESP. But,
in those applications where improved wet-scrubber performance in the submicron
range is required, the use of charged drops and particulate appears warranted.
The following are specific issues that should be faced by future work.
1) Because practical systems will incorporate drops and particles having
very different residence times, and because the drops interact with the
gas as a turbulent jet, the modeling of the large scale drop-gas mixing
is necessary to further refinement of the performance model. In the CDS-I
and CDP configurations, the interaction is further complicated by
electrohydrodynamic contributions to the mechanics.
2) Prediction of the performance taking into account polydispersity of
particulate is necessary if the models are to be seriously used in
predicting performance in some practical applications. Developments
of the model in this regard could follow the same lines as being presently
used in connection with ESP's by Nichols of the Southern Research Institute.
3) This work suggests that a "complete" mixing model for the particulate
collection at the inter-drop scale is meaningful. Although perhaps not
a first priority in the development of charged drop scrubbers, it is
important that at some point the true nature of the drop-particle interaction
especially when collection is dominated by the electrical forces, be
studied in a fundamental way. Clearly, models that represent that
collection process In the CDS configurations as involving a laminar
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particle trajectory are not consistent with what is actually taking
place in a practical system.
4) The experimental tests reported here indicate that although the
self-discharge of drops in the CDS-II configuration does take place with
a typical characteristic time T_, the observed decay is several times
slower than expected. The implication of this finding is that the CDS-II
system may have merits over the CDS-I system, where the loss of drops
by self-precipitation is at the rate expected and characterized by T.,.
K
Of the three charged drop configurations, the CDS-II is the most poorly
understood apparently because of some shortcomings in the self-discharge
model. For these reasons, the model for self-discharge of bi-charged
systems of drops deserves further scrutiny.
With the objective of greatly improving on the residence time of an
ESP required for collection of submicron particulate, it is clear from this
study that the most promising avenue for further development is in the
direction of using EPB's or EFB's. For industrial applications, where large
amounts of material must be extracted from the gas, the EFB appears
preferable to the EPB because of the convenience readily incorporated into
a system for handling the particulate collected on bed particles in a
fluidized state.
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Sec. 1.1
1 Introduction
1.1 Submicron Particulate as an Environmental Control Problem
In terms of being a threat to human health, all particles inhaled
are not equally dangerous. According to Drinker and Hatch (1954) and
Brown, et al. (1950), the pulmonary system acts as a size-selective
filter. The air is delivered to the lungs at first through relatively
open channels. These branch into progressively narrower passages before
reaching the regions where the actual exchange of oxygen and carbon
dioxide takes place. Relatively large particles, diameters, exceeding
perhaps 5 micron, have a sufficiently high inertia that they can impact
on the walls of the upper respiratory system. In the mucous lining of
this region the particles can be transported outward through mechanisms
available in the nose and mouth. A greater fraction of smaller particles
find their way into the lungs. Of these, those that are extremely small
tend to be in a state of Brownian diffusion with the gas molecules them-
selves. Hence, they tend to be retained in the air and eventually exhaled.
Particles in the intermediate diameter range from .8 to 1.6 micron tend
to be retained in the walls of the lungs. They tend to be neither caught
through impact in the upper respiratory system nor permanently entrained
in the gas so that they are removed in the exhaling process. By many, all
particles less than 5 micron are considered hazardous to health, and this
is one reason for a growing interest in particulate control systems that are
effective in the submicron range.
Further incentive to develop more effective means for collecting sub-
micron particulate comes from recent studies by Natusch (1974) which indicate
the tendency for the most dangerous pollutants to concentrate on particle
6
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Sec. 1.2
sizes in this same range. Submicron particles of fly-ash have been shown
to exhibit concentrations of such trace elements as cadmium and arsenic
that increase with decreasing particle size. Evidence tends to support the
hypothesis that the predominance of these elements on the smaller particles
results because the trace elements are volatilized in the combustion process
and reabsorbed or condensed on the fly-ash particles after leaving the
combustion zone. Because the surface area per unit mass for the smaller
particles is the greatest, the amount of the trace elements on the smaller
particles per unit mass is greater.
In a way, these submicron particles that pose the most difficulty to
the respiratory system, are a catalyst for inducing absorption of objectionable
materials into the body.
1.2 Incentives for Developing Charged Droplet Scrubbers
With the exception of fabric filters, conventional dust collection equipment
exhibits poor efficiencies in this submicron range (Sargent, 1969). Commonly
installed types of equipment rely directly on the inertia of the particulate to
effect its removal. In the cyclone, the gas stream flows rapidly around an
annulus, resulting in a centrifugal force that causes the particles to move
to the outside and be sedimented. In scrubbers,water drops are either injected
into the flow at a relatively high speed, as in the spray design, or are
accelerated from rest by a rapidly moving gas stream, as in the venturi design.
Particles of sufficient mass are unable to follow the gas as it diverges around
the drop, and hence are collected. In fabric filters, the gas follows a tortuous
path through the medium and deposits particulate first on the fibers, and then,
as the filter is used, upon agglomerates. Especially for extremely fine particles,
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Sec. 1.2
diffusion is also an important collection mechanism. In the electrostatic
precipitator, the particle in passing through the device is first charged by
an ion flux and then precipitated upon plates by the same field that charged
it. Although not exactly inertia dependent, this process is also sensitive
to the particle size. Except for the filters, typical devices based on these
processes allow a major fraction of the submicron particles to pass through
uncollected. In addition, the filters are often unable to withstand the
necessary operating conditions. Electrostatic precipitators are certainly
superior to cyclones and scrubbers in the submicron range and can be designed
to achieve high efficiency in this range.
This report is concerned with a class of devices that is hybrid
between inertial wet scrubbers and electrostatic precipitators. As in
the conventional wet scrubber, drops are used as collection sites for the
fine particles. However, rather than depending solely on inertial forces
to cause impact between the fine particles and the drops, electrical forces
are used. For this reason charged droplet scrubbers are also closely related
to the conventional electrostatic precipitator, with the drop surface playing
the role conventionally played by electrodes.
Although our primary concern is with collection sites which are
water drops, it should be recognized that the investigations more generally
relate to a wide class of devices that make use of particles of all sorts
as collection sites for other particles. Many of the principles developed
in the following chapters are as applicable to systems of solid particles
used as collection sites as to those using liquid drops.
Of the many reasons that can be given for efforts to develop a
technology of charged droplet scrubbers, two are consistent with the
actual nature of these devices. First, in the general area of air
pollution control the inertial wet scrubber has a well-established position.
8
-------
Sec. 1.2
The scrubbers are used not only to control particulates, but for control
of gaseous effluents as well. It is a well-known fact that the efficiency
of inertial scrubbers in the removal of particles much below a five micron
diameter range is poor. The use of electrical forces in improving this
efficiency so that such devices function as charged droplet scrubbers in
the range of one micron and less is attractive, since the capital investment
associated with additions to existing equipment have the potential of being
relatively small.
The second incentive comes from the fact that the conventional
electrostatic precipitator is a capital intensive device. At least for
submicron particles having reasonable electrical characteristics, the
electrostatic precipitator can be made to function effectively provided that
devices are scaled to provide the required residence time. In the engineering
of environmental control systems, greater flexibility would be available
if devices were developed having the collection efficiency of an electrostatic
precipitator but by contrast representing a greater investment in operating
costs as compared to capital costs.
Of course the use of charged droplets implies that the system is "wet".
This is by contrast with the systems involving a conventional electrostatic
precipitator. There is however a current increase in the use of wet-wall
electrostatic precipitators, and this fact tends to underscore the in-
creasing market for devices that have many of the characteristics of the
electrostatic precipitator but the capital investment characteristics of a
wet inertial scrubber.
-------
Sec. 1.3
1.3 Scope and Objectives
Nature gives examples of how drops can scavenge particulate from the
atmosphere. McCully et al. (19.56) describe how falling raindrops
effectively reduce the number density of particulates in the range of
1 - 50um. Further, the existence of atmospheric electric fields has
encouraged investigations, such as those of Zebel (1968), of possible
influences of particle and drop charging on the collection of particulate
by the drop. Because of these meteorologically oriented interests alone,
it is not surprising that the idea of using electric fields to enhance
collection of particulate on drops is often suggested as an approach to
controlling particle emissions in industrial gasses.
One of the objectives in the following chapters is to key on what
is unique in the use of drops and electric fields in collecting fine
particles by providing a classification based upon the fundamental
mechanism for the electrically induced collection of particle on drops.
In Chapter 2 an overview of the basic significant collection mechanisms is
used to compare and relate various charged droplet systems and conventional
wet scrubbers and electrostatic precipitators. This chapter is intended not
only to provide a classification for devices, but to promote comparisons
as well. Primarily in the patent literature, but also in the formal
literature, there are described a collection of seemingly widely different
devices. Chapter 3 is a review of relevant literature based upon the
classifications available from Chapter 2.
There have been remarkably few research efforts into charged droplet
scrubbing with a) sufficiently high charged-drop densities to be of
industrial interest and b) experimental parameters carefully enough controlled
10
-------
Sec. 1.3
that comparisons could be made between theoretical models and experimental
results. Research oriented toward meteorological phenomena does not
recognize the dominant role of collective effects that occur at practical
drop densities. Configurations having practical air-pollution-control
objectives have generally incorporated many collection mechanisms and
failed to control and identify parameters so that meaningful scaling laws
could be verified. The primary objectives in Chapters A,5, and 6 are
experiments that can be used to test knowledge of the electromechanical
dynamics of a) systems of charged submicron particles, b) charged super-
micron systems of droplets and c) systems involving both charged droplets
and charged fine particles in charged droplet scrubbing configurations.
These experiments show in specific terms how the characteristic times
enunciated in Chapter 2 come into play.
The theoretical models developed in these later chapters not only
are sufficiently refined to relate the basic theoretical models to the
actual experimental systems, but also can be used to project the performance
characteristics of devices scaled to industrial sizes. Considering the
relatively small scale of the experiments, this will seem to some, well
acquainted with the realities of scaling process control systems, to be a
presumptive statement. But the dominant feature of the charged-drop
scrubber is the collective interaction of drops and particles through the
electrical forces. If the essential scaling parameters are not recognized,
a large experiment can easily fail to confront the scaling question, while
a properly designed smaller experiment can be successful.
In Chapter 7, the implications of the experimental and theoretical
findings for full scale industrial applications are summarized. Finally,
11
-------
Sec. 1.3
in Chapter 7, there is a summary of the "state of affairs" for charged
drop scrubbers, and some views as to how efforts should proceed toward
control of particle pollutants on an industrial scale.
12
-------
Sec. 2.1
2 Conventional and Charged-Drop Sutmicron Particle Control in Perspective
2.1 Residence Time as a Basis for Comparisons
The objective in this chapter is the identification of fundamental
factors determining the performance of submicron particle control devices
in simple enough terms that a comparison can be made easily between al-
ternative approaches. For this comparison, the key performance character-
istic is taken to be the gas residence time required to achieve the desired
cleaning. A total active volume V handling a gas rate of flow F would have
an average residence time
Tres - I
The residence time is indeed a way of representing the required device
volume and hence at least to some degree reflects the "cost" of the device.
Of course this is an over-simplification. A refined comparison of systems would
translate this volume into capital investment and operating costs. It would
consider the materials within the volume on the one hand and the energy
requirements for operation on the other. However, the more refined the
evaluation, the more difficult it becomes to achieve the perspective required
to make preliminary judgements.
The point in this chapter is the overview that follows from relatively
simple comparisons. To be practical, devices must incorporate a collection
mechanism characterized by time "constants" that are shorter than the
residence times. In the following sections, these times are identified
and used as a basis for comparing charged-drop devices to each other and to
conventional devices. In the next chapter, the basic mechanisms outlined
13
-------
Sec. 2.2
here are further used to classify and organize the variety of patents and
literature related to charge-drop scrubbing. Then, in the remaining chap-
ters, the characteristic times identified here are quantitatively incorporated
into detailed descriptions of device performance which are related to critical
experiments.
The "conventional" competition to charge-drop devices is considered
first in the following sections on wet-scrubbers and electrostatic precipi-
tators. Charged-drop scrubbers, which are the subject of the remaining
sections, are a hybrid of these devices. In the configurations of most
interest in these sections, charged drops (typically exceeding 20 microns
in diameter) are used as collection sites for oppositely charged submicron
particles. If compared to a wet-scrubber, the effects of fine particle
inertia conventionally responsible for causing impaction, are replaced by
an electric force of attraction. If compared to an electrostatic precipi-
tator, the charged-drop scrubber replaces the electrodes with drops.
2.2 The Inertial Impact Wet Scrubber
The collection of particles on drops through inertial impaction,
pictured in Fig. 2.2.1, depends on there being a relative velocity w
between the gas and a drop. Because of viscous drag, particles entrained
in the gas tend to follow the gas around the drop. But because of their
inertia, a fraction of those particles that would, in the absence of the
2
gas, be intercepted by the geometric cross-section TVR of the drop, have
sufficient inertia to impact the drop surface. By definition, those
2
particles approaching the drop through the cross-section Try shown in
Fig. 2.2.1, impact the drop surface.
14
-------
Sec. 2.2
Fig. 2.2.1 Inertial impact scrubbing viewed from drop frame of reference.
Gas entrained particles approaching the drop within the cross-
2
section Try impact the drop.
Particle-Scrubbing Time T The effectiveness of inertial impaction in the
removal of a particle depends upon the importance of the inertial force
acting on the particle, as it accelerates to avoid colliding with the drop,
relative to the viscous drag force tending to make the particle follow the
gas around the drop. Based on the mass of a spherical particle having radius
2
(a) and mass density Pa> and on an acceleration w /R, the typical inertial
/ o O
force is -^fla p&w /R. Based on a Stoke*s drag model with n the gas velocity
corrected by the Cunningham factor, the viscous drag force tending to divert
the particle around the drop is 6Trn aw. The impaction parameter K , which
is the ratio of inertial to viscous drag force
15
-------
Sec. 2.2
2
Ks 5 f
therefore characterizes the fraction of the geometric cross-section of
the drop that is successful in collecting particles. Walton and Woodcock
(1960) and Calvert (1970) show that to a useful approximation
(2)
s
This expression correlates data measured in actual scrubbing situations
for K >70.1. As an example, for w » 10m/ sec, a - 0.5pm, R » 50um, K =0.7.
S
For smaller values of the impact parameter, collection increasingly depends
upon the Reynolds' s number of the flow. This is a consequence of impaction
on the downstream side of the obstacle resulting from the eddies established
there.
As it travels with velocity w relative to the gas , one drop cleans a
2
gas volume nw(y) each second. Hence, with n particles per unit volume, a
2
drop removes mrw(y) particles from the gas each second. The number of
particles removed per unit time from a unit volume in which there are N
2
drops is therefore N(nirwy ) so that
^ - N(nwy2) (3)
dt
2
By rewriting the right hand side as n/[l/wNy ], the characteristic time can
be identified in Eq. (3) as (1/nwNy2) and from Eq. (2) it follows that
T -
SC
.
S
This is a time typical of that required to appreciably reduce the original
density of particles. If T were constant in Eq. (3), it would be the time
S C
16
-------
Sec. 2.2
to reduce n by the factor e . Usually, the drop velocity is continually
changing as a result of the drag of the gas. In general, the details of
the collection law are a matter for refined analysis, but the minimum
collection time expected from such a system results from substitution of
the drop injection velocity for w. To be practical, a device must have a
collection time that is short compared to the gas residence time.
For purposes of comparison with other devices, it is convenient to
limit discussion to collection of submicron particulate, hence K < 1,
s
and approximate Eq. (4) by
w Na p
To be practical in removing submicron particles, an inertial impact device
must have TSC < Trcg.
Drop Scrubbing Life-Time T A second time that is critical to the per-
SR
fonnance of an inertial scrubber characterizes the tendency of the drops to
decelerate to the gas velocity as in a spray scrubber, or accelerate to the
gas velocity, as in a venturi scrubber. The fact that w appears to the
third power in Eq. (5) suggests that this time, during which the drop retains
sufficient velocity to effectively clean the gas, is also a critical
parameter.
The tendency of the drop to approach the velocity of the gas is
represented by the balance of drop inertial force with viscous drag
-^rrp-R -j— * 6irRnw (6)
For the present purposes, where drop radii are in the range 25-200|jn
17
-------
Sec. 2.2
and w la typically 10m/ sec, the drop Reynolds number _ £ (p = gas mass
n g
density, r| - gas viscosity) is in the range 10-40, and the use of Stoke 's
drag is consistent with the order of approximation of interest.
It follows from Eq. (6) that the time characterizing the slowing of
the drop to the gas velocity is
2
In identifying T , collective interactions of the drops with the gas flow
SK
have been ignored. That is, it is assumed that in the gas stream the drops
are sufficiently separated that their mutual hydrodynamic interactions are
not a factor in determining the transfer of momentum between gas and drops.
Thus it is that the drop number density does not appear in Eq. (7).
If the scrubbing life-time of a drop T R falls short of the residence
time required of the gas, then drops must be supplied in such a way that
their life-times in the cleaning volume are short compared to the residence
time. In this mode of operation, the gas recirculates through the drop
injection volume or is held up by pressure forces in this volume. In
either case, a given volume of gas is subject to many "passes" by the drops.
Characteristics of Submicron Inertial Scrubbing With the relevant time
constants in view, the following observations can be made:
a) In the sub-micron range, the efficiency of the inertial scrubber
-4
decreases dramatically with decreasing particle size: r eta . For example,
sc
9 3
using as representative scrubbing conditions w - lOm/sec, N - 10 drops /m ,
3 3 —5 2
p » 10 kg/m , n ^ 2 x 10 nt-sec/m , 1 micron diameter particles have a
_2
particle scrubbing time T - 2 x 10 sec. Under the same conditions,
SC
18
-------
Sec. 2.3
0.3 micron particles have T ^2.5 sec.
sc
b) The drop scrubbing time, T R, acts in parallel with the particle
scrubbing time, T , to limit the performance of a system. Normally, the
gas must interact with the drops for several T *s to be reasonably cleansed.
s c
This time, however, is based upon the maximum difference in velocity between
the drop and particles, occurring at injection. If T „ is much greater than
Sit
T , then the relative velocity between the two species is approximately w
over a period sufficient to remove most of the particles. If the opposite
is true, then the relative velocity over most of the drop trajectories is
much less than w, and collection practically vanishes. This condition sets
a lower limit on the particle size that can be effectively cleaned by in-
ertial scrubbing.
Tsc <
-------
Sec. 2.3
the electrodes into a hopper. By a "conventional" electrostatic precipitator
it is meant that particles are precipitated onto electrodes by means of an
imposed electric field. That is, the charges responsible for the precipitating
field largely reside on the electrodes, and not on the particles themselves.
The crucial time in an imposed field precipitator is that necessary
to remove a particle, having mobility b and an associated velocity bE in
the direction of the imposed electric field E. For example, in the plane
parallel geometry of Fig. 2.3.la with the distance between the charging
region and the collecting electrode defined as s, the precipitator collection
time is characteristically
V • SB- <«
w
For successful operation, T must be short compared to the gas residence time.
Of course, it would be entirely possible to design a highly inefficient
precipitator having a residence time long compared to T ....one incorporating
by-passing paths for the gas or having reentrainment problems. Because of
the mobility b, the precipitation time T clearly depends on particle size
and so there are a spectrum of such characteristic times relating to the
performance of a device in removing polydisperse particulate. In the
turbulent flows of practical precipitators the collection process even for a
monodisperse particulate is far more complex than portrayed in writing Eq. (i).
But, more realistic models turn out to also be characterized by T and it will
be used for the rough comparisons which are the point of this chapter.
More generally, electrostatic precipitators are described in terms
of an effective precipitation perimeter S and a flow cross-section A, as
sketched in Fig. 2.3.1b (White, 1963). The precipitation time is still the
20
-------
Sec. 2.3
essence of the matter, as is seen by writing the particle conservation
equation expressing the loss of particles from an incremental length Ax of
the precipitator section in terms of the particles removed from the gas to
the electrodes. The particle concentration is assumed to remain uniform
at every cross-section.
AU [n(x + Ax) - n(x)] - -SE bnAx
w
(2)
Here, E is the electric field at the precipitation surface, U is the mean
gas velocity and n is the particle density. The particle removal is
JfT
U
u
L
(a) (b)
Fig. 2.3.1 A conventional (imposed-field) electrostatic precipitator
configurations, a) plane parallel geometry b) generalized
geometry
described by Eq. (2) in the limit Ax •*• 0.
That the essence of the device performance is determined by the
precipitation time relative to a residence time can be seen by writing this
expression with x normalized to the length i of the precipitator.
dn
SE bfc
r w
L AU
-]n
(3)
Specifically, Eq. (3) shows that the particle density decays exponentially
as the gas passes through the device. The efficiency of removal is
determined by the parameter AU/SEwb£, which will be recognized as the ratio
21
-------
Sec. 2.3
of a generalized precipitation time
pc SEwb (4)
to the gas residence time T » fc/U. Note that for plane parallel
1T6S
geometry of depth d (into paper) S » 2d and A - 2sd. Thus, Eqs. (1) and
(4) are consistent. For high efficiency, a device must be designed to
make T « T . Detailed models add refinement to the picture but are
pc res r
nevertheless in agreement that T is the time characterizing the electro-
pc
static precipitation process in a well designed device.
In the inertial scrubber, and in the charged drop devices to be
considered in the following section, a time constant in addition to the
collection time is necessary to properly characterize a device. In the
inertial scrubber it is a life-time TgR for the decay of relative drop gas
velocity, while in the charged drop devices it is the time that a drop
retains its capacity to attract particles. Is there an analogous "second
characteristic time" required to place the conventional precipitator in
perspective? Consider some possibilities:
One process that brings into play another characteristic time is the
ion-impact and diffusion charging of the particles as they pass through the
corona flux prior to the collection process. However, the ions are of
-4
relatively high mobility (bi ^ 2 x 10 ) so that this charging time is
usually very short compared to the residence time. Hence, the charging
time is not an important factor in making comparisons.
However, the charge relaxation time of the particles (effectively,
the resistivity) is an important factor in the collection of highly
resistive particles. Because insulating particles tend to retain their
22
-------
Sec. 2.4
charge even after contacting the electrode, fields produced by build up of
charge in the collected dust on the electrodes compete with the imposed
field tending to turn off the corona and even establish "back-corona".
But the particle relaxation time pertains to the processing of particles
once collected and not to the collection process itself. For example, the
wet-wall precipltator characterized by the same typical collection time
T derived here, has little problem with highly resistive particles.
pc
In comparing the electrostatic precipitator to other devices, only
one characteristic time will be used.
2.4 Hierarchy of Characteristic Times for Systems of Charged Particles
and Drops
Three ubiquitous characteristic times are basic to the dynamics of
systems of charged particles and drops. They pertain to seemingly very
different configurations. Nomenclature is summarized in Table 2.4.1.
The particles are of number density n, charge per particle ±q, mobility B
and radius R. Table 2.4.1 summarizes the three time constants T , T and
Si C
T_ discussed in this section.
R
Unless otherwise specified, the interaction between drops and
particles is assumed to occur in a volume bounded by equipotentials.
That is, external electrodes are not used to produce even a part of any
possible ambient field. The submicron particulate is termed the "particle"
system while the collection sites are called "drops".
If a volume is filled with submicron particles charged to the same
polarity, then I& typifies the time required for these particles to self-
precipitate on the walls. This time is based on the system parameters of
particle number density n, particle charge q, and mobility b. Note that it
23
-------
Sec. 2.4
Table 2.4.1
Summary of times characterizing systems of charged drops and particles
Designation
Description
Schematic
=
~
a ~ bqn
Particle self-discharge
or self-precipitation
time.
t
ff)
*
e
Tc = bQN
Drop-particle collection
time or time for precipita-
tion of particles due to
space-charge of drops
T. 5
R ~ BQN
Drop self-discharge or
self-precipitation
time
-12
Summary of Nomenclature (e = 8.85 x 10 )
number density
charge
drop
particle
N
n
Q
q
B
b
R
a
PR
I
pa
24
-------
Sec. 2.4
does not involve the dimensions of the device. As a variation of this con-
figuration, if a similar volume is filled with regions of positively
charged particles and other regions of negatively charged particles, then
T typifies the time required for the oppositely charged particles to inter-
£1
mingle. If, to prevent space-charge fields, positively and negatively
charged particles are mixed, then T (based on the density of one or the
Si
other of the species) is the time required for self-discharge and perhaps
self-agglomeration of the particles.
The time required for collection of fine particles on oppositely
charged drops is typically T . This collection time is also based on the
mobility of the fine particles, but the charge-density NQ of the drops
rather than that of the particles (nq). The residence time of the gas
must be at least of this order for the device to be practical. Provided
that the charge density of the drops exceeds that of the particles, this
same time constant T characterizes particle precipitation onto the walls
of a volume filled with drops and particles having the same polarity.
For a system of charged drops, T_ plays the role that T does with
K a
respect to the particles. Thus, in a system of like-charged drops, TR
is the self-precipitation time of the drops, while in a system of oppositely
charged drops where there is no space-charge due to the drops, this same
time-constant governs how long the drops retain their charge before dis-
charging each other and perhaps agglomerating.
A simple model that motivates the physical significance of T , T_ and
3- R
T in the role of inducing self-discharge among oppositely charged particles,
among oppositely charged drops or particle collection on drops is shown in
Fig. 2.4.1.
25
-------
Sec. 2.4
X
X
X
X
X
X
£ N^
a ** ^*^-N»^
Fig. 2.4.1 Two-"particle" model for electrical discharge and possible
agglomeration due to micro-fields.
If the effects of inertia are ignored, the equations of motion for the two
charged spheres are:
dt
(1)
dt
(2)
Strictly, these expressions are valid when the spacing £ is large
compared to R + a. However, as the spheres are drawn together most of the
time is spent when they are relatively far apart. Hence, for systems of
26
-------
Sec. 2.4
relatively tenuous particles (of main interest here) Eqs. (1) and (2)
are adequate.
Subtraction of Eq. (1) from Eq. (2) gives an expression for the
relative velocity (£«£_- £J
K. Si
1
dt 3T£_
where
I = f (3)
and
T =
3(qB-K}b)
With the initial spacing taken as £ , and provided £ »R+a, integration of
Eq. (3) gives a time T for collision. Three limiting cases are summarized
in Fig. 2.4.2. First, consider a system of oppositely charged particles
alone. Then using as the number density n the particle density of one of
the species, n - ^C^) » and the time for collision T becomes •=• T .
Second, consider the collection of particles charged to one sign by
drops charged to the opposite sign. In an array of drops, the "last"
particle to be collected is midway between two drops. Hence an estimate
3
of the collection time for this worst case is given by making N ^ l/(2£ ) .
Also, note that typically qB«bQ. This can be seen by estimating the
respective mobilities using a Stoke1 s drag model (b •> q/6irr|a, B - Q/6trriR)
and taking the respective charges as being the saturation values due to
impact charging in a field EC (q ^ 127T£oa2Ec, Q ^ 12TreQR2E ). Then,
27
-------
Sec. 2.4
qB ja
Qb " R
(4)
It follows from this limit that the collection time is characterized by
T .
Q -*- q
B
i
n
bQ > > qB
IT
^r T
6 c
q
b
of
It,
-K
-^
3
'o~*~
Q "
B
1
N .
7T
— *• T - 3-
TR
Fig. 2.4.2 Limits of collection time for two particle model that give the
three time constants when these are interpreted as self-discharge
and drop-particle agglomeration times.
Third, consider the case of a system of oppositely charged drops
having total number density N. Using the same limiting arguments as for
the particles, it follows that the time that they will retain their charge
is approximated by T_.
That the same characteristic times r& and TR also respectively typify
28
-------
Sec. 2.4
the self-precipitation of systems of like-charged particles alone or like-
charged drops alone follows using the planar geometry of Fig. 2.4.3. For
example, for particles, Gauss' Law requires that the electric field intensity
E at the walls is
w
\ - 1; »>
Conservation of the charge within the control volume shown requires that
the net charge decrease at a rate determined by the electrical current
nqbE caused by the migration of particles to the walls.
^ w
(nqs) - -2nqbEw (6)
1
t .
-H
JrT
+ tj +
•H
* t! +
-T T1
1 -1- 1
.i+_.t *
t t +
+
'
t
E
w
Fig. 2.4.3 Simple model used to illustrate roles of Ta and T as self-
a R
precipitation times for like-charged particles and like-
charged drops respectively.
Combined, these two laws show that the particle density decreases at a
rate determined by the equation
29
-------
Sec. 2.4
, T s
03
and so it follows that the self-precipitation of unipolar particles is
typified by T .
3,
The same arguments can be applied to the dynamics of a system of
like charged drops. In Eq. (7), n -»• N and Tfl •*• TR. Hence, TR
typifies the rate at which unipolar drops are self-precipitated from a
volume.
From several points of view, it is of course possible to criticize
the simple models used to motivate the three characteristic times T , T ,
fl C
T_. For example* in a bicharged system of drops or particles, a given par-
ticle or drop is subject to attractive or repulsive forces from more than
just its nearest neighbor. In an extreme case, the positive and negative
particles or drops might form a cubical lattice of alternately positive
and negative polarity. Then the net electric force on a given particle
and drop would vanish. Even so, the given drop or particle would be in an
unstable equilibrium. Given initiating noise, the rate of growth of the
instability representing its departure from the equilibrium is characterized
by T or T , as the case may be.
a K
The appropriateness of T for the characteristic time for collection
of particles on drops can be further supported by a more refined laminar
flow model that gives a detailed description of the collection of a
continuum of charged particles on a drop having net charge Q in an ambient
electric field E and with a relative gas velocity w. (This model is
o
taken up in detail in Sec- 6.2.1) There are in fact 12 possible collection
30
-------
Sec. 2.4
regimes, determined by the drop charge, the ambient field, and the slip
velocity. Of most importance are those regimes in which the drop carries
2
a charge exceeding the saturation charge 12ire RE in whatever ambient
field E may exist. Then, the electrical current caused by the collection
of particles is ±2 - - bnqQ/eQ and the rate at which particles are collected
is this current per drop multiplied by the number of drops per unit volume
and divided by the charge per particle.
From Eq. ($, it is clear that this more refined laminar flow picture of the
particle collection agrees that the characteristic time is still T£. The
details of the collection transient depend on the regime, but, so long as
the drops are charged significantly, the characteristic collection time is T .
Yet another approach to the drop collection of submicron particles
pictures the particle distribution in the void region between drops as
determined by turbulent mixing. According to this model, which is similar
to the Deutsch model for the precipitator (White, 1963), mixing supplies the
particles to the immediate neighborhood of the drop where electrical forces
then dominate in depositing the particles onto the surface. This model,
taken up in Sec. 6.2.2, also results in a time for significant collection
characterized by T£.
Devices can be envisioned that make use of drops as collection sites
in an ambient electric field imposed by means of external electrodes. The
drops are in this case "polarized" by the field. For purposes of comparison,
it is useful to recognize that even if the drops have no net charge, but
are polarized by the ambient field so that they collect particles over a
31
-------
Sec. 2.5
hemisphere of their surface, T remains the basic collection time. However,
Q Is interpreted as the charge on the collecting hemisphere.
For the self-discharge of oppositely charged drops, it is possible
that drop inertia can become an important factor. This has not been
included here because in systems of relatively tenuous drops the inertia
is usually not an important factor. However, in specific instances it is
convenient to have a ready means of determining the relative importance of
inertia in increasing T_, and this is provided in Sec. 5.3.1.
K
2.5 Classification and Comparison of Basic Collection Configurations
A summary of configurations representing the basis for devices that
collect submicron particles is given in Table 2.5.1. It is natural to
include the two representatives of conventional technology that are nearest
relatives of devices that make use of charged drops: the inertial scrubber
and the electrostatic precipitator. In the table, the collection process
is characterized by whether or not the particles to be collected are charged,
and whether or not the drops, if present, are charged. In addition, a
distinction is made between devices that involve an ambient electric field
(one associated with many charged particles and hence having an average
value over distances that are large compared to the interparticle spacing),
and those that primarily involve only a microscopic field (having essentially
no space - average value over distances greatly exceeding the interdrop or
interparticle spacing). A .further distinction is made between ambient field
configurations in which the fields are "imposed" by means of charges on
electrodes bounding the active volume or are "self-fields" Induced by the
net charge on particles and drops within the active volume itself.
INS & ESP The characteristic times also included in Table 2.5.1 are
32
-------
Sec. 2.5
Table 2.5.1 Summary of Basic Configurations for Collecting Submicron Particles
i
Characteristic times T>, T , T are summarized in Table 2.4.1
a c R
Desig-
nation
System
Particle
Charge
Drop
Charge
Ambient
Field
Characteristic
Times
INS
ESP
SCP
SAG
CDS- 1
CDS-II
CDP
EIS
EFB &
EPB
Inertial Scrubber
Electrostatic
Precipitator
Space- charge
Precipitator
Self-
agglomerator
Charged Droplet
Scrubber
ii
ii
Charged Drop
Precipitator
Electric
Inertial Scrubber
Electrofluidized
and Electro-
Packed Beds
none
unipolar
unipolar
bipolar
unipolar
(+ or -)
ii
unipolar
or
bipolar
unipolar
none
ii
unipolar
or
bipolar
none
-
-
-
unipolar
(+ or -)
ii
bipolar
unipolar
a) uni-
polar
b) bipolar
none or
bipolar
none
imposed
self
none
(nq
-------
Sec. 2.5
the basis for making comparisons between systems. With the understanding
that the collection lifetime of a drop is typified by a second time constant
T „, inertial scrubber (INS) technology is represented by the collection time
T . Further conventional competition comes from the side of the electro-
sc —
static precipitator (ESP), which has a characteristic collection time T .
pc
SCP The space-charge precipitator relies on precipitation on the
walls caused by the self-fields induced by charge on the particles them-
selves. As discussed in Sec. 2.4, the characteristic time for this type
of particle collection is T - e /nqb. Note that according to Gauss' Law
the electric field c.t the wall is of the order nqs/e , where s is a typical
dimension of the active volume. Thus, T is equivalent to the collection
d
time T in a conventional precipitator provided that nqs/e •*• E . Clearly,
to be competitive, the self-field must be on the order of the electric field
intensity that can be imposed by means of electrodes. This places a lower
limit on the range of particle densities that can be practically used in a
space-charge precipitator. At high particle densities it is indeed possible
to make nqs/e approach the breakdown limitation encountered in the con-
ventional precipitator, but for refined cleaning, the collection time T
is far too long to be of practical significance.
SAG With the particles charged to both polarities, so that there is
no ambient self-field, there is electrically induced self-agglomeration
also characterized by the typical time T . (Sec. 2.4.). Agglomeration results
in electrical discharge between the particles of opposite polarity. Hence,
to be useful as a mechanism for increasing particle size prior to collection
34
-------
Sec. 2.5
by some other means, the agglomeration must be combined with a continual
bipolar recharging of the particles. Because an agglomeration event only
results in a doubling of the particle volume, self-agglomeration has been
generally regarded as too alow a process to be of practical interest.
That it is characterized by the same time T as the self-precipitator further
3.
dampens enthusiasm for making use of electrically induced agglomeration.
In a way, the self-precipitator is a self-agglomerator with the agglomeration
event one between a particle and an electrode. But the result of this
event in the self-precipitator is the removal of the particle from the
volume rather than simply a doubling of the particle volume.
With the first four configurations of Table 2.5.1 as a background,
consider now the heart of the discussion....the configurations CDS-I and CDS-II
exploiting Charged Droplet Scrubbing. Charged drops are used as collection
sites for oppositely charged particles.
CDS-I First, consider charged drop scrubbers in which unipolar drops are
used. For example, the drops are charged to positive polarity and the par-
ticles charged to negative polarity. If the drop charge density dominates
(|NQ| > |nq|), as would be the case with gas containing relatively little
particulate, there is an ambient self-field associated with the drops. This
field results in a self-precipitation of the drops with the characteristic
time TD. The situation is analogous to inertial scrubbing. The collection
K
process is limited in this case by loss of collection sites by self-
precipitation. However, for an inertial scrubber, the limiting time T ,
can be considered to be constant if the drop size is fixed. Thus, its
influence can be circumvented by injecting the drops at a higher velocity.
In the case of a charged drop scrubber, this is not true. Increasing the
35
-------
Sec. 2.5
charge on the drops decreases both T and TD in such a manner that their
C K
ratio decreases. In fact, if particles and drops are both charged to
saturation in a field E (meaning the largest charge possible by ion impact
2 2
charging, (see Sec. 5.4.4 > (Q " 12TT£oR EQ and q - 12TT£oa EQ) and if Stoke's
law is used to approximate both mobilities, the collection time and drop
self-precipitation time are simply related
T B " R
c
The ratio of the effective life time T_ of a drop to the cleaning time T
K c
is essentially the ratio of particle to drop size. This emphasizes the
point that to be practical, the charged droplet scrubber using unipolar
drops must incorporate a sufficient supply of charged drops that the
effective drop lifetime can be much shorter than the gas residence time.
This means that a drop is removed by its own field long before its capacity
to collect particles is significantly reduced.
As a limiting case, in Table 2.5.1, that CDS-I charged droplet scrubber
configuration is identified in which space charge associated with the par-
ticles just cancels that due to the drops. That is, the particle loading
is sufficiently high that JNQJ * |nq|. In this case there is no ambient
field and hence no self-precipitation of the drops. Thus, T is no longer
R
a limiting lifetime of the drops. But, note that the collection time is
then T » T , or the same as would be obtained in the space-charge precipi-
tator that would be realized in the absence of the drops.
The picture that now begins to unfold is one in which the performance
based on the collection time of the charged-drop scrubber approaches but
36
-------
Sec. 2.5
does not surpass that of an electrostatic precipitator. To see this
directly, assume that there is no limit on the supply of charged drops,
so that TR is not a limiting time. Then, for the charged drop scrubber
to compete favorably with the electrostatic precipitator, the ratio
T E
-£- . -S (2)
pc (NQs/eo)
must be unity or less. Because NQs/EQ is the self-field induced by the
net charge on the drops at the walls of the active volume (assuming again
that NQ » nq), Eq. (2) makes it clear that for the charged drop scrubber
to compete favorably with the electrostatic precipitator, this self-field
must exceed that imposed in the conventional device by the electrodes. In
the electrostatic precipitator, the maximum E is usually determined by
electrical breakdown and this also imposes one upper limit on NQ in the
charged drop scrubber.
In practice it is difficult to generate charged drops with sufficient
density that the limit on NQ is set by electrical breakdown. Rather, the
loss of drops due to self-precipitation, reflected by Eq. (1), is the
dominant factor in limiting the effective field NQs/eQ.
The charged drop scrubber at least requires the same residence time
as the conventional precipitator. In fact, the drop loss represented by
TR is likely to make the performance fall short of that for an electrostatic
precipitator. However, it must also be understood that in terms of residence
time, the conventional electrostatic precipitator, with which the comparison
is being made in Eq. (2), is (short of fabric filters) the most viable
class of devices for removing submicron particles. The fact that inertial
37
-------
Sec. 2.5
scrubbers are viewed as competitors of the electrostatic precipitator in
collecting particles even below 10y suggests that there is more to making
a choice of systems than is simply represented by the residence time.
A comparison of the charged drop scrubber with its other "relative"...
the inertial scrubber...would tend to cast the charged drop scrubber in a
somewhat more favorable light. To make this second comparison, again ignore
consideration of the effective lifetime of the drop in either an inertial
scrubber (T „) or charged drop scrubber (TO) and compare the collection
sR K
times. Using T from Eq. p.2.5) and TC = eQ/NQb, n ^ nc» and saturation
2
charging of particles and drops in a charging field EC> (Q = 12ireoR E )
Tc _ w3pa2a3 (3)
T ™ 22
sc 226ne RE
° c
For charging of the drops and particles to improve the performance of the
inertial scrubber, the ratio of Eq. (3) must be in the range of unity or
less. Note the dramatic dependence on the particle radius a. Typically,
the ratio is unity for particles somewhere under a micron diameter. This
is the range where the inertial scrubber usually loses its particle collection
3 3
performance. For example, let 2a - 0.4y, w - lOm/sec, p « 2 x 10 kg/m ,
3
n - 2 x 10 kg/m-sec, R - SOvmand E - 10 v/m and Eq. (3) gives (T /T ) - 0.3
o c sc *
Thus, for particles of this size the charging of the drops and particles
would be expected to significantly improve the performance of a conventional
scrubber.
38
-------
Sec. 2.5
CDS-II One way to seemingly avoid the extremely short effective lifetime
of charged drops caused by self-precipitation is to employ a mixture of
oppositely charged drops. In the charged drop scrubber with bi-charged
drops, a short collection time T is obtained while space charge neutrality
is preserved even at low particle loadings. The basic limitations remain
for this second class of configurations, as can be seen by recognizing the
dual significance of the characteristic time T_. In the context of bipolar
K
drops, it represents the typical lifetime of a charged drop before it is
discharged by an electromechanically induced encounter with another drop
having the opposite polarity. Because of this dual role of TD, the basic
K
limitations on the CDS-I and CDS-II systems are the same.
CDP In the Charged Drop Precipitator, particles and drops are charged
to the same polarity. In the case of most practical interest, the charge
density of the drops dominates that of the particles (NQ » nq). (If
nq » NQ the drops do not participate in removal of particles from the gas.)
Then, the electric field intensity E at the walls where the particles are
precipitated is determined by Gauss' Law to be E - NQs/2e . This deduction
follows from the same reasoning as in Eq.(2.4.2)with the field induced by
drops rather than particles. In turn, Eqs. (2.A.6)and (2.4.7) describe the
particle collection, with the only alteration being that E - NQs/2e .
Hence, just as for the CDS interactions, the removal of particles is
governed by the collection time T . But rather than being scrubbed by the
drops, the particles are precipitated on the walls by means of the drop's
self-fields. Unlike the SCP, however, the CDP has an all important second
characteristic time TR typifying the lifetime of a charged drop in the
volume. Because TR < TC, the time varying nature of N plays an essential
39
-------
Sec. 2.5
limiting role in the collection process.
EIS Yet another collection configuration relies on inertial impact for
collection and only makes use of the electric field to drive the charged
drops through to the gas. Hence, in the electric inertial scrubber, the
particles are not charged. This variation of the inertial scrubber has a
collection time T that is given by Eq. (2.2.5), with the relative velocity
sc J
w approximated by
w - BE (4)
where E is the ambient electric field intensity. If the drops are assumed
charged to saturation in a field E and if Stoke 's drag is used to evaluate
c
B, then the relative velocity of Eq. (A) becomes
/K
Both the inertia of the gas (finite Reynolds number) and of the drop have
been ignored. But Eq. (5) serves to illustrate that typically w is on
the order of lOm/sec. The quantity n/e^E is itself a characteristic time
which in air and for E - 5 x 10 V/m is not likely to be less than 10~ sec.
Thus, for lOOymdiameter drops, Eq. (5) gives lOm/sec. Relative velocities
achieved using the electric field will be in the same range as those ob-
tained by mechanical means. One limit on w resulting from an electric drive
is set by the breakdown strength of the gas and device insulation. But, it
is important to keep in mind limits encountered because of space charge as
well. This is particularly true because one incentive for considering the
electrically driven inertial scrubber is the possibility of extending the
time that the drop retains a velocity relative to the gas. If drops of a
single polarity are injected, then the dimensions of the interaction region
AO
-------
Sec. 2.5
are limited by the requirement that the self-field from the drops at the
walls not exceed the imposed field. For a region having a typical dimension
s, this means that the imposed field must be greater than NQs/c . Because
the lifetime of a drop in the volume is of the order s/BE, it follows that
this lifetime is less than TD « e /NQB. If, to avoid the space charge field
K. O
associated with unipolar drops, a system is envisioned that uses counter-
streaming drops of opposite polarity, a similar limitation on the lifetime
is encountered. In this case, the drops tend to discharge each other in
the characteristic time TR.
Electrically driven inertial scrubbing is a likely contributor to
the performance of any system of charged drops in an ambient electric field.
However, for the reasons outlined, it does not appear sufficiently
attractive relative to the charged drop scrubbers to merit development in
its own right.
EFB & EPS As a last configuration, consider a broad class of systems
composed of "sites" that are not charged prior to being injected into the
active volume. Rather, because an electric field is imposed they are either
charged or polarized within the active volume. Various mechanisms lead to
devices having essentially the same engineering characteristics. Although
the collection sites have been regarded as drops, in these configurations
practical considerations make it more likely that the sites are solid
particles. The fact that the active volume must be filled by ambient field
makes it necessary that the collection sites he dense if there is to be any
merit relative to the ESP.
First, suppose that the collection sites are perfectly insulating.
Application of an ambient electric field results in polarization of the
41
-------
Sec. 2.5
site, with electric field lines tending to be drawn into the site, as
sketched in Fig. 2.5.1. Typically, this induced polarization is represented
by a relative permittivity reflecting volume polarization at the molecular
scale. Positively charged particulate will be collected by the hemisphere
of the collection site that terminates field lines directed into the site,
while negatively charged ones will be collected over the hemisphere exposed
to the outward directed field. The poles of the site play the same role
for oppositely charged particles as do the electrodes of the electrostatic
precipitator. Particles to be collected can therefore be unipolar or
bipolar. In addition to the polarization associated with molecular scale
dlpoles, it is possible that solid particle sites are permanently polarized
or become polarized because of surface charges created by frictional
electrification. Polarization of this type is essentially independent of
the applied field, and hence can result in collection even in the absence
of an applied field.
Second, suppose that the sites are sufficiently conducting that
the charge relaxation time based on the site properties (e/a, where £ is the
site permittivity and C is its conductivity) is short compared to the mean
time for collision between the sites. In a fixed bed, this collision time
is essentially zero, whereas in a fluidized bed, at low electric field
strengths, it is determined by the turbulence of the bed. At higher field
strengths it can be influenced by the electric field itself. In any case,
with each encounter between the sites there is a polarization of the
contacting pair induced by the imposed field which tends to make them
separate with a net charge. This process results in a continual recharging
42
-------
Sec. 2.5
of the sites at the expense of an electrical current carried between the
electrodes used to impose the ambient field. At any instant the net
charge in a volume enclosing many particles tends to be zero. In a sense,
the fluidized bed in this state, or the fixed bed in a state where the
particles are continually in contact and the field distribution determined
by electrical conduction between sites, uses the electrical current to keep
the sites active as collection sites. The limitation on effective lifetime
of the particles for collection (represented by T as in the cases where the
K
collection fields are associated primarily with the charge initially placed
on the site) is therefore obviated. Of course, in addition to the net charge
on each particle there is an induced polarization of the site, again much
as depicted by Fig. 2.5.1
Fig. 2.5.1 Collection particles polarized by means of ambient electric
field imposed by means of external electrodes.
-------
Sec. 2.5
Regardless of the detailed mechanisms for establishing an electric field
over part or all of the collection site, each of these configurations, whether
in the form of a fluidized bed or a packed bed, is typified by the same
considerations. The site surfaces play the same role as the electrostatic
precipitator electrodes. Hence, the collection time is of the form given
by Eq. (2.3.4) for the conventional precipitator. Hovever, the precipitation
perimeter S is replaced by an effective collection surface area of the sites
per unit length in the flow direction, and A can be approximated by the effective
flow cross-section through the device.
For spherical collection sites having radius R, a device having the
overall cross-sectional area A will have approximately
S y 8 u
s : u™2< a- >3'
where the mean distance between site centers is taken as aR. Here the
particles are assumed to be unipolar and hence are collected over only
half of the site surfaces. Bipolar particle charging would exploit the
full site surface but would result in essentially the same collection time.
It would, however, avoid the problem of charge build-up within the bed.
The effective flow cross-section is essentially that of the system reduced
by the geometric cross-section of the sites.
A " Asvst[1 - ^i' " Asyst[1 * S1 (8)
syst (aR)z syst a
and hence it follows from Eq. (2. 3. 4) that the collection time is approximately
where E is the average electric field intensity on that part of the site
44
-------
Sec. 2.5
collecting particles » To be consistent with other approximations inherent
2
in writing Eq. (9), u/a is assumed small compared to unity. It is worth-
while to observe that the collection time T. takes the same form as for
be
devices having sites that carry net charge, provided the charge on a hemisphere
_ o
is used to replace Q. This charge is Q, /0 = 3ireR E , where E is the ambient
•!•/ *• O O
electric field. Because E « :=E , Eq. (9) can also be written as
W L O
Tbc •
A comparison of the collection time for the sites in an ambient field
to the collection time of the electrostatic precipitator is made by taking
the ratio of the respective collection times. For purposes of comparison
consider an electrostatic precipitator with cylindrical electrodes having
radius r. Then, if the limiting values of E are the same in both cases,
^ - a3(f) (11)
pc
As is clear from the derivations of the time constants, this amounts to a
ratio of effective collection areas in the two configurations.
From the comparison afforded by Eq. (11), it is clear why the use of
collection sites in an ambient field has been considered in the context of
packed or fluidized beds. One of the main advantages gained from using the
particles as collection sites is lost once external electrodes are used to
produce an ambient field throughout the active volume. Unless the collection
time using the "drops" is short compared to that for a conventional precipitator,
it is difficult to argue for the use of "drops" rather than electrodes. In
fact, to produce drops with sufficient density to be competitive is difficult.
45
-------
Sec. 2.5
However, in the packed and fluidized bed configurations the density
of collection sites can be made sufficiently high that the effective surface
area is greatly increased over that of a conventional precipitator. Sites
in these cases are more likely to be solids than drops. It follows from
Eq. (11) that to compete with a conventional electrostatic precipitator,
the fluidized bed must have an a of approximately
<* 1 (|)1/3 (12)
For example, using sites having radius 100pm, the collection time in the
EFB types of configurations competes favorably with an electrostatic
precipitator having r » O.lm if a < 10. As a second example, suppose that
r = O.lm and a = 3 in a bed composed of sites having R - 300y. Then, from
Eq. (11) Tbc/T « 0.05. Better than an order of magnitude less residence
time is required. The packing required to make a = 3 can be easily obtained
in a fluidized bed, where the sites have a sedimentation velocity exceeding
lOm/sec which is consistent with a device having a relatively high gas
velocity.
It is clear from these comparisons with the conventional electrostatic
precipitator that the electrofluidized or electropacked bed configurations
are, at least from the basic point of view, very attractive as an approach
to the control of submicron particulate. In fact, they can be envisioned
in a broad range of applications. These not only include the control of
submicron particulate, as highlighted here, but also control of a wide range
of particle sizes and types. In the following chapters, the focus of
attention is on the electrically augmented scrubber configurations. However
it should be understood that information gained from these investigations
46
-------
Sec. 2.5
is applicable in many cases to the electrofluidized and electropacked beds
considered in this subsection. For further discussion of the EFB as an
air pollution control device, see Zahedi and Melcher (1974).
47
-------
Sec. 3.1
3 Survey of Devices and Studies
3.1 Charged Drop Control Systems
Processes that must be incorporated into any system making use of
charged drops for the collection of particulate are summarized schematically
in Fig. 3.1.
drop production
and charging
partic.1 e
treatment
drop-particle
interaction
drop removal
Fig. 3.1 Overall charged drop scrubbing system
The basic collection mechanism, the drop-particle interaction, is emphasized
in Chapter 2, and of course is at the heart of any system. But, practical
systems differ according to (i) the technique used for generating and charging
the drops, (ii) the method of particle treatment prior to collection of
particulate by the drops, and once the interaction has taken place, (iii)
the means provided for removal of the drops. In fact all of the processes
shown in Fig. 3.1 can take place within a single region, but more likely they
occur in physically separated regions.
Of the three ancillary processes, only that concerned with drop
production and charging requires discussion here. This is because conventional
techniques for particle treatment, such as charging by ion impact, are famlliar
from precipitator technology (White, Chap. 5, 1962). Also, drops can be
intentionally made large enough to be removed from the gas with relative ease
48
-------
Sec. 3.1,
so that their removal is again a matter of applying standard technology.
Examples of devices that can be used at this stage are the ESP and the
centrifugal separator (cyclone). It is convenient to classify methods of
making charged drops according to:
a) the manner in which the drops are formed in a mechanical sense.
Mechanisms are of two types: i) Mechanical atomization, in which a
liquid bulk is broken up into drops. This is typically done in stages
by first forming liquid sheets or jets or jets that reduce to drops
which in turn subdivide to the required size, ii) Condensation; a
saturated phase is condensed on nuclei leading to droplets that can
be made to grow to the proper size.
b) the means used to charge the drops. Again, methods fall into one of
two categories: i) Bulk charging; the drops are charged after they
have been established essentially as mechanical entities. Charging
by subjecting drops to the combination of an electric field and an
ion flux from a corona discharge is an example (ion-impact charging)
ii) Charging at birth. Condensation on ions is a charging mechanism
in this category. Another is influence or induction charging, which
occurs as drops are in contact with a reservoir of charge and under
the influence of a "charging" field.
The formation of charged drops usually amounts to adding one of the
electrical charging methods to a conventional mechanical process. Although
the electric field can be used to augment the instability of sheets, jets,
and drops in an atomization process, the main source of energy for making the
drops is usually mechanical or perhaps thermodynamic. In the case of influence
charging, no electrical energy is required in principle and with corona charging
49
-------
Sec. 3.2
the process is typically in a region removed from that where the particles
are formed. Hence, the electric field energy does not usually contribute
in an essential way to the energy supplied to the mechanical drop formation.
The electrohydrodynamic spraying technique for producing charged drops is an
exception because it does make use of the electric field to form the drops
in a mechanical sense. Fluid pumping, atomization, and charging are to
some degree accomplished in a single process.
The main way in which the drop processing will effect the viability
of the charged drop scrubber is through the operating costs. As will be
apparent from the chapters that follow, the amount of charge that can be
induced on a drop is not usually a limitation to the performance. Far more
charge can in principle be placed on a drop than is optimal for minimizing gas
residence time required for cleaning. As will be seen, this is because too
much charge results in too short an effective drop lifetime. For this reason,
a more detailed account of techniques for generating charged drops, including
specific experimental results and identification of the essential physical
processes is relegated to Sec. 5.4.
3.2 Patents
In the summary of patents directly relating to the use of electric
fields and drops for collecting particulate given in Table 3.2.1, primary
emphasis is given to the drop-particle interaction. The nomenclature used
conforms to that introduced in Sec. 2.5 and summarized by Table 2.5.1. Also
Included is a categorization of the method of: (a) charging and producing drops
(b) charging particulate, and (c) removing drops, if any. INS, ESP, and SCP
interactions encompass conventional mechanical scrubbing and electrostatic
precipitation, and are included in Chap. 2 only for purposes of comparison.
50
-------
Table 3.2.1 Summary of Patents Relating Directly to Electrically-Induced Collection of Particles on Drops
(See Table 2.5.1 for Classification by Configuration) * designates cases where drop-particle
interaction is not described and must be inferred
Date
1934
1960
1970
1970
1933
1944
Designation
(See Table
2.5.1)
Wet-wall
ESP + EIS
EIS
EIS*
EIS*
CDS- I or
CDS- II*
CDS- 1
Method of
Drop Pro-
duction and
Charging
induction
and /or ion
impact
induction
induction
induction
"frictional"
ion impact
or Induction
Particle
Treat-
ment
ion
impact
none
none
none
charged
in com-
bustion
zone
ion im-
pact
Method of
Drop Removal
electrical
precipitation
settling
space charge
precipitation
inert ial
inertlal
inertial im-
pact or pre-
cipitation
Inventor
Wintermute
Schmid
Marks
Marks
Wagner
Penney
Patent No.
1,959,752
2,962,115
3,520,662
3,503,704
1,940,198
2,357,354
Title
Liquid Flushing for
Discharge Electrodes
Apparatus for Separating
Solid and Liquid Particles
for Gases and Vapours
Method and Apparatus for
Suppressing Fumes with
Charged Aerosols
Smokestack Aerosol Gas
Purifier
Apparatus for Cleaning Gas
Electrified Liquid Spray
Dust Precipitators
CO
(D
O
N>
-------
Table 3.2.1 (cont.)
1944
1950
iQsn
I960
1967
1967
1957
1958
1968
1971
CDS-I
CDS-I
PT»C T
CDS-I
CDS-I
CDS-I
EIS &
CDS-I
EIS &
CDS-I
CDS-I
CDS-I
ion impact
or inductioi
induction
ti
ion impact
ii
it
Spinning
disk induc-
tion
induction
induction
bubbles
instead of
drops
charged by
Induction
Jion im-
pact
ion
impact
ion
impact
ii
it
ion
impact
ion
impact
"natural"
ii
inertial im-
pact or pre-
cipitation
ii
inertial
impact
ti
settling
inertial
impact and
precipitation
inertial im-
pact & pre-
cipitation
settling and
precipitation
Penney
Oilman
Peterson
ii
Romell
Ransburg
DeGraaf ,
Hass , Van
Dorsser and
Zaalberg
Ziems &
Bon i eke
Owe Berg
2,357,355
2,523,618
2,525,347
2,949,168
3,331,192
3,440,799
2,788,081
2,864,458
3,384,446
3,601,313
Electrical Dust Pre-
cipitator for Utilizing
Liquid Sprays
Electrostatic Apparatus
(Improvement on Penney fs)
it
Electrical Precipitator
Apparatus of the Liquid
Spray Type
it
Gas Scrubber
Electrostatic Gas Treating
Apparatus
Liquid Electrostatic
Precipitation
Apparatus for Disinfecting
Gases
Method and Means for the
Removal of Liquid or Solid
Particles from a Volume of
Gas
en
fl>
o
N>
-------
1961 "EFB"
1965 SAG
1972 CDS-I
drops not
charged but
polarized by
ambient
field
bubbles
surround
charged
particle
which 'bees"
its image
and "agglom-
erates" with
it
induction
in a
venturi
fric-
tional
electri-
fication
by gas
ion
impact
ion
impact
precipitation
-
"conventional"
devices ; e.g.
centrifugal
separator
Vicard
Allemann,
Moore &
Upson
Vicard
2,983,332
3,218,781
3,668,835
Process and Apparatus for
the Purification of Gases
Electrostatic Apparatus
for Removal of Dust
Particles From a Gas
Stream
Electrostatic Dust Separator
C/J
(D
r>
U)
-------
Sec. 3.2
Hence, they are not included in Table 3.2.1.
In any patent, there is always the question of whether or not what is
claimed is physically possible. Thus, the designations are based on what can
be inferred from the claims made and certainly not on proffered evidence from
a clear correlation between controlled experiments and theoretical models.
By far the most significant in the list for the use of electrically induced
collection of particulate on drops are the 1944 patents due to Penney. These
recognize the crucial difference between having collecting surfaces consisting
of electrodes firmly fixed in position and drops that are free to respond to
the electric field with even greater mobility than the particles to be collected
What is generally evident from the patent literature is an interest in
charged drop scrubbers that extends over a period of 40 years. Even so, there
is no clear identification and verification of the essential scaling issues
underlying the practicality of such devices.
Devices that use charged particles that are not drops as collection
sites are the subjects of patents summarized in Table 3.2.2. Here, some of
the limitations inherent to a drop system can be obviated. For example, the
collection site density can be made sufficiently large that the use of an
ambient electric field to polarize the sites is justified (EFB and EPB types
of devices). Also, frictional electrification is available as a mechanism
for producing collecting fields associated with the sites.
The patents of Table 3.2.2 are included because some of the most
practical applications of the concepts developed in the following chapters
probably will be to systems making use of collection sites other than drops.
54
-------
Table 3.2.2 Certain Patents Relating to the Use of Electrically Induced Agglomeration
in the Control of Particle Pollutants
Date
Desig-
nation
(See
Table
2.5.1)
1956
SAG
1960
CDS-I
Ln
1961
EFB
1961
EPB
Description
Inventor
Patent No.
(U.S. unless
otherwise
noted)
Title
Bi-polar impact charging of solid
particles used to induce agglom-
eration
Frictional electrification of
solid pellets used to induce
collection of naturally charged
or uncharged particles
Particles such as polystyrene
spheres, triboelectrified by
fluidization are used to
collect dust which is
"naturally" charged
Semi-insulating packed bed of
spheres in ambient field
collect particulate charged by
ion impact
Prentiss
Johnstone
Silverman
et al.
Cole
2,758,666
2,924,294
2,992,700
2,990,912
Carbon Black Separation
Apparatus for Cleaning Gases
with Electrostatically Charged
Particles
Electrostatic Air Cleaning
Device and Method
Electrical Precipitator and
Charged Particle Collection
Structure Therefore
CO
o
•
U)
to
-------
Table 3.2.2 (cont.)
1922
1960
1929
1939
1973
SAG
SAG
EPB
EPB/
EFB
CDS- 1
Bi-polar Impact charging of
solid used to induce
"flocculation"
Bi-polar impact charging
to induce self-agglomeration
Packed bed of electrete
particles with particulate
apparently only charged by
"natural" processes
Particles used as collection
sites in ambient a-c field.
Particulate charged by "contact"
with bed particles which flow
downward in vertical duct with
cross-flow of gas
„ . ,
oi polar impact charging used
to induce agglomeration
— • 1.
Mdller and
The Lodge
Fume Co.
Jucho
Watson
Edholm
Melcher &
Sachar
British
183,768
British
846,522
British
292,479
Swedish
96717
3,755,122
Method and Device for Separati
Suspended Particles from
Electrically Insulating Fluids
Especially Gases
Improvements in or Relating
to Electrostatic Precipitation
Improvements in or Relating
to the Separation of Impuritie
from Circulating Air, Gas, or
Vapor
Satt Att Befria Gaser Fran
Dari Suspenderade Stoft-
partiklar Jamte Harfor Avsedd
Anordning
Method for Inducing Agglomeratl
of a Particulate in a Fluid
Flow
w
n
n
N>
-------
Sec. 3.3
3.3 Literature
Once it is recognized that charge and field effects on particle inter-
actions are of interest in such widely separated areas as meteorology, colloid
chemistry, and industrial process control, it is not surprising that the lit-
erature of the basic area is extensive, in some respects highly developed,
and somewhat fragmented. There are a large number of investigations reported
on charge effects in the stability and aging of aerosols: (Fuchs, 1964; Devir,
1967; Gillespie, 1953; Gillespie, 1960; Kunkel, 1950; Muller, 1928).
Other reports relate to cloud-drop interactions with ions, particulate, and
droplets. An excellent overview of the electrical behavior of aerosols is
given by Whitby and Liu (1966). The spectrum of phenomena is, of course,
relevant to the use of drop-particle interactions in cleaning industrial
gases. The type of phenomena with which these studies are concerned is
generally in the category of self-agglomeration (SAG). As discussed in
Chap. 2, such processes are not generally useful on an industrial scale.
The large number of parameters and processes that could be brought
into play can be reduced by recognizing at the outset certain limitations
on the practical systems of interest here. First, the drops are in the
range of 10 - lOOym. Penney states that there is little point in introducing
the drops unless they themselves are easily removed (Penney, 19A4a, Table 3.2.1),
which tends to place a lower bound on the size of useful drops. He gives an
example of drops in the size range of 0.1 - 0.5mm, with lOym as a lower
bound. Typical devices such as inertial impact scrubbers, cyclone scrubbers
and the like, as well as electrostatic precipitators, begin to have limited
capabilities as the particle size is reduced much below lOvdu. Hence, lOym is
a typical lower limit on the range of drop size of practical interest.
57
-------
Sec. 3.3
Second, for industrial applications concern is with processes that occur
in seconds, rather than aging processes that take minutes or more to pro-
duce a significant effective change in particle size. This is a major reason
for considering interactions between particles and relatively large drops.
A simple collision results in a drastic change in effective size.
Considerable literature exists for studies of Interactions between
isolated "drops" and various types of charged particles. The manner in which
a particle acquires charges from a sea of ions in an ambient electric field
is fundamental to the theory of electrostatic corona charging as used in
conventional precipitators. With a primary motivation from problems in
atmospheric electricity, many authors have studied the interplay between drop
charging in an ambient field and the relative motion of the gas in which both
drops and ions are entrained (Pauthenier and Moreau-Hanot, 1932; Whipple and
Chalmers, 1944; Gott, 1933; Gunn, 1957).
As long as the particle inertia is not an important factor in the par-
ticle collection, the charged particles can be viewed as heavy ions, and much
of the theory developed in a meteorological context is helpful in understanding
the particle collection process. In the next chapters, the rate of particle
collection on an isolated drop is incorporated into models. The derivations
summarized in Sec. 6.2.1 follow most closely those of Whipple and Chalmers
(1944). With the objective of refining the theory for the collection of
extremely small particles, Zebel (1968) has extended the Whipple and
Chalmers analysis to include a diffusion boundary layer around the drop.
His analysis appears to be of value mainly because of the light it sheds on
the processes by which the particles are actually collected. The addition
of diffusion to the model allows a prediction of the diffusion boundary layer
58
-------
Sec. 3.3
thickness. For relatively strong electric forces, the charging rate is identical
to that predicted by Whipple and Chalmers.
By using ions, Gott (1933) has verified the Whipple and Chalmers model
of electrical charging. Kraemer and Johnstone (1955) consider the interactions
between a charged aerosol and a single charged or potential-constrained
spherical particle. Their work also relates largely to an inertialess rep-
resentation of the particle collisions with the spherical collector, but it
includes some numerical representations of the effects of particle inertia.
They make the comment that, in general, the effects of inertial impact and
other distinguishable collection mechanisms can be represented by super-
imposing collection efficiencies computed for the mechanisms considered
separately. This is an especially good approach if one of the mechanisms is
dominant. In this work, that viewpoint is implicitly taken.
Kraemer and Johnstone also consider effects of particle space charge on
the collection process, but do not include an ambient field. One of their
interaction mechanisms which involves the mutual attraction of charged drop
and particle charges of opposite sign is a model for the CDS mechanism. The
"-4K..," collection efficiency is consistent with Whipple and Chalmers in the
limit of no ambient electric field. Hence, their experimental observations
on the collection efficiency of dioctylphthalate aerosol particles on a
spherical collector are in agreement with the predictions of this model, and
hence lend support to its use. Complications of self-consistent field and
particle charge are addressed in the theoretical work of Smirnov and Deryagin
(1967). The effects of finite particle size and inertia are brought into the
picture in various numerical studies (Paluch, 1970; Sartor, 1960; Semonin
and Plumlee, 1966) aimed at understanding cloud drop-droplet interactions.
59
-------
Sec. 3.3
From the point of view of scrubber technology, adding electrical forces
to a conventional scrubber by charging particulate and drops should improve
the performance. Numerical modeling corroborates this expected improvement
(Sparks, 1971). But, the charging adds additional parameters to a theoretical
model, and numerical studies inherently include so many parameters that it
is difficult to achieve the physical insights necessary to understand the basic
limitations on the collection process. In the submicron range of interest
here, field effects are in fact dominant, and by exploiting this fact, the
number of parameters can be greatly reduced. It is in this way that the
basic engineering limitations can be perceived.
Not included in any of the theoretical models or controlled in any
basic experiments is the effect of gas turbulence. The turbulence referred
to here is not just in the wake of an isolated drop, but rather the turbulence
associated with the bulk gas flow. The structure of this turbulence is a
function not only of the relative motion of gas and drops, but also of the
means used to inject the gas and drops into the volume. In much of the work
to be described in Chap. 6, drops and gas are injected as a turbulent jet.
Practical devices are almost certain to involve turbulent flows. What are
the implications of the associated mixing for the rate of collection of par-
ticulate by the drops? Moreover, unanswered questions arise because the drops
unlike a mounted sphere, are free to move in response to the turbulent eddies
and to the field.
Faith et al. (1967); Hanson and Wilke (1969); Anonymous (1970) and
Marks (1971) suggest the use of charged drops for implementing a space-charge
type of precipitator. The drops are either charged by induction during their
formation at a nozzle, or by ion impact after being injected into the flow
60
-------
Sec. 3.3
of dirty gas. In either case, their self-fields are responsible for the
collection of the drops and/or particles on conducting walls. These devices
are in the category of charged drop precipitators (GDP). The use of space
charge to replace one of the electrodes in a conventional precipitator is
an application of charged drop technology that uses the conventional collec-
tion mechanisms of the wet-wall ESP. The objective is a simplification of
systems, or perhaps an improvement in capacity to handle low-conductivity
particles (Oglesby et al., 1970). Such devices are not generally percieved
as related to charged drop scrubbers, because the drops do not significantly
collect the particulate. However, there is a close relation in the sense
that, according to the arguments given in Chap. 2 and experiments presented
in Chap. 6, such devices have collection times related in a basic way to the
charged drop scrubber. The true CDP configuration is subject to the same
limitations on residence time for cleaning and drop residence time as the
CDS configurations.
Marks (1971) describes device* in which the entering particles are not
intentionally charged. The mechanism by which they are collected by the
drops before the drops are space-charge-precipitated is not specified. One
possible mechanism is EIS interactions, with the drops moving under the
influence of the space-charge field and collecting particles by inertial
impact. Such a mechanism of collection is possible in the devices described
by Hanson as well, although there the particles have the same sign of charge
as the drops, hence the Coulomb contribution to the particle-drop interaction
tends to obstruct collection.
Eyraud et al. (1966) and Joubert et al. (1964) describe the use of
charged drops for collecting submicron biological particles. Their interaction
61
-------
Sec. 3.3
is one in which the drops are introduced and charged in the immediate vicinity
of a corona wire. The arrangement is otherwise similar to that of a single-
stage tube-type precipitator. Again, the interaction mechanism is not
specified. The author cites the ease with which the drops are removed by
the precipitator, but alludes only to the mechanism by which the drops pick
up the particles (before being themselves removed) with the statement:
"Furthermore, each drop plays the role of a high-voltage electrode for a.
very limited region of the gas to be cleaned". This implies the CDS type
of interaction. However, particles and drops seem to have the same charge,
so it is difficult to see how such a mechanism can be effective. But
certainly the field-induced radial velocity of the drops caused by their
charging and the imposed electric field can lead to an EIS type of induced
inertial impact scrubbing.
A pioneering endeavor showing the advantages of using charged drops
in the CDS-I configuration to improve wet-scrubber performance is recently
reported by Pilat, Jaasund and Sparks (1974). Their work illustrates that
a conventional scrubber (INS) operating under practical conditions can in
fact have a significantly improved performance in the CDS configuration. The
experiments reported are for practical rather than controlled conditions, and
hence do not lend themselves to the quantitative scrutiny necessary to verify
laws for the scaling of such devices. More is said in Chap. 7 about the
relation of these results to the models developed in Chap. 6.
One of the main points of Chap. 2, supported by critical experiments
in Chap. 6, is that CDS-I, CDS-II and CDP types of devices are characterized
by residence times for cleaning of the same order. Moreover, operating with.
sufficient charge density to equal that provided by drops in these other
62
-------
Sec. 3.3
devices, the cleaning time for SCP devices is of this same order. Hence,
it is possible to obtain improvements in the performance of an inertial
scrubber by (i) charging the participate alone (SCP), by (ii) charging
drops and particulate to the same sign (GDP) and by (iii) charging the drops
and particles to opposite polarity (CDS-I or CDS-II), Because each of these
interactions is akin to that occuring in an electrostatic precipitator, it
is important to have the ESP as well as the INS in view in forming conclusions
as to the significance of collection efficiencies.
63
-------
Sec. 4.1
4 Electrically Induced Self-Precipitation and Self-Discharge
4.1 Objectives
By interrelating models and controlled experiments, an examination is
presented in this chapter of self-precipitation (SCP) and self-discharge
(SAG if the particles also agglomerate mechanically) in submicron aerosol
systems.
There are two broad objectives. First, unipolar and bicharged aerosols
are used as the fine particulate system in Chap. 6 where collection by systems
of charged drops is developed. Study of the dynamics of the charged aerosol
alone establishes the degree of confidence that should be associated with the
theoretical models for self-precipitation and self-discharge processes as
they occur along with other processes in the more complex systems. Also,
much of this chapter is concerned with experimental controls that are used
in Chap. 6.
Second, the SCP and SAG processes are important in their own right
for understanding charged drop scrubbers. As discussed in Chap. 2, the SCP
is in fact useful as a bench-mark in establishing how charged drop collection
devices relate to the electrostatic family of collection devices. In previous
attempts to examine SCP and SAG processes, often either the size and charge
were not well controlled, or the charge was insufficient to cause electrostatic
effects to be dominant. (For work on the SCP mechanism, see Dunskii and
Kitaev, 1960; Foster, 1959; Faith, Bustang and Hanson, 1967; Hanson and
Wilke, 1969 and for the SAG mechanism see DallaValle, Orr and Hinkle, 1954;
Devir, 1967.) This is not the case in the experiments to be described in
Sec. 4.8. An evaporation-condensation generator is used to produce an aerosol
sufficiently monodisperse that light scattering techniques may be used for
64
-------
Sec. 4.2.1
sizing. Two other devices allow the aerosol to be charged to a high level
with very little loss of particles and the magnitude of this charge to be
determined. These techniques are the subject of Sees. 4.4 - 4.7. Because
the residence time of the charged aerosol is also well controlled, all
parameters necessary to make an absolute prediction of performance are
available.
A significant result of this chapter, again brought out by the
calculations and born out by the experiments is that the loss of charged
particles either through self-precipitation on the walls or through creation
of neutral particles by self-discharge is characterized by the same time
scale T = eQ/nqb. To emphasize this point, the evolution of the particle
concentration for a variety of systems, both stationary and moving is
discussed. The results in one case from Sec. 4.2.3 are used to predict
the performance expected of the self-discharge experiment of Sec. 4.8.
Another is used to calculate a calibration curve for a device from which
both the charge density and mobility may be determined. For those not
primarily interested in experimental technique, Sees. 4.2, 4.3 and 4.8 are
the essence of this chapter.
4.2 Theory of Self-Precipitation Systems
4.2.1 General Equations
The flux density T of charged submicron particulate can be represented
for the present purposes as having contributions from self-diffusion, from
migration in the face of the electric field, and from convection due to the
motion of the surrounding gas.
"F - -D Vn + nb¥ + nv (1)
B
65
-------
Sec. 4.2.1
Here, D is the self-diffusion coefficient which can be evaluated from the
B
expression (Hidy and Brack, 1970, p. 171).
(1 * >
_Q
where X is the mean free path of the gas molecules (^6 x 10 m at STP) and
A* is a function that can be considered a constant, 1.2, for Knudsen numbers
(X/a) much less than one. The term in parenthesis accounts for the slippage
of gas around the particle and is known as the Stokes-Cunningham correction.
-10 2
As an example, for a particle with a radius of O.SMm: D_ • 1.3 x 10 tn /sec.
Conservation of particles is described by the equation
V • T + f£ = 0 (3)
a t
Given the gas velocity v, Eqs. (1), (3) and Gauss' Law
V * e "I = nq (4)
represent the evolution of the particle density. Flows of interest are
likely to be essentially incompressible, so that V • v - 0, and Eqs. (1),
(3) and (4) combine to give
22 - DRV2n - f- n* (5)
dt B E0
where
^Jl = ia + (v + bi) . Vn (6)
Hence, the left hand side of Eq. (5) is the rate of change with respect to
time of the particle density as seen from the frame of reference of one of
the particles. (With diffusion included in the model, this particle is
defined in an average sense.) The local density decreases for two reasons
66
-------
Sec. 4.2.1
represented by the terms on the right in Eq. (5): diffusion away from regions
of elevated density and migration away from regions where the space charge
generates a field tending to make the like charges repel.
Effects of Brownian Diffusion The gradient in particle concentration
giving rise to diffusion is typically caused by the presence of absorbing
surfaces. From Eq. (5) it is evident that in a system characterized by a
length scale I between these absorbers, appreciable particle removal occurs
in times of the order T. such that the rate of change on the left is
- D r
dc V
accounted for by the diffusion term on the right; n/T, = D n/d2. Hence,
Tdc " ^DB ^7)
As a typical example, particles of 0.5ym radius between absorbers having a
6
spacing & - 1cm will be lost to the walls on a time scale of T, ™ 7.7 x 10 sec.
Clearly, particle removal by Brownian diffusion is unimportant in processes
that must occur in seconds or less. The actual time scale is determined by
the term that dominates on the right in Eq. (5). If the second term dominates,
then similar dimensional arguments show that the characteristic time is
t « e /nqb. If attention is again focused on aerosol particles O.Sym in
radius with a charge and within a field typical for the highly charged
aerosol systems to be considered: b - 10 m/sec/V/m and nq = 10 coul/m ,
then T - 1 sec. In laminar or turbulent flow, the length scale & determining
EL
the diffusion is the thickness of a boundary layer and so can be small
enough to greatly reduce T , . But even with layers having typical thicknesses
-4
of 10 m, the time scale for dlffusional deposition is too long to be of
interest.
67
-------
Sec. 4.2.2
4.2.2 Laminar Flow Systems
In the absence of the diffusion term, Eq. (5) can be integrated to give
T = _o _ ,Q*
' '
•. i+ ' •'
Remember that this expression pertains to a particle of fixed identity which
when t » 0 is surrounded by particles having density n , and which moves
along the particle line
~ - bE + v (9)
Hence, to evaluate the detailed distribution of n, specification must be made
of the geometry and boundary conditions which (together with Poisson's equatto 1
determine E. Some examples show how the Eqs. (8) and (9) can be used to
establish a qualitative and even a quantitative description in specific cases
Closed Volume of Still Gas A closed container having walls that are
not sources of n initially filled uniformly with particle density n will
self-precipitate particles on the wall in such a way that the density every-
where is either given by Eq. (8) or is zero. Thus, at any instant, the volum^
is filled by regions of zero density and uniform density given by Eq. (8).
To see this, consider that an arbitrary particle moves from some location (a)
when t = 0 to a second location (b) also within the volume in time t. The
density at location (b) is given by Eq. (8). During the same interval of
time a particle at some other location (c) has moved to the position (a).
Because Eq. (8) also applies to this particle (if the position (c) is within
the volume) then the density at (a) after the time t has elapsed is the same
as at (b). The points are arbitrary, so it follows that the density decays
68
-------
Sec. 4.2.2
throughout the region connected by particle lines (Eq. (9)) to points within
the volume in a uniform fashion. The exception comes from the cases where
a particle line originates at a boundary. In that case, the density along
the line is zero because there is no source of particles at the wall.
Flow Through Duct of Uniform Cross-Section Even though a steady-state
process when pictured from the laboratory frame of reference, the evolution
of the particle density in a duct (for example a space-charge precipitator)
is nevertheless represented by Eq. (8). Let the flow be fully developed and
in the z direction: v « U(x,y)i . If the duct cross-section has a smallest
z
dimension that is short compared to distances over which the charge density
associated with the particles decays appreciably, then the electric field
is essentially transverse E * E , and Eq. (9) for the particle trajectories
becomes approximately
£ = bET + U(x,y)iz (10)
For slug flow with particles introduced at z » 0 with a uniform density
profile n *• n at z = 0, the decay of density follows by first recognizing
that the z component of the particle trajectories, Eq. (10), is
and since this expression can be integrated and substituted into Eq. (8),
- i
(12)
n i . z
o 1 + —
UTa
The effective time is simply the transport time, in this case the same for
69
-------
Sec. 4.2.2
each particle at a given location z.
If the profile of either the velocity or the density is not uniform,
the relation between the particle time (in terms of which Eq. (8) is
represented) and the position in the duct is determined in part by Gauss'
Law. In Sec. 4.8 experimental study is made of the self-precipitation in a
cylindrical duct. Although Eq. (12), evaluated with U the mean flow velocity
gives a reasonable picture of the density decay, a more detailed theory
recognizes the parabolic velocity profile. A straightforward numerical
analysis, in which the particle density is taken as uniform at z = 0, first
recognizes that the particle density is given by Eq. (8) along the lines of
Eq. (9), which become
dz = 2U[1 - (f)2]dt
dr = bE (r)dt
(13)
where U is the mean velocity and R is the duct radius. From the first of
these expressions, the particle originating at some radial position r in the
z=0 plane reaches the plane Az in the time At = dz/2Ufl - (—) ]. Its
K
density there follows from Eq. (8) while the change in radial position is give
by Eq. (13b), which can be approximated using the electric field evaluated
in the z = 0 plane. Because E is purely transverse, it follows from Gauss'
Law that this field is
dr (14)
o
so that given n(r), E (r) follows by integration. The density profile is
thus found at the plane z - Az, in turn the electric field in this plane
70
-------
Sec. 4.2.2
is determined from Eq. (14) and then the process repeated to find the profile
in the plane z = 2Az.
Figure 4.2.1 shows the evolution of particle density found by including
the detailed effect of the parabolic velocity profile. The spatial decay
of the particle flux is compared to the decay of the slug flow and to an
experiment in Fig. 4.8-2.
n/n
UT_
- 0
- 1
I I I 1 1 1 1 L
-1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0
1 1 1 1 1
n/no
1 1 1 1
_£_. o
UT.
- 1
- 2
m d
- 3
i i l l i
1.0 -0.8 -0.6 -0.4 -0.2 0
iiii
0.2 0.4 0.6 0.8 1.0
r-c«
•) Poiseuille Flow
r-c»
b) Slug Flow
Fig. 4.2.1 Self-precipitation in a cylindrical channel with radius 0.95cm
carrying a flow with F - 1.08 x 10~ m /sec
Because the precipitation field is due to the charge itself, it is to be
expected that the rate of decay, whether it be temporal or spatial, is
typically slower than that associated with "imposed" field systems such
as the conventional precipitator. Fig. 4.2.2 makes a comparison of the
typical decay laws to emphasize this point.
71
-------
Sec. A.2.3
10
Fig. 4.2.2 Comparison of typical decay laws for self-precipitation and
"imposed" field types of devices.
4.2.3 Turbulent Flow Systems
If the gas is in a state of turbulence, then the density distribution
of a submicron system of particles is strongly influenced, even when the
mean flow is zero. Nevertheless, the ubiquitous time constant T retains
a
its significance. To see this, consider limiting cases in which the turbulence
completely dominates and renders the distribution of particles uniform
throughout the volume of interest.
Closed Volume of Gas With no Mean Flow If a container having volume
V enclosed by a surface S is filled with charged particles and kept thoroughly
mixed, perhaps by means of a mixing vane or a fan, the integral form of the
particle conservation equation gives the rate of loss of particles to the
72
-------
Sec. 4.2.3
walls directly. Because there is no normal velocity at the walls,
•fr J ndV - - r nbl • nda (15)
dt V S
This expression applies in general. But because the mixing guarantees that
the distribution of n is uniform, and because Gauss' Law relates the total
flux of E normal to the container to the total charge enclosed, Eq. (15)
becomes
(nV) - -nb $ E • nda - -nb(M) (16)
Hence, the volume V of the container cancels out and the decay in density is
predicted by the familiar expression
dn 2,
" ~
The solution is again given by Eq. (8)
Steady Flow Through Region With Complete Mixing The remarkable fact
is that because of Gauss' Law, self-precipitation is at most influenced very
little by the specific nature of the geometry. In the cases of complete
mixing, the geometry has no effect. This is further illustrated by considering
an important type of situation in which particles enter and leave a volume V
(of arbitrary geometry) entrained in a gas having the volume rate of flow F.
Under steady state conditions, conservation of particles requires that
F(nln - nout) - * nbE • nda (18)
S
With complete mixing within the volume, n is constant over the enclosing
73
-------
Sec. 4.3.1
surface and equal to the density n at the exit. Under the assumption that
the electrical contribution to the flux of particles at the inlet and outlet
of the container can be ignored, Eq. (18) becomes
"out
This expression can be solved for the exit particle density n . Definition
of the residence time as T = V/F (see Sec. 2.1) and T = e /n. qb makes it
res a o in
possible to write this expression in the form
"out _ ,
nin res a
to again emphasize the crucial role of T relative to the residence time.
EL
The dependence of n ../n, on T /T is shown in Fig. 4.8.4 which compares
•**•* in, tGS cl
this prediction to experimental results.
4.3 Analysis of Self-Discharge Systems (SAG)
4.3.1 Mechanisms for Self-Discharge
Langevin and Harper Models In the previous sections, it is clear how
the space charge of the unipolar aerosol particles generated an electric
field which resulted in the drift of these charged particles toward the
boundaries. However, in the case where the system contains equal amounts of
positive and negative particles, so that no macroscopic electric field is
created, the model which represents the drift of oppositely charged particles
under the influence of their mutual fields is not as straightforward. Whereas
before the Brownian motion of the particles could be ignored because the
electric field generated by reasonable particle densities resulted in a
74
-------
Sec. 4.3.1
relatively large drift velocity, here it cannot be so easily dismissed. In
its most primitive idealization the pertinent electric field is that of a
charged sphere, which decays inversely with the square of the distance.
At reasonable separation this results in such a small drift that often it
cannot compete with diffusion processes.
To arrive at some criterion for deciding whether diffusion or migration
is dominant, it is helpful to reduce the problem to one of two oppositely
charged spheres, as shown in Fig. 4.3.1. The equation governing the separation
between the spheres can be reduced to (Harper, 1932)
Fig. 4.3.1 Self-discharge model consisting of a pair of oppositely charged
particles
75
-------
Sec. 4.3.1
dr
o
where the first terra on the right side of the equation includes the effects
of diffusion and the second the effects of electrostatic attraction. Here,
both q and b are defined positive. The diffusion coefficients are determined
by the Brownian motion of the particles (Eq. A. 2. 2) and are constants, independent
of the particle separations. This will not be true in the case of turbulent
diffusion to be examined in the next chapter. From this equation it is clear
that there exists a finite sphere of influence for the forces of electrostatic
attraction. If the particles are initially separated by a distance greater
than a , where
(l+b_ +
ao =
(D+ + D_T '
then a collision will not occur. However, if the initial separation is less
than a , coalescence between the two spheres will take place. Within a
constant factor, the above critical distance corresponds to the separation
at which the thermal energy of the spheres equals that required to separate
them by an infinite distance. For initial separations less than a the gas
is incapable of giving the spheres sufficient energy to achieve complete
escape, while for greater initial separations it can.
Next, consider the situation where instead of just two isolated
spheres, there are an infinite number of oppositely charged ones distributed
in such a way that over dimensions large compared with the initial particle
separation r , there is no macroscopic (ambient) electric field. The
objective is to find the rate at which charged particles are lost from the
76
-------
Sec. 4.3.1
system. (It is assumed from this point on that the oppositely charged
spheres have the same magnitude of charge. If this condition were not made,
then the system could not be specified by just three species of particles:
positive, negative, and neutral. Depending on the differences between the
initial charges, additional species would be generated. This considerably
increases the complexity of the system. An example of how such a process
can be dealt with is found in the classical literature on Brownian coagulation
of aerosols (Overbeek, 1952).) To begin, assume that r is small compared
with a . Then the interparticle electric fields will be dominant in determining
the motions of the particles. The rate at which negative particles drift
across a sphere of some arbitrary radius smaller than r surrounding a
positively charged particle is on the average
G_ « $ n_v_ • da -
This is the rate at which a single positive sphere removes negative ones from
the system. Remember that the mobility b of a particle is defined as a
positive quantity. In a unit volume, the total rate at which negative
particles disappear through this process would be
+ b )
-------
Sec. 4.3.1
where it is termed the Langevin or very high pressure limit (Cohine, 1958;
Thomson and Thomson, 1969) .
To see the significance of this result, consider the opposite extreme
where the initial separations are large compared with the radius of the
electrostatic sphere of influence. A different view of the recombination
process must be taken. The motion of the particles is dominated by diffusion
until they approach the central particle to within a distance a . Once
that point is reached, they are guaranteed to be captured. Thus, the
calculation becomes one of strictly diffusion with the conditions that the
charged particle density be some constant far away from the central oppositely
charged sphere and be zero at the distance a . The rate at which these
particles diffuse into the sphere of electrostatic influence is then (Hidy
and Brack, 1970, p. 177):
G± = 47T(D+ + D_)a0n± (6)
In ion recombination this limiting situation is termed the Harper or high
pressure model.
If the expression for the radius of the sphere of influence, Eq. (2)
is substituted into Eq. (6), it is consistent with the Langevin model, Eq.
The same expression for aerosol recombination is applicable independent of
the initial concentration, even in the extreme case where actually diffusional
effects are chiefly responsible for bringing oppositely charged particles
together.
ti
Effects of Debye-Huckel Shielding One final observation should be made
In both of the previous developments the field responsible for the drift of
the charged particles toward an oppositely charged central sphere is assumed
78
-------
Sec. 4.3.1
to be determined just by the charge on the central one. The collective effects
of the other charged particles are ignored. An estimate for this effect
can be made in the limit where Brownian motions dominate the electrical ones
in these outer regions. This theory, first developed by Debye and Huckel
for strong electrolytes (McDaniel, 1964), confirms that the other charges
produce a shielding effect that causes the electric field to decay much more
2
rapidly than 1/r . The result indicates that for distances greater than a
Debye length, defined as
JekT
?«A
the charged particles are fairly well screened from the influence of the
central one.
In the case where there are just two species of equal size carrying
equal, but opposite charges, and the density of each species is related to
its mean spacing by
(8)
o
with the use of Eq. (4.2.2), the expression relating the three critical
lengths of the system becomes
(9)
If 1/4TT is approximated by one it follows that the three lengths can follow
one of two possible ordering schemes:
79
-------
Sec. 4.3.2
a < r < a (lOa)
o o db
a. < r < a (lOb)
db o o
If case (a) is the correct relation for a given physical situation, then
11
use of the Debye-Huckel potential is justified. However, this leads to a
very small modification of the coagulation rate (Hidy and Brack, 1970, p. 300)
If the particles are so highly charged that case (b) applies, the Debye-
Huckel picture no longer applies. It does not make sense to speak of a Debye—
ii
Huckel length that is small compared with the mean particle spacings. Since
a > r , the coagulation process will be determined by the drift of the
particles in their mutual electric fields. This rate (Langevin) has been
previously shown to equal that of case (b) (Harper, 1932). Thus, the
shielding can be argued to have little influence on the agglomeration rate
of the system.
12 3 —7
As an experimentally typical case, let n =10 /m , b = 10 m/sec/V/m
DD - 10 m /sec, and q = 10 coul. These values imply that both r and
o o
a are on the order of lOOMm, and a,, is approximately lOym. Thus, neither
diffusion processes nor electrostatic ones can be considered dominant.
However, since both limiting models yield the same discharge rate, it seems
reasonable that the same expression will also apply in the region in which
both are of equal importance.
4.3.2 Self-Discharge Dynamics
Conservation of either the positive or the negative species of particles
within a fixed volume V enlosed by the surface S can in general be represented
by
80
-------
Sec. 4.3.2
n+dV - - <|>+dV - > I\. • nda
" ~ ~
where F is given by Eq. (4.2.1) without the diffusion term and 4>+, given by
Eqs. (4) and (5) , represents the particles lost due to discharge with particles
of the opposite polarity. With Eqs. (4) and (5) representing the latter, for
incompressible flow (V • v « 0) and with recognition taken of Gauss' Law,
(V * e E * n.q. - n_q_) Eq. (11) becomes
3n+ _ _ -n n q(b + b ) n+b+
—=- + (v ± b±E) • Vn± - - * -^
3t v " ± ' ± e
o
(12)
This expression includes both effects of self-discharge and self-precipitation.
However, if the particles are injected into the system in pairs, or initial
conditions preserve charge neutrality at each point within the volume and
electrodes are not used to impose an ambient electric field, then space
charge neutrality is maintained. This is seen by assuming at the outset that
n » n = n, b » b_ = b so that Eq. (12) reduces to
and observing that Gauss1 Law is then identically satisfied by E « 0
because n+
-------
Sec. 4.3.2
with a solution
"ITTxT" T a 2no(x)qb
As anticipated by the discussion in Sec. 2.4, Eq. (15) states that if the
particles are initially uniformly distributed, then the decay is of the
same form as discussed for self-precipitation. In fact the time constant
T is the same if it is defined in terms of the total charged particle
3.
concentration 2n . If the initial concentrations have some spatial
o
distribution, then the subsequent decay at a given point can be described
by the above relation with a time constant based on the initial conditions
at that point.
Convective Systems For fully developed flow in the z-direction so that
v = U(x,y)i and steady-state conditions Eq. (13) becomes
"Zt
O(x.y) H - - *&• (16)
Unlike the situation for self-precipitation, no conditions on the particle
concentration at z = 0 are necessary to be able to find a solution to Eq. (16)
/ ^ i U(x,y)e
n(x.y.z) _ ,, , z x-1. o /•„ v\ __ 2__ /17v
n\x,y) - (1 + £ (x,y)) ' VX'y) ' 2n (x,y)qb <17>
Q ci U
The implication is that the concentration along every particle line (x,y) v
decay at rate determined by its concentration and the velocity at z = 0.
If the time constant Tfl is based on the total charge concentration, slug flow
82
-------
Sec. A.3.2
with a concentration that is uniform across the inlet gives rise to a self-
discharge process that is described by an expression identical to the one
for self-precipitation.
o a on
In experiments to be described in Sec. A. 9, the quantity measured
is the fraction of the original flux of charged particles that remains at
some position downstream. The flow for that experiment is modelled as plane
Poiseuille (boundaries at x » ±s/2 and y = 0, where w » s)
U(x)=Uc[l- ()]; U- (19)
and the concentration is essentially uniform at the inlet. The volume rate
of gas flow is F, while the total entering particle flux is given
s/2
Y -f wn U(x)dx = n F (20)
O ) 0 0
-s/2
Downstream the total particle flux becomes
s/2
Y - / wn(x,z)U(x)dx (21)
-s/2
After integration and normalization to the input flux, the fraction of the
aerosol that has not been discharged at a location z downstream is found to
be (Dwight, 1961)
Y(z) , 3
(1 -
Y 2 \ "^ r r- • M -' i » (22)
83
-------
Sec. 4.4.1
2n qbz
where D = I + —~^ —
o c
This expression is compared to experimental results in Sec. 4.9.
4.4 Generation of Monodisperse Submicron Aerosols
4.4.1 Classification of Techniques
Several of the methods for producing monodisperse particles in the
range of lOOym in diameter can be modified to manufacture submicron
aerosols (Browning, 1958). Perhaps the easiest is the dispersion of a
powder. Besides being commercially available, there are several types of
aerosols that occur naturally, such as lycopodium spores. The problem is
to find a means of easy dispersal, because the presence of moisture and tribo—
electric charges causes the materials to cake. The dispersion difficulty
can be overcome if the particles are mixed with a liquid to form a suspen-
sion, and the latter is atomized, and then heated until all the liquid has
been evaporated. The difficulty here lies in guaranteeing that each droplet
formed contains only one particle. If this is not true, the aerosol will be
quite polydisperse. In addition, droplets that contain no particles will
form residues after evaporation and contribute to the non-uniformity of the
particle size distribution. There are also ways of controlling the atomization
process of a pure liquid to produce uniform droplets, as through vibration
of an orifice plate. Unfortunately, these methods become very difficult in
the small size ranges desired.
There is a broad category of techniques, involving condensation, which
work particularly well in this regime (Fuchs, 1966). Basically, they consist
of vaporizing a material and then allowing it to recondense in a controlled
manner. This is usually accomplished by allowing it to cool slowly in the
84
-------
Sec. 4.4.2
presence of condensation sites. If the latter were not included, the vapor
would either condense on the walls of the container or, if the vapor became
very supersaturated, would spontaneously recondense, forming a polydisperse
aerosol. A device of this variety is used in the experiments and will be
described in greater detail in the next section.
4.4.2 Liu-Whitby Generator
This particular approach was first developed by Sinclair and LaMer
(LaMer, Inn, and Wilson, 1950). Their method was considerably simplified
by Rapaport and Weinstock (1955) and still further refined by Liu and
Whitby (Liu, Whitby and Yu, 1966; Tomaides, Liu and Whitby, 1971). In its
present version (Figs. 4.4.1 and 4.4.2), the process begins with the
atomization of a solution of a very volatile material and a relatively in-
volatile one. In these experiments the former was selected to be ethyl alcohol
and the latter dioctylphthalate. This dispersion is accomplished with a
collision atomizer (Green and Lane, 1965), which produces an aerosol in the
range of about a micron in diameter. The particle laden gas then passes through
a heated zone with the temperature adjusted so that all the material is
vaporized. The vapor laden gas then passes through a drift zone where it
slowly recondenses onto sites corresponding to the impurities in the
original solution that remained after the evaporation of each drop. This
process is not uniform across the channel, as can be seen from the conical
condensation zone. This tends to cause the particles near the wall to be
slightly different in size from those in the middle (Nicolaon, Cooke, Dans,
Kerker and Matijevic, 1971). If an especially monodisperse aerosol is
desired, Just the central region should be sampled and the remainder dis-
carded. The size of the particles produced can be varied by altering the
85
-------
Sec- 4.A.2
1/8" ORIFICE
COMPRESSED
PREPURIFIED
NITROGEN, 15 PSI
5.1 LITERS
MINUTE
1
THREE ORIFICE
COLLISION
NO. 65 DRILL HOLE
MADE FROM STANDARD
COPPER FITTING
40 MESH SCREEN
HEATING TAPE, l"x4FT.
(384 WATTS WITH LINE VOLTAGE)
110 V
VARIABLE TRANSFORMER
20"
2 CM. I.D. PYREX
GLASS TUBE
NO. 47 DRILL HOLE
NO. 74 DRILL HOLE
4 H
1 VALVES , f
I
-------
Sec. 4.4.2
COMPRESSED GAS INLET
AEROSOL OUTLET
BAFFLE
SPRAY OUTLET
i — LIQUID FEED PIPE
Fig. 4.4.2 Collision atomizer (Liu, Whitby and Yu, 1966)
percentage of DOP in solution from a maximum of about lym in diameter when
pure DOP is used. This variation of size with concentration and the
recommended heater voltages are given in Fig. 4.4.3 for the device described
by Liu and Whitby. These should serve as an estimate only. Methods for
checking the actual size of the particles produced in a given situation will
be discussed in Sec. 4.5.
The device requires approximately 15 minutes to warm up and operates
quite stably and reproducibly over extended periods of time if certain
87
-------
Sec. A.A.2
precautions are taken. First, the solution will tend to degrade over a
period of time, resulting in a polydisperse aerosol. The presence of water
hastens this process. For this reason the solution cannot be stored for
prolonged periods, and pure ethyl alcohol, rather than denatured alcohol,
should be used. It is important that the aerosol should not be overheated.
The proper value of the heating tape voltage can be determined by setting
the pressure at the desired level and examining the Tyndall spectra of the
output as the voltage is raised. The aerosol will appear polydisperse for
voltages too low and too high. As indicated, the size is determined
principally by the percentage of DOP in solution. However, the velocity at
which the aerosol flows through the heating and condensation zones, hence the
pressure applied to the atomizer, is also an important factor. Any time that
the pressure is altered to change the aerosol flow rate, the heater voltage
will have to be reset, and the size of the particles should be rechecked.
The curve of Fig. 4.4.3 should be regarded as approximate, and the size
checked from the Tyndall spectra prior to each experiment.
!—\ T
10
t.o
0.1
0.01
T
T
I
I
I I
I I
10
100
Fig.
4.4.3
0.001 0.01 0.1 1.0
DOP CONCENTRATION, Z
Calibration curve showing the variation of the number median
diameter of the aerosol with the volumetric concentration of DOP
in the atomizer
88
-------
Sec. 4.5.1
4.5.1 Light Scattering by Small Particles
Since the particles produced by the generator are so uniform in size,
relatively simple optical methods can be employed for sizing. The procedures
to be described are relatively uncomplicated and can be included in the
start-up operation of the system. Before these methods are described in
detail, it would be helpful to review several general aspects of the phe-
nomena. The problem is usually posed in the following way (Fig. 4.5.1)
(Van De Hulst, 1962). Monochromatic light of wavelength A is incident on
A*
a sphere of radius a and refractive index n^. A plane of polarization is
then defined by the incident and scattering directions. The incident
radiation is resolved into two perpendicular components, one in the plane,
E , and the other perpendicular to it, E . The light scattered can then
ol or
also be resolved into a parallel and a perpendicular component. The first
is a function of only E ,, and the second just of E . In terms of the
amplitude of the incident radiation and its orientation to the scattering
plane, the scattered far-field can be expressed as
(1)
Many radii away from the particle, these fields decay inversely with the
distance from the sphere, independent of the particle size. The angular
dependence is, however, a strong function of the size and the physical
nature of the particle.
If the particle is very small compared with the wavelength of the
incident radiation, the scattering is termed Rayleigh. In that case the
89
-------
Sec. 4.5.1
perpendicular component leads to uniform scattering and the parallel com-
ponent to a variation that equals the perpendicular in the forward and
backward directions, but decays to zero in directions perpendicular to the
direction of the incident beam. For reference, the scattering functions are:
•= jof;
ja| cos0;
_ 2ira
I- X
(2)
si
Fig. 4.5.1 Light scattering from a single sphere
As the particle size increases and becomes comparable with the wavelength of
the radiation, the scattering is classified as Mie. The patterns begin to
acquire structure, as evidenced by the development of lobes in several
directions, with the major peaks occurring in the forward and backward
directions. The number and position of these peaks is strongly dependent
90
-------
Sec. 4.5.2
on the ratio of the circumference of the particle to the wavelength of the
light, a. , and the refractive index of the droplet material, n«. As the
radius increases further, much of the scattering is concentrated within
a steadily decreasing angle about the forward direction. This is termed the
diffraction limit, because the pattern in the forward direction begins to
resemble the Fraunhofer pattern for light incident on a disk or a circular
aperture:
ct2J (asin8)
si(e)
Since the size of the submicron particles of interest is commensurate with
the wavelength of visible light, optical techniques can be used to take
advantage of the complex Mie patterns produced. In fact, it is possible
to accurately size an aerosol from about 0.1 to about l.Oym in diameter.
4.5.2 Higher Order Tyndall Spectra
If instead of monochromatic light, a distribution of wavelengths, as
emitted from an incandescent source, is incident upon these submicron par-
ticles, it follows that the scattering will be the superposition of many
patterns, each attributable to a different wavelength. As noted previously,
the patterns will in general have peaks in different locations, except in
the forward and the backward directions. Physically, this implies that if
white light is directed at the particle, the scattered light will appear
colored. The larger the particles, the greater the number of peaks in the
patterns and consequently, the more times the spectra orders are repeated.
By noting the position and the number of peaks of a selected color, an
estimate can be made of the size (Sinclair and LaMer, 1949; Kitani, 1960).
To quantify this, the scattering patterns for all the wavelengths in this range
91
-------
Sec. 4.5.2
can be evaluated. The approach that is usually taken is the following.
Red (X = 0.629ym) is selected as the color, and its pattern calculated
numerically (Gumprecht and Sliepcevich, 1951; Zahedi, 1974), as well as
that for green (X = 0.524um). The latter is chosen because the eye is most
6
sensitive to this wavelength, and, since both colors are contained in the
incident radiation, the scattered red radiation must be at least as large
as the scattered green to be seen as red. The peaks in this ratio are the
angles at which red will be seen. The variation of these angles for OOP
(nn= 1.486) is shown in Fig. 4.5.2. The circled points indicate situations
in which a peak exists but has a magnitude less than one. Thus, the scattered
radiation appears green.
6.0
5.0
Br.d
4.0
J.O
2.0
I
e
e
e
e
o
e
•
e
o
o
1 >
o
e
e
o
e
e
a
e
e
e
'o ' -'o »
e
e o
I I
o
o
e
«
e
e
c
e
o
e
o
o
e
e
e
o
e
o
o
©
o
e
e
e
o
e
o
e
e
o
e
e
o
o
e
o
o
e
o
o
e
e
o
e
e
e
©
e
o
o
o
o
e
e
o
o —
o _
o
e -
e
e -
o
o _
e
o
e
e
e
o
o
e
o
e
e
e
e
e
o
20
40
60
120
140
160
ISO
Fig. 4.5.2 Tyndall red angular positions for DOP. Each point is numerically
calculated. Circled points indicate a peak, but for which the rati
of red to green is less than unity.
QO
-------
Sec. 4.5.2
The apparatus used is deceptively simple (Fig. 4.5.3) (LaMer and
Sinclair, 1943). It consists of a sealed chamber with inlet and exit
ports and an observation window. Light from a high intensity incandescent
bulb is made parallel by a lens and focused across the chamber into a light
trap on the other side. The entire structure is then rotated past the
observation point. Because the incident light is unpolarized, the patterns
of the parallel and the perpendicular components are superimposed.
AND EXIT PORTS
I
1.2 cm
T
LIGHT TRAP
3" DIAMETER CTLISLR1CAL
BRASS CHAMBER. 1" HIGH
BRASS
LJ ' j
/ l ;
f \ \l
X
/
1
^ — -
SN
I
f
FOCUSING LENS HIGH INTENSITY LIGHT
PYREX WINDOW
POLAROID FILTER WITH TRANSMISSION
AXIS PERPENDICULAR TO PLANE OP l~
PAPER
1.2
cm
ALL INSIDE SURFACES ARE BLACKENED.
"18 cm
V
Fig. 4.5-3. Tyndall spectra observation device ("Owl")
A polaroid filter is used to select just the perpendicular component since
this usually leads to a sharper pattern. In a typical experiment the angles
corresponding to the reds are noted and then sought in the calibration curve
of Fi8- 4-5.2. As can be seen from the figure, the curve does not vary
93
-------
Sec. 4.5.3
smoothly but advances in jumps. This sets a limit of the order of a few
hundreclths of a micron on the resolution attainable with this method. Due to
the overlapping of the patterns for an aerosol that is not precisely
homogeneous, there is an upper limit on the size. If a becomes less than
about 2, the pattern starts to resemble the Rayleigh case. The peaks
broaden to such an extent that it becomes almost impossible to localize
them. In this region it is usually necessary to employ the method re-
lying upon the polarization ratio, to be described in Section 4.5.3. If
no colors are visible in the scattered radiation, only a diffuse white light
the aerosol is polydisperse. The two most frequent causes are incorrect
heating in the generator and a decomposed solution. If properly adjusted,
the generator will always produce an aerosol which exhibits Tyndall spectra.
The colors will not be deep reds, blues, and greens, but will be somewhat
dampened. The reds, for example, will appear a bright pink. For this reason
the method requires some practice and patience, and must usually be performed
in a darkened room.
4.5.3 90° Scattering Ratio
In the event that the particle size is so small that the location of
the single red occurring near 90° becomes unresolvable, the polarization
ratio can be used in some cases to give an estimate of the particle radius
(Heller and Tabibian, 1962; Maron, Elder and Pierce, 1963; Laller and Sinclair
1943), If unpolarized light is incident upon the sphere, then the ratio of
the intensity of the parallel scattered radiation to the perpendicular portion
leads to a curve as given in Fig. 4.5.4 for DOP. For very small radii the
ratio appraoches zero, as is expected from the previous discussions of
Rayleigh scattering. For a given wavelength, the ratio at first increases
94
-------
Sec. 4.5.3
V1!
1.0 _
1.0
2.0
3.0
4.0
5.0
Fig. 4.5.4 90° scattering ratio for DOP
with radius, until it reaches some maximum value and then begins to oscillate.
Since a value of the ratio does not necessarily correspond to a unique value
of the radius, additional information giving a rough estimate of the size is
usually required. For this generator the calibration curve of the radius
versus DOP concentration is usually sufficient. Even with this information
it is difficult to deduce the correct average radius from some measurements.
Any real aerosol will be distributed over a range of sizes. In the case of
the Tyndall spectra this does not cause irreparable harm, because the
calibration curve varies relatively slowly. Here, however, even a relatively
small standard deviation of the particle size distribution can cause
aignifleant errors, first because the ratio varies very rapidly with a in
some regimes, and secondly because it oscillates as a ranges over a fairly
95
-------
Sec. 4.5.4
small spectrum.
In spite of its shortcomings the method does give valuable informa-
tion relatively easily. Experimentally, the technique is straightforward.
Unlike the Tyndall approach, the wavelength here is fixed. This means
that a laser is used as the light source. If the laser is polarized, then
it is usually most convenient to orient the polarization vector at 45° with
respect to the scattering plane. (It should be noted that some lasers that
claim to be unpolarized actually are polarized. Even worse, this polarization
oscillates at a relatively slow frequency (1 Hz) between two perpendicular
directions and is especially inconvenient experimentally.) The aerosol is
injected into a blackened chamber (Fig. 4.5.5) together with a second source
of clean air. This accelerates the aerosol into the single outlet and
produces a stable filament. The intersection of the laser beam and the
filament defines a relatively small scattering volume. The detector is
usually a photomultiplier tube with a Polaroid filter covering its input.
The tube is placed far enough away from the scattering volume that the solid
angle intercepted by the detector is relatively small (1.5 x 10" steradian).
In performing a measurement the polaroid is oriented first in the plane and
then perpedicular to it, and the ratio between the two measurements formed.
One other precaution should be taken. In some cases the photomultiplier
tube will have different responses to the different polarizations. This
point should be checked before any data is taken.
4.5.4 Extinction
If a parallel beam of light passes through a region containing
aerosol particles, then the amount of power remaining In that portion of
beam propagating in the forward direction will diminish according to
96
-------
Sec. 4.5.4
AEROSOL INLET
CLEAN AIR INLETS
LASER POLARIZED AT 45° AND PROPAGATING
INTO PLANE OF PAPER
POLAROID FILTER ORIENTED IN PLANE OR
PERPENDICULAR TO PLANE OF PAPER
. 6 ctn
f
7.5cm
AEROSOL OUTLET CONNECTED
TO ASPIRATOR
TO PHOTOMULTIPLIER
(RCA 931)
Fig. 4.5.5 90° scattering apparatus
(Lothian and Chappel, 1951):
(4)
where A is the cross-sectional area of the beam and i(z) its intensity.
In the limit of small concentrations and short path lengths, this can be
approximated by
KO) -
M _
(5)
1(0) ~ tuxsi
A condition for the application of these relations is that the particle
concentration be dilute enough for secondary scattering to be ignorable.
One criterion for this is that the particles be separated by at least 100
radii (LaMer and Sinclair, 1943). For aerosols produced by the Liu generator,
this will always be true. If the size of the particles is known, then such
97
-------
Sec. 4.5.4
a measurement will yield the particle concentration upon evaluation of
the extinction coefficient KS£. As with the previous scattering parameters,
Kg£ is a function of o^and n^. Such a variation is given in Fig. 4.5.6 for
the case of DOP. K „ increases from zero to a rather broad maximum in the
range of a from 3 to 5, and then begins to oscillate. If the curve were
extended to very large a^, the extinction coefficient would be seen to
approach a limiting value of 2. Thus particles very large compared to the
wavelength scatter twice as much light as is incident upon an area
corresponding to their geometrical cross section.
i.o
Fig. 4.5.6 Extinction coefficient for DOP spheres as a function of da
If the particles are not monodisperse or the radiation not monochromatic
then an appropriate averaging procedure must be used. Fortunately, there is
a range of o^ for which K . is relatively constant. By using a laser as a
light source and using particles monodisperse enough to exhibit Tyndall
spectra, the variation of a can be made to lie within this band.
98
-------
Sec. 4.5.4
The above relation also contains the conditions that the incident
beam be parallel, i.e., have no divergence, and the detector be sensitive
to only the forward traveling radiation. One method of accomplishing this
with a point source is shown in Fig. 4.5.7. If a laser is used, the condition
on the incident beam is well satisfied even without the use of a pinhole and
lens arrangement. However, such is not the case with the detector. Depending
on the acceptance angle of the detector, 8., the value of the coefficient K .
Q 8 *
to be used in interpreting experimental results may have to be modified
(Brillouin, 1949). For a finite angle, radiation will be detected which
the above calculation assumes to be scattered. For visible wavelengths and
submicron particles this effect can usually be ignored if the detector angle
is less than about 5 degrees. If the a is large (ct^ > 50), then to exclude
all the scattered light the detection angle must be extremely small (6, < — ).
SOURCE
••?• ••*
•
*/.*.• •.••••*•.*.••
COLLIMATING LENS SCATTERING VOLUME
LENGTH L, CROSS-
SECTIONAL AREA A
FILTERING LENS
APERTURE
4.5.7 Light extinction system for a divergent light source
There also exists the alternative of using a large enough angle to include
the diffracted portion of the scattered light corresponding to the central
lobe (9d * — ). In this case the correct value of the coefficient would
DKTF.CTION
APF.RTURF
99
-------
Sec. A.6.1
be approximately one. Finally, if the width of the cell is made sufficiently
small compared with its length, then the detection angle over most of the
cell will be smaller than the limiting value without the use of a lens and
a pinhole.
The experimental system appears in Fig. 4.5.8. Light from a polarized
Helium-Neon laser passes first through a beam expander and then through a
Polaroid filter. The first allows easier alignment of the beam and the axis
of the extinction cell, and the second serves as an attenuator. The light
is then split and passed through the two cells, blackened on the inside to
prevent reflection of the scattered light. The detection angle is therefore
small* During operation one cell contains the aerosol and the other serves
as the reference. With no aerosols the outputs of the two phototubes are
equalized. The difference between them corresponds to the amount of the
light scattered by the aerosol from the beam. The use of a differential
signal also serves to significantly reduce the noise associated with a slow
variation (M Hz) in the laser output. Prior to any experiment the
reference signal is measured, since a coating of oil will form over the
light entrance and exit ports, reducing the incident radiation from Its
initial value. For this reason the measurements should be performed relatively
rapidly, and each should be followed by a flushing of the system with clean
air. The length of the cells should be selected so as to allow enough
attenuation for the absorption or transmission to be accurately determined.
In this apparatus the option of either a 7.5 cm or a 30 cm-inch cell provides
sufficient flexibility.
4.6 Ionic Charging of Sutanicron Aerosols
4.6.1 Diffusion and Impact Charging
100
-------
Sec. 4.6.1
BEAM SPLITTER
ICA PHOTODIODES
(IP42) KB
IWt
3S
S
y
U-
1
-INLETS OUTLETS ^
, II
/ i cm \ j O I"-"
* 30 V' if
cm
^L
JC
1
/
^
IRROR
ATTENUATOR •* '
MIRROR
F
BEAN EXPANDER
POLARIZED —
HE-NE LASER
Fig. 4.5.8 Light extinction system for a laser light source and a
detector aperture determined by cell dimensions
Two models have been developed which fairly accurately describe the
limiting processes by which particles are charged if exposed to an ionic
atmosphere (White, 1963, p. 126). In the absence of an ambient electric
field, diffusion of the ions onto the surface will lead to an accumulation
of charge according to
4ire akT
C"ae2n.t
4ire kT
o
m
(1)
where n. is the ion density far away from the sphere, T is the temperature,
—19
e is the unit electron charge (1.6 x 10 coul), k is Boltzmann constant
(1.381 x 10* °^g c'), and a is the radius and m the mass of the sphere.
The ions are assumed to carry one unit of charge. As charge is collected,
the charging rate will continuously decrease, never, however, becoming zero.
If there is an ambient electric field, EC, present, the mechanism is
101
-------
Sec. A.6.2
termed impact charging. Depending upon their polarity, ions will flow onto
the sphere at points where the field points either in or out. If the
particles are considered to be perfect conductors, the charging of the sphere
proceeds as
,, . x ; T = - — ; q = 12-ffe aE (2)
qc (1+At/Tj) i njC^ Hc o c
It is evident that after several time constants have elapsed, the charge on
the sphere becomes relatively constant. The calculations above have assumed
that the sphere is at rest. If this is not true, the velocity of the sphere
must be compared to that of the ions in the ambient electric field to determine
precisely which charging equation should be used or, Indeed, whether there
will be any charging at all. (See Sec. 6.2.1 for a detailed discussion.)
In an actual device both mechanisms are present. However, for very
small particles diffusion is the primary mechanism, and for large ones it
is impact. The particle size at which these effects are commensurate depends
on the strength of the ambient field. For the relatively large charging field*
used here, the crossover point occurs at radii on the order of about O.lym.
Upon specification of the particle size and charge, the particle mobility can
be calculated. Experimental corroboration of these models has been given by
Hewitt for submicron OOP aerosols (Hewitt, 1957).
4.6.2 High Efficiency Charger for Submicron Aerosols
The device used is a modified version of the design cited by Langer
et al. (1964) (Fig. 4.6.1). It consists of a small plexiglass box with two
inlets and one outlet. The aerosol enters the charging region through the
lower glass tube. To minimize the effects of the ionic wind, the diameter
102
-------
Sec. A.6.2
IB selected so as to produce an aerosol velocity of at least 10m/sec in the
charging zone. Upon the outlet is soldered a metal washer at a 45-degree
angle. The source of the ion flux is a small loop of platinum wire bent
slightly and positioned so as to be equidistant from the outer edge of the
vasher. This guarantees that ions will be drawn just from the tip of the
loop and will flow so as to intersect the aerosol stream. The resistors are
added to stabilize the corona. If air is used for both the generator and the
accelerating gas, the voltage-current relations for the positive and negative
corona will be similar. In this experiment prepurified nitrogen is used.
This leads to a positive corona very similar to that using air, but a negative
one which exhibites a current which increases much more rapidly with
voltage. This is attributed to the increased mobility of the negative ions
-2 -4
in such a gas, on the order of 1.45 x 10 as compared with 1.28 x 10 for
the positive ones (Cobine, 1958, p. 38). Use of a much larger resistor, however,
allows control over this current.
To start up, the aerosol is turned on and sufficient clean gas
introduced to produce a stable filament. The voltage is then set at a value
slightly greater than that necessary to initiate the corona. This is usually
in the range of 6 to 10 kV with currents of a few microamperes. The amount
of accelerating gas may then have to be increased to regain a stable filament.
If much higher currents are used, the amount of accelerating gas needed will
result in considerable dilution of the aerosol. The position of the corona
loop is then adjusted so that the ionic flux causes the aerosol stream to be
depressed slightly. This assures that all of the aerosol is exposed to the
ions. If adjusted as suggested, the charger will operate stably and re-
producibly for extended periods. When shutting down, the aerosol should be
103
-------
Sec. 4.6.2
first turned off, then the accelerating gas and corona. When starting up
again, the reverse order should be used. This will minimize the contamination
of the wire. To be certain that the corona is always operating properly, a
high intensity beam of light is focused on the charging zone. If the stream
appears to fluctuate or back corona is seen on the washer, the charger should
be shut down and cleaned. This involves washing the outlet tubing with
alcohol and briefly placing the corona loop in a small flame to heat it to
incandescence. This burns off any oil that may have been deposited. The
device should then be reassembled and recalibrated.
+ - 100 Ml
R - 1000 MTC
0.6cm ALUMINUM ROD
ACCELERATING GAS INLE
» j
AEROSOL INLET
1
f
8 MM ID PYREX
TUBING
T
Lj
— — •
"- —
, *
_ — •
1 — .
V \
1 jO.lmm
1 (OJWIRE W
3 LOOP
V"
•»
PLATINUM
tTH 3mm
—
I BRASS WASHER *^* j"
BRASS TUBING
6mm
— --J "f
Fig. 4.6.1 Aerosol charger showing alternative resistors for positive and
negative charging
104
-------
Sec. 4.7.1
4.7 Analysis of Submlcron Aerosols for Charge Density and Mobility
4.7.1 Imposed Field Analyzers
To ascertain the electrical properties of the aerosol, the charged
stream is passed through an analyzer. Two types used in the experiments of
this and the next two chapters are shown in Fig. 4.7.1 (Taxnmet, 1970). The
radial flow configuration (Hurd and Mullins, 1962) with the additional feature
of air injection to prevent contamination, is particularly useful in dealing
with the DOP, because precipitation on the walls results in an appreciable
leakage current unless the conduction path is broken by a surface that
remains free of contamination.
By an imposed field analyzer it is meant that the electric field
associated with the applied voltage V between the electrodes (in either system)
is much larger than that due to the space charge of the aerosol. In that
case, Eqs.(4.2.5) and(4.2.6)are approximated by ignoring the space charge
2
term (proportional to n ) and taking the electric field as being -V/s in
the x direction. (Of course, diffusion is also ignored.)
£-0 (1)
|| - bE + v - -b I Ix + v (2)
Thus, the particle density n is constant along particle trajectories, and
these trajectories are found from a known E and v. The volt-ampere
characteristic of the analyzer can be found without recourse to the specifics
of the velocity profile provided that the particles can be taken as uniformly
distributed with density n over the cross-section in the entrance region of
the analyzer. The trajectory of a particle starting at the entrance surface
105
-------
Sec. 4.7.1
position (a) in Figs. 4. 7. la and 4.7.1b will either be intercepted by the
current collecting bottom electrode or it will pass out of the system. As
a function of voltage, the volt-ampere characteristic divides Into two regions,
At low voltages, only a fraction of the particles are collected. Those
entering above a critical value of x, x , are not collected while those
below are. To compute the total current collected in this region of V
observe from Eqa. (1) and (2) that the particle density is constant along
all of the trajectories which terminate on the collecting electrode because
these emanate from the entrance region x < x where n - n . Hence, in this
part of the characteristic,
I - - / nqbE da - I ^^L da (3)
A * A 8
where the integration is over the area of the collecting electrode. With the
multi-electrode system of Fig. 4. 7. la, A is the total area of the collecting
surface. The velocity makes no contribution to the integration because it
is zero at the electrode. Because n • n at all positions on the electrode
Eq. (3) becomes
n qbA
With the voltage raised above the point where all entering particles
are collected, the total current is simply that entering the analyzer because
of the aerosol convection
5 rsat
where F is the volume rate of gas flow.
106
-------
Sec. 4.7.1
(a)
15.2-
cm
T
0.16
cm
AJ Brass plates +V
r=- separated by 0.16 cm
thick plexiglas
spacers
Fig. 4.7.1 Analyzer configurations (a) plane flow with multiple parallel
electrodes (b) radial flow with air injection to prevent leakage
current•
107
-------
Sec. A.7.1
It follows that the ideal imposed field analyzer characteristic is as shown
in Fig. A.7.2. Combining Eqs. (4) and (5) shows that the saturation voltage
is
sat bA
(6)
sat
sat
Fig. 4.7.2 Ideal imposed-field analyzer volt-ampere characteristic for
either of configurations in Fig. 4.7.1
Typical data taken using the radial flow configuration is shown in
Fig. 4.7.3. In addition to the low voltage linear dependence and high
108
-------
Sec. 4.7.2
voltage saturation of the current, there is an evident current 1(0) even
with V " 0. This is the result of self-precipitation, and in dealing with
aerosols of high charge density, as is the case here, can itself be the
basis for inferring the aerosol parameters. Before pursuing this point in
the next subsection note that the space charge density n q can be determined
using the data of Fig. 4.7.3 and Eq. (5) regardless of whether or not space
charge effects are important.
4.7.2 Space-Charge Effects
It is to determine the mobility that the slope of the linear region
of the curve is used and that is ambiguous to a degree that becomes less
tolerable as the space charge current 1(0) becomes on the order of 1 .
ScLC
Both the mobility and the charge density contribute to 1(0), but because
the latter is known from measurement of I , it is possible to use 1(0)
Sett
as a measure of b. In the radial flow configuration this is done by
exploiting the results of the following analysis.
An analytical model for the space charge current follows directly
from Eqs. (4.2.s)and (4.2.6) if the flow is represented as having no x dependence.
(This is the equivalent of slug flow in the radial geometry.)
Hence, the radial component of Eq. (4.2.9) is simply
dr . _JL_
dt 2Trrs
which, with the assumption that the aerosol is injected at the radius r
o
with a uniform concentration n , can be integrated to give
109
-------
0.6
0.5
0.1 _
100
200
300
400 500 600
V - volts
700
800
900
1000
Fig. 4.7.3 Typical analyzer V-I characteristic determined using the radial flow air injection configuration
of Pig. 4.7.ib. F - 1.08 x 10'VVsec,
H*nc. fro. data b - 1.45 x l
o
N>
-------
Sec. 4.7.2
The particle density, in terms of the tine measured in the frame of
reference of the particle, is given by Eq.(4.2.8). The radial distribution
is deduced by combining this expression and Eq. (9).
IL. . _ _ . T = _° _
no TTs 2 2 1 a nn*b
0 1 + [£f (r2 - ro2) ] i- °
a
Thus, the particle concentration at all radial positions is also uniform.
The difference between the radial particle current at the outer
radius of the analyzer where r • r. and at the inlet, where r « r is the
total self-precipitation current, which is twice the self-precipitation
current 1(0) measured at one of the electrodes. Hence,
21(0) - F[n(rQ) - nOr^Jq (11)
Substituting the appropriate values of n(r) from Eq. (10) leads to
the expression
KO) . 1 (T/T ) irs(r 2 - r 2)
I8at 2 [ - ^— ] ; T 5 - * ° (12)
8flt 1 + (T/Ta) F
Note that T is the residence time of the gas in the analyzer.
To assess the faithfulness of the slug flow model the flow is pictured
as Poiseuille,
v(x,r) -^r- [(s/2)2- x2] (13)
TTS r
Using a numerical approach taking advantage of the solution from Eq.(4.2.8),
111
-------
Sec. A.7.2
it is possible to calculate a curve for the fraction of the current entering
the system that is precipitated on the plates between radii r and r,.
These results are displayed in Fig. 4.7.4. The upper curve corresponds to
the results for a slug flow with the same flow rate. Since the simplified
model agrees reasonably well with the exact one, the analytic expression
developed there will be used to calculate the mobility of the charged
particles.
21(0]
sat
0.5
0.4
0.3
0.2
0.1
Slug
I
0 0.2 0.4 0.6 0.8 1.0
T/Ta •*•
Fig. 4.7.4 Self-precipitation for a radial flow: comparison of exact solution
for Poiseuille flow with one from slug model
Once the saturation current and the self-precipitation current are
measured, it Is possible to calculate both the inlet charge density and
mobility. The former follows from Eq. (5)
V - rsat/F
(14)
112
-------
Sec. 4.8.1
In turn, Eq. (12) allows calculation of the ratio of the residence time to
the self-precipitation time
2I(0)/I8at
sat
l-2I(0)/Isat
Since the charge density and volume flow rate are known, the particle mobility
can then be calculated
C'e
If the space-charge current is not appreciable, then the imposed- field
analysis is appropriate and b is determined from a measurement of the slope
in the region V < V .
8&b
4.8 Self-Precipitation Experiments (SCP)
With the objective of underscoring the role played by T& with respect
to the dynamics of the charged submicron particles, two types of experiments
are now described that are in the category of SCP devices. The first of these
illustrates self-precipitation in a laminar flow system, while in the second,
complete mixing is used to illustrate self-precipitation when the flow is
dominated by turbulence.
4.8. 1 Laminar Flow Experiment
In the apparatus of Fig. 4.8.1, self-precipitation from a laminar flow
takes place in a metallic duct of circular cross-section. The aerosol is
generated and charged by means of the apparatus described in Sees. 4.4 and
4.6. Then, it is injected into the duct at a position that can be varied by
sliding the rigid injection tube in or out of the coaxial duct. By making
the injection tube rigid, the geometry of the flow into the system is maintained
113
-------
Sec. 4.8.1
essentially invariant, thus assuring constant inlet conditions as the
duct length z is changed. At the exit the analyzer is used to measure
the particle density and mobility. The radial flow apparatus and measuring
techniques are described in Sec. 4.7.
To make the self-precipitation measurements meaningful, the residence
time T . in the tubing connecting the outlet to the analyzer must be short
compared to that in the duct. In the experiments, this residence time In
the connecting tubing is about 0.05 sees. The volume rate of flow
-4 3
F - 1.08 x 10 m /sec, and hence residence time in the duct is on this order
2 ••
for z < [4F/7TD JT • 2cm. Also, the Reynolds number for the duct flow is
R * ApF/TrnD ~ 400, which assures a laminar flow.
CHARGER
AEROSOL
GENERATOR
, 9 cm
(ANALYZER)
Fig. 4.8.1 Laminar flow self-precipitation experiment
Aerosol generator, charger and analyzer respectively described in
Sees. 4.4, 4.6 and 4.7
114
-------
Sec. 4.8.1
The experimental results are the data points of Fig. 4.8.2, which
show the outlet concentration as the duct length is varied. In essence,
this is the decay in particle concentration over the length of a duct of
fixed length. The broken curve is based on the slug flow model of Sec. 4.2.2,
Eq. (4.2.12). Also described in Sec. 4.2.2 is a more detailed analysis which
includes the parab6&lc profile of a fully developed laminar flow. This
theory results in the solid curve of Fig. 4.8.2.
0.5
• of
0.4
0.3
0.2
0.1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Fig. 4.8.2 Self-precipitation of aerosol from experiment of Fig. 4.8.1
Broken curve is based on slug flow model, Eq. (4.2.12), while
solid curve is reamlt of theory Including effect of parabolic
velocity profile (Sec. 4.2)
115
-------
Sec. 4.8.2
As is evident by the correlation of the simple slug flow model with
either the experiment or the more detailed parabolic profile model, the
essence of the SCP device in laminar flow is not extremely sensitive to the
details of the flow. Chief among the ways in which the experiment does not
correspond to the assumptions of the theory are (1) the inlet particle profile
is not exactly uniform but is in fact established by a complex mixing zone
where the particles are injected through a "T", and (ii) the flow is not
fully developed until the boundary layer extends well into the duct.
z > 0.04pF/n - 20cm (Schlichting, 1968, p 231). Hence, the parabolic profile
does not fully develop until the channel has a length on the order of 20cm.
In support of this latter point Is the fact that for short duct lengths the
data tends to follow the slug flow theory more closely than the fully
developed flow theory.
4.8.2 Turbulent Flow Experiment (SAG)
A very simple experiment that emphasizes the universality of the
self-precipitation model with complete mixing is shown in Fig. 4.8.3.
F "in
CHARGER
AEROSOL
GENERATOR
MAGNETIC
STIRRER
ANALYZER
Fig. 4.8.3 Self-precipitation experiment with mixing. Aerosol generator,
charger and analyzer respectively described in Sees. 4.4, 4.6 and 4 ?
116
-------
Sec. 4.9
The theoretical basis for this class of SCP phenomena is described in Sec.
4.2.3. The ancillary apparatus is similar to that of Fig. 4.8.1, except that
the self-precipitation volume is now arbitrary, both in geometry and electrical
properties of the wall materials. The residence time is in fact varied by
changing the container, which in the experiment consists of various glass
flasks. Mixing within the volume is obtained by means of a magnetic stirrer
at the bottom of the f.lask.
The solid curve of Fig. 4.8.4 is the decay in outlet concentration
caused by self-precipitation as a function of normalized residence time,
predicted by Eq. (4.2.20 ). The three data points are the result of
experiments performed using three different flasks. There seems to be
little doubt but that if complete mixing is assured (without in the process
incurring inertial impaction on the walls or on a fan used to induce the
turbulence) the simple model for the SCP interaction is an excellent one.
In the experiments summarized by Fig. 4.8.4, the discrepancy at the largest
residence time is probably due to incomplete mixing in the relatively large
volume used.
The SCP model with complete mixing is important in the context of
changed drop scrubbers, because the drops are almost certainly injected into
the active volume as a turbulent Jet, tending to have the same effect on the
distribution of particulate as does the magnetic stirrer in the experiment
of Fig. 4.8.3. Thus, the electrically induced contribution to performance
in the absence of drop charging is represented with considerable generality
by Eq.(4.2.20) and the solid curve of Fig. 4.8.4.
4.9 Self-Discharge Experiments (SAG)
The major difficulty in studying the dynamics of blcharged systems
117
-------
Sec. 4.9
1.0 I
T
\*
; I
^
>
s
t
>
>
s
^
l_
F n
,3r » 7 « » 10
"res/ a
Fig. 4.8.4 Self-precipitation with mixing. Solid curve Is predicted by
Eq. (4. 2 .20). Data points are experiments performed using
three different flasks having different volumes V so that
residence time T is varied whil.e holding T fixed.
res s
of particulate with space charge neutrality comes from simultaneously
obtaining two families having opposite polarity, equal mobilities and
densities. In the experiments described here, aerosol particles of the s«
size are used for both families, and hence the requirement is for equal
charging of both families. This is difficult because the charging characteristic!
of positive and negative corona chargers tend to be very different.
To obtain as high a degree of control as possible over variables while
changing the effective length of the interaction duct, the output of the
aerosol generator is split into two equal portions, which are then inserted
118
-------
Sec. 4.9
into separate chargers as shown in Fig. 4.9.1. These are mounted on a
movable platform, and their outlets connected to straight sections of
grounded copper tubing. The diameter of these (3.17mm I.D.) is selected so
as to represent a negligible delay to the flow. The outputs of these tubes
are combined in a nozzle which injects the flow into a rectangular channel
(d - 9.55mm x w - 3.18cm x 61cm). The outlet is then led directly into a
multi-electrode parallel flow analyzer (Sec. 4.7.1) consisting of five sections
stacked one upon another, and then to an exhaust. The volume flow rate of
the aerosol is measured along with the analyzer V-I characteristics.
•
t 1 1
v LJ
4 r i
. . .@
f»
V
t_ • — 1
• * J----1
\ BRASS TOP
FUXIGLA5 SIDES
AND BOTTOM'
COPPER n
(3mm 11
1
•/•-I
BINC ^*
))
\
z 1
?
^ w
Fig. 4.9.1 Charged aerosol experimental system
One charger is adjusted for positive corona, and the other for
negative. Since the charge acquired by a particle through the impact process
is proportional to the charging electric field, the magnitudes of the voltages
applied to the platinum loops are set about the same. The gas flow rate se-
lected produced an average velocity within the channel of 0.37m/sec,
119
-------
Sec. 4.9
implying a Reynolds number of R -75, based on an effective diameter
dw/(2w + 2d) » 3.66 x 10 m and a laminar flow. To begin, the nozzle is
placed as close as possible to the analyzer. The analyzer V-I characteristic
is measured, with and without aerosol. This is necessary because with the
multi-electrode type of analyzer used, the accumulation of a film of DOP
on the inner insulating surfaces results in a leakage resistance. The
current from this resistance associated with each analyzer voltage is
then subtracted from the measured currents. The results are given in
Fig. 4.9.2. As discussed in Sec. 4.7.1, the initial slope and the satura-
tion value of the current together with the gas flow rate provide the
information necessary to calculate the mobility of the particles and their
3.0
I(xl09 A)
2.0
1.0
I I
I
_L
50
100 150
V(volts)
200
250
Fig. 4.9.2 Analyzer curves for self-discharge experiments with bicharged
aerosols F - 1.1 x 10 m /sec
n+q " 1.8 x 10"5 coul/m3 b+ - 2.9 x 10"7 m/sec/V/m
n_q - 2.3 x 10~5 coul/m3 b_ - 2.4 x 10~7 m/sec/V/m
120
-------
Sec. 4.9
charge density. Note that because the aerosol enters the analyzer with
space charge neutrality* the imposed-field analyzer characteristic tends to
be sufficiently accurate for the deduction of charge density and mobility.
By measuring the currents I. and I_ on each of the sets of electrodes (see
inset of Fig. 4.9.3) the decay of each species is ascertained. It is
evident from the data of Fig. 4.9.2 that the magnitudes of the positive and
negative charges are about the same, and the entering aerosol practically
charge-neutral.
Next, with the analyzer voltage set high enough so as to capture all
charged particles (V > Vgat), the nozzle is pulled back in discrete steps,
and the currents from both sets of plates noted. These values, corresponding
to the amount of current, both positive and negative, associated with
particles which have not yet self-discharged, are plotted in Fig. 4.9.3.
3.0
l(xl(T A)
2.0
1.0
T
T
T
T
I_ (POSITIVE PARTICLES)
+v
4-
(NEGATIVE PARTICLES)
_L
0 10 20 30 40 50 60 70
z(cm) - distance from nozzle to analyzer entrance
Fig. A.9.3 Experimental self-discharge of bicharged aerosol in laminar
flow as a function of distance down the duct. Solid curve is
theory based on Eq.(4.3.22) with the Initial condition
found by extrapolation back from the first data point. Inset
defines analyzer currents
121
-------
Sec. 4.9
This variation can be compared to the theoretical predictions from Eq. (4.3.22)
Since the first point was taken 5cm downstream of the nozzle, the theory
is used to infer the entrance current. The solid curve in Fig. 4.9.3 is
predicted using the charge-density and mobility measured for the negative
particles.
From the mobility measurements, it appears that both positive and
negative particles carry essentially equal magnitudes of charge. Thus,
the product or products of a discharge event can be considered effectively
neutral. The relatively sharp transition in the measured I-V character-
istics from the linear to saturated regimes also indicates that there is
relatively little variation of the mobility among the particles. Although
the magnitudes of the charge densities are slightly different, the amount
of net charge introduced is not sufficient to cause self-precipitation to
be comparable with self-discharge.
As in the laminar experiments of Sec. 4.8.1, the flow exhibits a
transition from a jet leaving the nozzle to a fully developed essentially
plane Polseullle flow within the range of channel lengths observed. The
calculations assume, however, that the flow can be modelled as plane
Foiseuille from the entrance onward. Thus, the degree of correlation between
theory and experiment represented by Fig. 4.9.3 is consistent with experimental
controls over the flow.
From the results of these experiments there can be no mistaking the
role of T in determining the rate of self-discharge among the submicron
bipolar particles. Whether this discharge results In mechanical agglomeration
and hence is in the category SAG must depend on the details of the particles.
For the DOP used In these experiments, self-discharge almost certainly is
122
-------
Sec. A.9
equivalent to self-agglomeration. What Is Important to the performance of
the charged drop scrubber Is not whether or not the discharge Is also an
agglomeration event, since there Is little change In the size of the particle
In any case, but that the blcharged particles lose their charge In the
same typical time T that the unipolar particles tend to self-precipitate.
Insofar as charged-drop scrubbing Is concerned, the particles are no longer
accessible for collection once they have discharged.
123
-------
Sec. 5.1
5 Electrically Induced Self-Discharge and Self-Precipitation of Supermicron
Drops
5.1 Objectives
If emphasis is to be given to any of the differences between devices
making use of charged drops for collection of particulate and the conventional
electrostatic precipitator, then it should be to the fact that the drops,
unlike electrodes, are themselves free to move in response to not only
imposed electric fields, but self fields and aerodynamic forces as well.
Because any charged drop collection device is strongly influenced by the
dynamics of the drops, it is appropriate in this chapter to isolate for
investigation this aspect of charged drop devices.
With the subject shifted from submicron particulate to supermicron
drops, the two objectives in this chapter parallel those of Chap. 4.
First, theoretical models and controlled experiments are used to develop
a picture of the dynamics of systems of unipolar and of bicharged drops.
Interest is confined to the self-precipitation of unipolar drops and
self-discharge of bicharged drops in turbulent flows, since these are of
greatest interest in practical applications. The comparison of theories and
experiments is essential to interpreting in a self-consistent fashion the
more complex experiments of the next chapter where systems of charged
submicron particles and supermicron drops interact.
Second, techniques for generating monodisperse uniformly charged drops
in the unipolar and bipolar systems are developed. Included is a discussion
of generating methods fihat are of interest foe large scale practical systems
but are not exploited in Chap. 6. Thus, Sec. 5.4 is in essence an overview
of the most likely methods for making charged drops in practical systems.
124
-------
Sec. 5.2.1
5.2 Self-Precipitation in Systems of Unipolar Drops
5.2.1 Mechanisms for Deposition
To a considerable extent, the results of Sec. 4.2 for the self-
precipitation of unipolar submicron particles anticipate those of this
section. Certainly after Chaps. 2 and 4 it should come as no surprise that
if electrical forces dominate, drops tend to be deposited on the walls at
a rate determined by TR = e /NQB (where N, Q and B are respectively the drop
number density, charge, and mobility) rather than T » e /nqb. But, typically,
a O
drops of interest in this and the next chapter are SOym in diameter, a size
sufficient to make inertia! effects of possible importance. (Inertial effects
are not represented by T_. ) Related to this fact is the influence of
turbulent mixing, which, because of the finite drop inertia, is a contributor
to the rate of loss of drops at the walls, and also plays an important role
in determining the space-time evolution of a system. The following discussion
shows that for the drops, several time constants, representing turbulent
diffusion, inertial effects of the drops, and electrically induced self-
precipitation can be on the same order. The discussion is intended to place
in perspective the use of simple models for electrically dominated self-
precipitation which will be compared to experiments in Sec. 5.5.
Turbulent Diffusion If the system is sufficiently agitated that it
may be classified as turbulent, then the inherent eddies provide a mechanism
far more effective than Brownian motion for diffusing flow constituents.
In the bulk of the flow, this process is dominated by the large scale motions
and characterized by a diffusion coefficient of the order (Levich, 1962, p.
141)
D_ s (AU)A_ (1)
125
-------
Sec. 5.2.1
where £_ is the length scale of these eddies, and AU the magnitude of the
associated fluctuation velocity. In channel flow, the large eddies are
limited by the channel width, s. It is of course, this turbulent mixing
that is assumed to dominate in determining the distribution of submicron
particles in the "turbulent mixing" models of Chap. 4. Because of the
appreciable inertia of the drops, the effect of turbulent mixing on their
distribution needs closer scrutiny than is necessary for the submicron par-
ticles. For a system with dimensions on the order of 1cm and fluctuation
—3 2
velocities of about lOcm/sec, D_ - 10 m /sec, and for drops 50ym in diameter D
»
is much larger than its Brownian counterpart, where
VP — 1 7 9
a2 8
TB - j- - 2.12 x 10 sec (2)
This large value for D does not apply throughout the system. In
the vicinity of the walls the fluid velocity vanishes, and along with it,
the coefficient of turbulent diffusion. In fact, the rate at which mass-
less particles are deposited on the boundaries is determined by their
Brownian diffusion through an outer thin laminar layer, (Levich, 1962, p.
150) whose thickness is a function of the level of turbulence in the outer
flow. Since D_ is so small, the fluid must become extremely agitated before
this rate becomes significant. At this point, the particle mass becomes
important, since it offers a way to short-circuit this last obstacle. For
high enough levels of turbulence, the drop can acquire sufficient velocity
outside of the Brownian diffusion layer to project itself across the layer
to the boundary. This requires that the stopping distance for the drop
126
-------
Sec. 5.2.1
with an initial velocity on the order of the velocity of the large scale
eddy velocity, All, be on the order of the thickness of this layer:
2pR2
where p« is the mass density of the droplet material and 1 the viscosity of
x\
air. (The scrubbing lifetime T8R is introduced in Sec. 2.2). In that event,
the flux density of the particles precipitating themselves on the boundaries
is given by Bavies (1966, pp. 235-246)
r - NAU (4)
where N is the droplet concentration some distance away from the wall.
The degree Co which the turbulent mixing influences the drop distribution
in the bulk of the interaction region also depends on the scrubbing lifetime
T relative to times characterizing the eddies. A drop entrained in a flow
sR
characterized by eddy time constants
T - s
will assume the velocity of the eddy if T_ is long compared to T „ but will
"iron out" the fluctuations if T_ is short compared to TS_. For drops of
_3
25ym radius, T R - 7 x 10 sec while the eddy time constant for a system
having All = lOcm/sec and JL, - 1cm is T « 10 sec. Hence, the large scale
eddies have a strong influence on the distribution of drops (T > T ) , but
the smaller eddies are likely to be penetrated by the drops (T_ < T R). For
the developments of this chapter, it is the former point that is important.
Because the small scale eddies do entrain submicron particles, the latter
point) the fact that mixing can occur relative to the drop, is important
127
-------
Sec. 5.2.1
to the drop-particle interactions to be taken up in the next chapter.
Electric Self-Precipitation With the drops given a unipolar charge
they acquire a migration velocity superimposed upon the random velocities
associated with the turbulence. The relative importance of turbulence and
self-precipitation in determining the distribution of drops is reflected in
the ratio of turbulent particle flux T^ to the electrically induced migratl
flux r_, associated with the self -field. In a channel of width s. A - .
£i T
and E = NQs/eo, so that
r_ BEN NQB/e T
£* OX
Thus, if the drop self-precipitation time TR is short compared to the lax*
scale eddy diffusion time T , the electric field is dominant.
T
For charging conditions typical of the drop experiments to be de-
scribed (N - 2 x 109/m3, Q - A x 10"14 coul, B - 5 x 10~6m/sec/V/m, R .
25ym),and the time necessary for significant self-precipitation of the drop*
is TR - eQ/N QB - 0.025 sec. If the system is turbulent to the extent that
AU - lOoa/sec and a - 1cm, then the large scale diffusional time is of the
order TT - 82/DT * s/AU s 0.1 sec. Hence, the self-precipitation is
dominant. But, for lesser drop charges, the turbulent diffusion and
electrical self -precipitation are of comparable importance in determininjt
the drop motions and deposition on the walls.
Note that if drop charge or density increases, then effects of the
finite drop inertia must eventually come into play. The effects of inertia
must be considered if
TsR
128
-------
Sec. 5.2.2
For typical conditions in the experiments of this chapter, T R - 7 x 10 sec,
which is somewhat shorter than TR. Thus, inertlal effects are at most of
marginal importance.
5.2.2 Self-Precipitation Model for a Channel Flow
The point of this section is that there is a regime in which electrical
effects are dominant in determining the space- time evolution. In this
regime, the appropriate model is similar to what would be used to describe
the self -precipitation of submicron particles in a turbulent flow. The drops
are considered to be entrained in a turbulent flow through a duct having
cross-sectional geometry that is uniform but arbitrary, with area A and
perimeter S. Conservation of particles for a cylindrical volume of
Incremental length Az in the flow direction and cross-section coinciding
with that of the duct, requires that
UA[N(z + Az) - N(z)] - - NB £ E • ndi Az (8)
S
where the integration is over the perimeter of the incremental section of
duct. It is assumed in writing Eq. (8) that the large scale eddies give
rise to sufficient mixing that the drop profile and mean gas velocity across
the channel are essentially uniform. Also, the spatial evolution is sufficiently
slow to justify the assumption that the space-charge generated electric
field is transverse to the flow. By Gauss' Law, this latter approximation
requires that
E • ndi - (9)
S o
BO that in the limit Az •»• 0,Eq. (8) becomes a differential equation for the
129
-------
Sec. 5.2.2
evolution of N(z).
dz ue0
If the drops enter the duct with density N , then it follows from Eq. (10)
that
i Ue
N 1 o o
This model could have just as well been introduced in Sec. 4.2.3 where
models are developed for self-precipitation of submicron particles from
turbulent flows. Of course, for the submicron particles, T0 •* T and
K a
*R * V
The restrictions on the use of Eq. (8) to describe drops, as compared
to submicron particles, are more severe. They come from two sides. If
the charge density NQ is so low that T > T_, where T is based on the large
scale eddies, then turbulent diffusion will dominate in determining the
rate of deposition on the walls. Thus, with only a little charge on the drops
the rate of spatial decay predicted by Eq. (11) is too low.
As NQ is raised so high that T < TgR, restrictions on the model from
the other side come into play because of inertlal effects. In this range,
the rate of decay from Eq. (11) is too high. Hence, to be valid the model
must be used where T_ is in the range
i\
TsR < TR < TT <12>
For the drops of interest in this and the next chapter, R * 25pm and
inertial effects are of only marginal importance. It is in fact possible
to make NQ large enough to bring inertial effects into play, but this is
likely to correspond to a charge density greater than optimal when the
drops are used to perform a scrubbing function.
130
-------
Sec. 5.3.1
5.3 Analysis of Self-Discharge Systems
5.3.1 Mechanisms for Discharge
The evolution of a system of bicharged drops is a function of processes
occurring on at least two length scales. There is the system scale, in
which the drops are distributed through mechanisms such as turbulent diffusion
and convection as well as self-field induced electrical migration. Because
the systems of interest in this section are initially composed of pairs of
charged drops having the same size and mobility but opposite sign of charges,
it is to be expected from the dynamics of bicharged submlcron particles
discussed in Sec. 4.2.3, that the drop distribution on this systems scale is
determined by turbulent diffusion and convection alone.
The second scale is of the order of the distance between drops. With
N the density of one species of drop, this distance is of the order
OR - 1 1/3 (1)
(2N)1/3
On this scale, oppositely charged drops are encouraged by the electrical
forces to mutually discharge. This tendency is possibly influenced by
molecular diffusion, but is almost certainly in the face of the fine scale
turbulent mixing. The following discussion of the self-discharge process
is intended to bring out the physical mechanisms involved on the interdrop
scale.
Turbulent Diffusion First, assume that the inertia of the drops is
negligible, in the sense that TSR is short compared to time scales of interest.
Levich (1962, p. 215) argues that for drops small compared with the microscale
of the turbulence t (at which viscous effects become significant) the
coefficient of turbulent diffusion can be expressed as
131
-------
Sec. 5.3.1
where Si is the scale of the turbulence. The volume rate of energy dissipation
o
(watts /m) can in turn be expressed in terms of the properties of the large
scale eddies
YT - p(AU)3/iT (3)
and 3 Is a constant of the order unity while p and n are the mass density
and viscosity of the gas respectively.
To establish that on the scale R — oR Brownian diffusion is over-
shadowed by turbulent diffusion, observe from Eqs. (2) and (4.2.2)
[AA/a « 1] that the diffusion coefficients are equal for diffusion having
the length scale
If this scale is even smaller than the drops, let alone distance between the
drops, Brownian effects can be ignored. Values typical of the experimental
system to be considered in this and the next chapter are R - 2.5 x 10 m
AU - 10~ ^m/sec and AT = s = 10~2m. Thus, Eq. (4) gives ^ < 10~7m and it
is clear that turbulent diffusion dominates molecular diffusion.
Again, for the moment ignoring effects of drop inertia, the picture
that evolves is one in which self-discharge is the result of turbulent
diffusion and migration induced by interdrop electric fields. The develop-
ments of self-discharge processes for submicron particles, Sec. 4.3,
illustrates that the electrically induced discharge occurs on a time scale
typically of the order TR • eQ/2NQB. For a drop system having N • 109/m3,
132
-------
Sec. 5.3.1
Q
- 4 x 10~ coul and B - 5 x icf m/sec, this time is T_ - 2 x 10~2 sec.
R
The fine scale turbulent diffusion is typified by a time scale T - H2/D
which in view of Eqs. (2) and (3) is
= g" - o (5)
t e\ p(AU)3
— 1 —2 —2
For AU s 10 m/sec and AT « 10 m, Tfc = 1.5 x 10 sec. That these times,
Tp and T , are on the same order illustrates the point that the flights that
K. •
bring two drops together through mutual attraction are protracted by
stochastic aerodynamic forces tending to play the role taken by molecular
diffusion for the submicron self -discharge process (Sec. 4.3).
In analogy with the calculation of self-discharge within aerosol
systems, the next calculation should be the radius of the electrostatic
sphere of influence. If attention is again focused upon the mutual dif-
fusion of two oppositely charged drops, the analogue of Eq. (4.3.2) for the
radius at which collision la guaranteed is
BO
Ao * Q
Here, the length scale for evaluating the diffusion coefficient, Eq. (13),
IB taken as A itself. Using the same typical numbers as before in this
-4
section, evaluation of Eq. (6) gives AQ * 3 x 10 m. This length is about
an order of magnitude smaller than the typical interdrop spacing given by Eq. (1),
Hence, further credance is given to the physical mechanisms involved.
Because initial separations are likely to be larger than A , the analogy
is continued with a model similar to the Harper one for ions. The rate at
133
-------
Sec. 5.3.1
which drops diffuse onto a sphere of radius AQ with a diffusion coefficient
that varies with separation, r, is according to Levich (1962, p. 216)
G - 128: (7)
Within a constant, this result is obtained by substituting Eq. (2) into
Eq. (4.3.6) for D-D - D_. Upon substitution for A , the flux of drops
to a single drop can be expressed as
G - 3NQB/eQ (8)
This will be seen to be almost identical to the result obtained if dif-
fusive and inertial effects are ignorable.
Effects of Drop Inertia That the time constant T _, reflecting the
time scale on which inertial and viscous drag effects are comparable, is
_o
on the order of 7 x 10 sec (Sec. 5.2) and that this is only somewhat shorter
than either T_ or T. makes it clear that if the charge density is increased
much above levels typical of optimal scrubbing conditions the effects of
Inertia will come into play. To refine the degree to which inertial effects
are important consider an opposite extreme In which the drops are sufficiently
charged for their initial separations to be less than AQ. Their motions are
dominated by the electric fields. However, because of the drop Inertia and
the fact that these fields show such a rapid spatial variation, the particle
velocities are less than those predicted for mass less particles of the sane
size and charge. This may lead to significant increases in the discharge
times. To ascertain this effect, an Idealized Langevin model is employed.
Instead of examining the flux of charged particles to an oppositely charged
central one, the bipolar system Is separated Into isolated oppositely charged
134
-------
Sec. 5.3.1
pairs, and the time required for each pair to discharge is evaluated. In
the limit where inertia is ignorable such a model predicts that discharge
occurs at precisely time TR, whereas the Langevin model predicts that half
of the charged pairs will have discharged within that time. The difference
±a due to the averaging inherent in the latter model.
The equations governing the motion of two drops of equal radius R,
but of opposite charge Q, starting from initial rest at some prescribed
separation (Fig. 5.3.1) are
Fig* 5-3«1 Geometry for two-particle model of discharge process between
two drops
dv Q2
- + 6miRv " + —
(9)
dv
-i
Aire
(10)
135
-------
Sec. 5.3.1
where v. - d^/dt, v2 - d£2/dt; £ • £2 ~ ^i* Tn*8* equations may be com-
bined Into a single normalized equation
2 R 2
where £ = 5/R; t = t/TflR; £ - -j — B ; B - Q/6irnR; the low Reynolds num-
o
ber mobility of the drop in an electric field: T _ - M/6irnR, the time needed
8K
for velocity of a drop injected at v to fall to v /e in the absence of
other forces; pR, mass density of drop material.
Before proceeding, two approximations implicit in writing the equa-
tions in the above form should be discussed. The first concerns the
modelling of the fluid drag by the Stoke*s relation. For larger-sized
drops carrying sizeable charges, the velocities during the latter stages
of discharge may be large enough so that R > 1. To check this, in
Fig. 5.3.2 the maximum velocity (occurring just before impact) is plotted
versus C with the initial spacing in units of drop radii used as a parameter.
The normalized velocity can also be expressed in terms of the drop
Reynolds number R :
- T*R v - TSR ( yf\ . I. &) R
) R R v2Rpr 9 p y
(12)
where p is the density of the surrounding gas. When the gas is air and the
drop is water, the above relation becomes
v - 1.11 x 102 Rm (13)
136
-------
Sec. 5.3.1
10'
IHANSITIO* nan ra*c TO INERTIA DOMIHATED HOTIOM
r -SO r -XOO
It
Fig* 5.3.2 Maximum discharge velocity occurring at instant of impact
From the results of later calculations, the points of transition from
drag-dominated to inertia-dominated motion are shown. Notice that for all
the initial spacings, these occur for R < 3. Thus, for the regimes where
7
drag is an important factor in determining the collapse times it can be
modelled by the Stoke1s relation. In regimes where the Stoke1s model is no
longer applicable, the motion is dominated by inertial effects. Criticism
of the Stoke's model is academic. There is a further related uncertainty as
to whether the drag curve found from measurements on a static drop can be
applied to one that is being accelerated. However, for situations where the
gas density is much less than that of the drop, these effects are usually
small.
The second approximation Involves the use of a simple Coulomb's law in
describing the attraction between the two charged drops. This is equivalent
137
-------
Sec. 5.3.1
to treating them as simple point charges and is applicable only when the
drops are separated by many radii. When the drops are within a few radii
of each other, the fields of one drop will induce a dipole moment on the
other. These will serve to further increase the attractive force. These
effects have been calculated (Davis, 1964) and found to be quite unimportant
unless the drop centers are separated by less than three radii. Thus their
effect has very little to do with the prediction of discharge times.
It is convenient for later calculations to reduce the normalized equa-
tion to one of the first order. Upon substituting v. • d£/d£, the equation
becomes
In the case of drag-dominated motion, the first term is small in com-
parison with the second. The equation is then easily solved for first
and next £(t)
I "
— (16)
In the limit where inertia is the dominating feature, the second
term can be neglected, and the remaining equation solved analytically
(17)
138
-------
Sec. 5.3.1
In this case, the discharge time becomes
(18)
To find T for the entire range of parameters C and £ , the differential
K — O
equation is numerically integrated. These results are plotted in Fig. 5.3.3,
as a set of points with the corresponding value of E written nearby. Also
shown are the lines corresponding to the analytic solutions for ^ with the
value for £• The smooth transition between the two limiting cases is
apparent. In the limit where the inertia of the drops can be neglected
and their separation is many times their radii, the expression for the
discharge time can be recast into a familiar form. Thus,
T „
R 3C 3 N QB
where N - 1/2^ is the initial concentration of one species of drop.
As will now be seen, this is essentially the familiar result of the Harper
model.
5.3.2 Self-Discharge Model for a Turbulent (Slug-Flow) Channel Flow
Consider now the spatial evolution of a system of bicharged drops in
a duct having cross-sectional area A. If the flow is turbulent, the velocity
profile is essentially uniform. Hence, conservation of one of the drop
species with a volume of length Az in the flow direction is represented by
UA[N(z + Az) - N(z)] - -NGAAz (20)
139
-------
Sec. 5.3.1
10
Fig. 5.3.3 Normalized discharge time T^
where NG is the number of drops per second discharged by N drops per unit
volume. With G given by Eq. (7) (the Harper model), in the limit
Az •*• 0, Eq. (20) becomes
dz
N2
u~ N e
(21)
Hence, the spatial decay of the drops having a given sign of charge and
entering the duct with the density NQ is
140
-------
Sec. 5.A
N , __L__ . o -
N . . z ' R -
where according to the extension of Harper's model, K* « 3. With the total
initial drop density 2N rather than 3N , this is the same expression that
would be found carrying the submicron particulate model of Sec. 4.3.2 over
to the drop system. The time constant of Eq. (18) is for discharge of drops
having the largest possible spacing, and hence would be expected to be larger
than implied from Eq. (22). In any case, the models strongly support the
crucial role of T_ in the self-precipitation process but do not pin down
the precise value of K'.
5.4 Techniques for Generation of Charged Drops
This section serves two purposes. First, it is intended to give an
overview of the main techniques for generating charged drops of the type
of interest in scrubbing devices. Second, the specific techniques used for
generating monodisperse systems of unipolar and bicharged drops for the
experiments of this and the next chapter are described.
From the point of view of forming the drops, most devices fall in
one of two categories. In the pressure nozzle or orifice plate, a fine
stream is ejected under considerable pressure through an orifice. Through
capillary action, this stream breaks up into drops. In the pneumatic
atomizer type of device, an air stream impinges on the water, greatly in-
creasing the effective atomlzation. In either of these approaches, drop
charging can be implemented by either charge induction through electrodes
vith elevated potential placed in the vicinity of where the drops break off,
or by means of a corona discharge and ion impact charging. Sections 5.4.1
141
-------
Sec. 5.4.1
and 5.A.2 illustrate the two types of mechanical drop formation with the
charging accomplished by means of Induction. Brief attention is given to
the alternative ion-impact charger in Sec. 5.4.4.
5.4.1 Fundamental Limits on Charging and Polarization of Isolated Drops
Both the Induction and ion impact charging mechanisms are limited by
how much charge can be placed on a drop without Inducing electromechanical
instability or fissioning of the drop. The maximum charge that can be placed
on a drop without an ambient electric field is called "Rayleigh's limit"
(Raylelgh, 1882), and is given in MRS units by
v -8* V VR?
where y is the surface tension. This is one upper bound on the drop charge.
_2
For water, Y " 7.2 x 10 newt/m and Eq. (1) is conveniently written as
-5 3/2
Q_ (coulombs) - (2 x 10 3)RJ/* (2)
nay
where R is in meters.
Similar electromechanical considerations place an upper limit on the
electric stress that can be applied to an uncharged drop In an initially
uniform electric field without producing rupture. This is a limit on the
maximum polarizing field. In this case, Instability results in two or more
drops which, because of the initial drop polarization, are likely to be
charged. The critical electric field is (Taylor, 1964)
142
-------
Sec. 5.4.1
-1/2
- 0.458 J -L- R
ay
0-458 R
o
For water drops in air, Eq. (3) becomes
,4
4.12 x 10
Cay
/R
Table 5.4.1 Rayleigh's Limiting Charge QD(. Taylor's Limiting
Kay
Electric Field Intensity E^, and the Saturation
Charge as a Function of Drop Radius R
R - m
icf6
ID'5
ID'4
ID"3
Q - coulombs
2 * ID'14
6.32 x 10"13
2 x 10"11
6.32 x l(f10
E
Tay
4.12 x 107
1.3 x 107
4.12 x 106
1.3 x 106
Q at E -10° V/m
c c
3.34 x 10~16
3.34 x 10~14
3.34 x 10~12
3.34 x l(f10
In estimating drop charges, use is made of the saturation charge on
a drop charged by ion impact in a field E (Eq. 5.4.20)
Qc - 12*eoR2Ec
-10 t
- 3.34 x 10 AVE (5)
c
Table 5.4.1 shows the dependence on drop radius of Rayleigh's limiting charge,
of Taylor's limiting electric field Intensity, and the ion-impact saturation
charge given by Eq. (5). Note first that, under the assumption of a charging
field E approaching the breakdown strength of air, the saturation charge is
c
less than Rayleigh's limit. Hence, there is some leeway on the drop charge
143
-------
Sec. 5.4.2
that can be used insofar as Rayleigh's limit is concerned. Second, only for
the extremely large drops are electric field intensities required to produce
rupture of an uncharged drop within a range where they might be encountered
in a practical device. (The breakdown strength of dry air between uniform
electrodes is about 3 x 10 V/m.) Thus, under practical conditions, there
does not appear to be any limit on the drop charging or polarization brought
about by instability.
5.4.2 Pressure Nozzles and Orifice Plate Generators with Charge Induction
For the purpose of generating monodisperse charged drops, the
multiple orifice pressure nozzle of Fig. 5.4.1 can be used. The charging
bars can be at different potentials v and v, relative to the orifice plate
so that charge induction can be used to produce a mixture of drops with
charges in two families. By making the voltages equal, unipolar drops are
generated. With the voltages equal and opposite, bicharged drops result.
ACOUSTIC
EXCITA-
TION
WATER
UNDER PRESSURE
o o
Fig. 5.4.1 Cross-sectional view of acoustically excited pressure nozzle with
Induction type charging electrodes
144
-------
Sec. 5.4.2
This type of generator has the virtue of behaving in a predictable fashion,
in part the result of acoustically exciting the orifice plate so as to
control the break-up of the streams into drops.
Used in "reverse" to specify the orifice, flow conditions and acoustic
excitation frequency, the following analysis is the basis for design of an
apparatus to generate charged drops of given size and charge.
Mechanical Atomization The actual generator consists of 512 orifices
arranged in two parallel rows approximately 5 inches in length. From each
orifice comes a cylindrical stream of water. This jet is unstable, in the
sense that infinitesimal disturbances upstream with a certain frequency can
result in a disturbance that grows without limit the further downstream
one proceeds (Melcher, 1963). The variation of this spatial growth rate
with frequency is shown in Fig. 5.4.2
1.0
6/6 -
III I I i i
I I I M I I i I
Fig' 5-4-2 Growth rates of instabilities on convecting liquid streams
(6)
where p is the density of water, Y its surface tension, c the jet radius,
and U Its velocity. All frequencies lover than
145
-------
Sec. 5.4.2
are convectively unstable in this sense, with a maximum growth rate occurring at
U
f - f » 0.11 — (8)
m c
If the source of this stream is vibrated at a frequency f in this range,
disturbances corresponding to a wavelength of approximately
U
X8 « ^ (9)
result. Downstream, the amplitude of the disturbance becomes sufficient to
cause the stream to break into drops. This size of the drops can be
determined from mass conservation
R " H c V (10)
In general, the stream contracts upon exiting from the pressurized region
behind the plate, and thus its size does not correspond to that of the
aperture. The coefficient of contraction, C , the ratio of the actual
stream area to that of the orifice, can be determined once the physical
characteristics are specified. The untapered orifices of the experimental
device have a diameter of 30.5lim and are fed from an effectively infinite
reservoir. The initial velocity of the drop is found to be approximately
lOm/sec. This implies a Reynolds number based on the orifice diameter, d
o'
of (Rouse, 1957)
R . WA = 300 (11)
y n
where n is the viscosity of the water. From Fig. 5.4.3, the coefficient
of discharge, C_, related to the flow rate, F, and the coefficient of con-
146
-------
Sec. 5.4.2
1.0
0.1 _
lo"1 10° lo1 io2 10 R loA 10 1°
y
Fig. 5.4.3 Coefficient of discharge for a circular orifice as a function
of Reynolds number
traction, GC, by (Rouse, 1957, p.55)
2
F - C
ird
D^f
(12)
(13)
can be determined to be 0.7, where D is the diameter of the reservoir and
Ap is the pressure difference across the orifice. Since d /D •*• 0, the co-
efficients of discharge and contraction are practically equal. This implies
for the initial drop stream radius
C d
c - --0- 10.7ym
(14)
The cutoff frequency for a stream of this size and velocity would be
fc - 150 kHz
(15)
A frequency of 54 kHz is selected to both coincide with one of the vibrational
147
-------
Sec. 5.4.2
modes of the orifice plate and be near f . The corresponding wavelength is
-4
1.85 x 10 m. The resulting drops have a radius of 25um, determined from
Eq. (10).
Charging With the acoustic frequency adjusted to a resonance of the
orifice plate, the vibration amplitude is varied until the break-up point of
the streams occurs just between the inducer bars of Fig. 5.4.1. At the
instant that drops break away, they act as one electrode of a capacitor,
with the other electrode the inducer bar. Hence, drop charge is of polarity
opposite to that of the inducer bar voltage. The time required for the
charges to migrate from the base of the stream to the tip, the relaxation
time, is approximately (Woodson and Melcher, 1968, p. 370)
TRe * f <«>
where £ is the dielectric constant for the material and a the electrical
conductivity. As long as this period is short compared with the time
necessary to form a drop, the charging mechanism will be effective. For
water, a varies considerably, but is typically 4oho/m, e - 80e and hence
the relaxation time is T ~ 10 sec. The time necessary to create a
Kt
drop is the inverse of the applied acoustic frequency. Thus, it is
evident from the extremely short time TR that on the time scale of the
drop creation, the water can be treated as a perfect conductor.
Because the inducer bar-drop system comprises essentially an ideal
two-terminal pair capacitance system, it is expected that the charge induced
is related to the inducer bar voltages by relations of the form
:i t:;]
D D
(17)
148
-------
Sec. 5.4.3
where the capacitance coefficients are functions only of e and geometry.
Symmetry requires that C - Cfe. The mutual capacitance C reflects the
charge induced on a given stream by the opposite inducer bar. This cross-
coupling is small, as can be seen by the fact that a complete screening model
gives a fairly accurate estimate for C and C,. That is, if it is assumed
that one of the drop sheets acts as a planar capacitor plate relative to
the nearer inducer bar, then all of the electric field lines from that bar
terminate on the nearest sheet of drops. For the left electrode of Fig. 5.4.1
with sheet spacing d, this field is essentially v,/d.
D
A more detailed view of the geometry is shown in Fig. 5.4.4, where the
spacing between streams in a given sheet is h and the spacing between drops
is essentially X^as given by Eq. (9). According to this complete screening
model, all of the flux that would terminate on the area X associated with
s
each drop in fact terminates on the drop just as it is breaking free. Hence,
- <">
This expression is useful for design purposes. For the experimental system,
d - 1.62 x 10~ m, h - 4.96 x 10~"4m and X - 1.84 x 10~4, and Eq. (8) gives
s
5 x 10~ F. The measured charging characteristics are given in Fig. 5.4.5.
They are essentially linear, deviating slightly toward the higher voltages.
It is thought that the intense field causes the streams to be attracted to
the bars, decreasing their separations and enhancing the charging for a
given applied voltage. Note that the measured inducing capacitance Is
4 x 10 F, as compared to S x 10 F estimated using Eq. (18).
5.4.3 Pneumatic Atomlzation With Induction Charging
By using an Inducer electrode in the vicinity of the region where the
149
-------
Sec. 5.4.3
T
Fig. 5.4.4 Geometry of inducer bar relative to one of the two sheets of drops
drops break away, pneumatic nozzles, of the type used to make fog, can be
adapted to produce charged drops. Such drop generators are shown in Fig.
5.4.6. Two devices, one an adaptation of a commercial unit and one with 10
nozzles (Herold, 1967; Reeve, 1967) are illustrative of the general class
of pneumatic-induction generators. Although they are found to give charge
densities NQ of the same order as obtainable with the orifice type generators
of Sec. 5.4.2, they also produce polydisperse nonuniformly charged drops.
Hence, they are not used in the studies described in Chap. 6. However,
the generators are applicable to practical devices. In each unit, the
atomizatlon air tends to maintain the electrical clearance between the
electrode and the metallic structure used to inject the water. The extent
to which the air is successful in this is reflected by the impedance seen
by the Inducer source, which is equivalent to a resistance of about 50 yfl
150
-------
Sec. 5.4.3
90 100
B
1 1 1 I
50 60 70 80 90 100
Fig. 5.4*5 Drop charge and mobility as a function of inducer bar voltage.
VD " va * vb» Q in units of 10 coul, B in units of 10~6m/sec/V/m.
151
-------
Sec. 5.4.3
AIR
WATER
1.6mm
ELECTRODE
A. 7mm
\\\ vy1
N
\
\?^^'^^^OX^
-*- o (VAY
air
\\\\ \
Inducer
electrodes
(a)
V
I
WATER
•AIR
0.5mm
ESS
plexiglas
1
T
7. 5mm
(b)
inducer electrode
Fig. 5.4.6 Pneumatic nozzles with induction chargers (a) commercial nozzle
with inducer electrode added (b) multi-nozzle unit with built In
chargers
152
-------
Sec. 5.4.4
and a capacitance of 7 x 10 F for the 10 nozzle unit.
As in the orifice type generator with induction charging, the drop
charge is a linear function of inducer voltage. Figure 5.4.7 shows the total
current carried by the drops as a function of inducer electrode voltage. These
tests are for a 60Hz inducer voltage, so that the drop current issuing from
the generator is a traveling charge wave. This illustrates the convenient
control that can be obtained by the induction method over the drop charge,
and allows simple induction measurement of the drop-beam charge-density by
means of an induction electrode downstream. Such measurements show that for
the multi-nozzle unit injecting into a channel flow having velocity 18m/sec
2
and cross-sectional area of 80cm , and with an inducer voltage of 200 volts,
-4 3
NQ is in excess of 2 x 10 C/m . Drop size ranges from 25um to a few ym.
With this range divided into three families by number, 10% are of average
diameter 22um, 25% are llym and 65% are 5ym.
5.4.4 Ion-Impact Charging
An alternative to the induction charging which is applicable to
either of the mechanical techniques for forming drops discussed in the previous
section, employs a corona discharge and an ambient electric field. In the
supermicron range of interest for the drops, the charging process is classically
modelled by what amounts to a zero flow limit of the laminar flow drop
collection model described in detail in Sec. 6.2.2. The role of the submicron
particles in that section is played here by ions originating in a corona
discharge. In a flux of ions created by an ambient charging field £ , the
drop acquires a charge
Q - Q,
t/T,
(19)
153
-------
Sec. 5.4.4
3
CO
c
at
3 2
a
8
Q
1
100 200 300
Inducer voltage (nns)
Fig. 5.4.7 Current carried by drops generated using 60 Hz inducer voltage.
Solid curve is multi-nozzle unit with 40 pst air pressure
while broken line is single commercial nozzle.
154
-------
Sec. 5.4.A
where the maximum possible charge, Qc> is
Qc - 12TreoEcR (20)
and the characteristic time for charging
4c
(21)
Here, n . , q . , and b. are respectively the number density, charge, and
mobility of the ions. Note that, except for the factor of 4, T± takes the
same form with respect to ions as does T for submicron particles.
£L
The theory of ion-impact charging is well described by White (1963,
pp. 126-136). However, there is one important difference between the ESP
charging and what is required for the scrubber drops. In the latter context,
it is undesirable to remove drops in the charging process and hence before
they can serve their scrubbing function. Thus, there is an additional
characteristic time, the precipitation time T = s/BE (see Sec. 2.3) in-
pc c
volved in properly designing the charging system. The distance s between
structures used to impose Ec must be large enough that drops are not pre-
cipitated before they are charged
Tpc » TI (22)
The maximum charge Q is 12 times the charge that would be required to
2
terminate a uniform electric field on the drop cross-sectional area irR .
Given fields of comparable magnitude for induction charging and impact
charging, roughly similar charges per drop are often produced. The
Induction charger of Sec. 5.4.2 illustrates this point. There, the charge
is required to terminate the inducing field on an area also somewhat larger
155
-------
Sec. 5.5
than that of the drop cross-section. Thus, it is not surprising that simple
point arrays of corona sources placed in the vicinity of the pneumatic
nozzles described in the previous section give drop currents similar to
those obtained with the induction chargers. Of course, because the corona
requires a threshold voltage for onset and differs considerably in its
properties between positive and negative polarity, there is not nearly the
flexibility in varying the charge as there is with the induction charger.
5.5 Charged Drop Self-Precipitation Experiments
The tendency of unipolar drops to self-precipitate is made dramatically
evident by simply observing the trajectories of drops with various levels
of charging. The drop generator described in Sec. 5.4.2 is used to produce
the beam of 50ym drops shown in Fig. 5.5.1. If injected into free space
with no charge, the drops decelerate within about 20cm from an initial velocit
of lOm/sec to about 8m/sec. They then traverse the remaining 20cm of vertical
height shown in the figure at an essentially constant velocity. The spreadina
is typical of a turbulent jet of drops and entrained air. Without charging
the spreading is caused by turbulent diffusion. With a charging voltage of
V - 30 volts, this diffusion is overtaken by the self-field spreading of
the jet. Further increases in V shown in sequence make the highly mobile
nature of the drops in their own fields evident. Based on the drop density
about 10cm from the orifice plate, T assumes the values OD^ 5 x 10~^ and 2 x irT
sec in the sequence of pictures. These times, which according to Sec. 5.2
characterize the drop self-precipitation process, are to be compared to the
residence time; the time taken by drops to traverse the length of the system
It is the objective of this section to experimentally explore the dro
dynamics resulting from drop injection into a system designed to control
156
-------
(a)
(b)
Fig. 5.5.1 Jet of 50ym diameter
drops ejected into open volume
between plane parallel electrodes
with 10 cm spacing. Residence time
for a drop in 40 cm length of system
-2
is about 5 x 10 sec.
(a) VD = 0, (b) VD = 200 volts,
T_ * 5 x 10~3 sec. (c) V_ - 300,
-3
TR * 2 x 10 sec.
(c)
157
-------
Sec. 5.5.1
5.5.2
the recirculation of air entrained by the drops. This system, shown in
cross-section by Fig. 5.5.2, is used in Chap. 6 for the study of charged
drop scrubbing of a recirculated aerosol.
5.5.1 Experimental System
Unless otherwise noted, the material used for the structure shown in
Fig. 5.5.2 is plexiglas. The drop generator is mounted at the top and the
spray directed downward. The drops first pass through a short section
containing a series of inlets. These serve as a manifold for the aerosol
when experiments of the next chapter are conducted. The drops then enter
a central channel 2.5cm wide and about 60cm long. At the bottom water is
allowed to drain in such a way that no gas escapes. An aspirator withdraws
from the bottom a small flow, slightly greater than that injected through the
inlet manifold. The remainder is drawn in by the slightly negative pressure
within the channel through leaks in the vicinity of the charging bars. The
gas is allowed to recirculate by means of the two side channels, each 2.5cm
wide. The recirculating flow is much larger than the inlet and outlet
contributions. Provision is made for a probe to be Inserted at the bottom
capable of moving vertically within the central section. The system can
normally operate continuously for approximately fifteen minutes. At this
point accumulations of water on the charging bars become sufficiently large
to bridge the gap between the bars and the grounded generator, causing the
system to become shorted. The apparatus must then be shut down and cleaned.
5.5.2 Drop Velocity Measurements
Although the drops are ejected from the generator at a velocity of
approximately lOm/sec, they are rapidly decelerated by the drag exerted
on then by the surrounding air. In the process the gas is accelerated.
158
-------
Sec. 5.5.2
Drop generator
Charging bars
1 — 1
I
p.
1
5
51.5
T
_L
L_
•••••
••••«
H1"
1 1
-* fc-
2.5
1
1
1 •
1 t
1 »
1 I
t 1
1 I
1 1
I k
1 I
1 1
' i
,> t
(2.51
i i
1 1
( 1
III!
!l»!
; !
i
i
i
•
i
— aerosol inlet
i:; i
2.5
i
\
Anemometer
Depth into paper
14
Aerosol
outlet
Fig* 5*5.2 Schematic of experimental system used to study dynamics of
unipolar drops and CDS-I, CDS-II and CDF collection of aerosol
All dimensions in cm.
159
-------
Sec. 5.5.2
In the experimental system the gas is allowed to recirculate, thereby
enabling its velocity to increase to some relatively stable value. During
injection into the central section, the two parallel sheets of drops evolve
into a jet which eventually spreads by turbulent diffusion to fill the cross
section of the channel. When the drops are uncharged, this position is
about 10cm downstream of the entrance of the middle section, and when the
charging bars are set at 200 volts, it moves upstream to a point about Sen
downstream of the entrance.
Knowledge of the variation of the drop velocity with downstream posi-
tion is of central importance in any attempts to correlate experiments with
the models previously introduced. In addition, the relation of the drop
velocity to the surrounding gas velocity is of critical importance in the
next chapter in determining the correct model to use in calculating the
rate at which charged drops collect charged submicron particles. Two
different experimental techniques are used. Both utilize a probe consisting
of a 3/8-lnch by 4-inch coarse chromel screen suspended from a mounting
designed to preserve the insulation of the probe (Fig. 5.5.3). In the first,
a very slow square wave (1 Hz) varying from zero down to some negative value
is applied to the bars. This is used to trigger an oscilloscope connected
to the probe. Fig. 5.5.4 shows the variation of the time at which the
probe current achieves half of its final value as a function of the position
of the probe (measured with respect to the charging bars). Over most of
the channel, the variation is linear, indicating that the drops are moving
at a constant velocity. This speed can be calculated from the slope of the
curve as 4.9m/sec.
One criticism of this experiment is that it only tests slightly
160
-------
Sec. 5.5.2
0.95cm x 10cm COARSE CHROMEL GAUZE
ALUMINUM CAP
INSULATION OF INNER CONDUCTOR
RUBBER SEAL
COAXIAL CABLE
•*- STAINLESS STEEL TUBING
Fig. 5.5.3 Current probe used to measure unipolar drop current impinging from abov
z(cm)
Fig. 5.5.4 Delay time as a function of distance downstream of charging bars
161
-------
Sec. 5.5.2
charged drops. Another is that it is unsymmetric in the sense that the
measured point is a transition between two physically different systems:
one in which the drops are uncharged and the other in which they are charged.
The latter exhibits self-precipitation of the drops, hence, possibly a
different amount of coupling to the gas, resulting in a different droplet
velocity. To rectify this, in the second experiment a balanced square-
wave of voltage is applied to the bars, thereby inducing positive and
negative drop regions. The frequency is set at 20 Hz. The signal from
the probe is fed into a lock-in amplifier, sensitive to signal frequency
and phase with respect to the signal applied to the bars. Measurements
are then taken of positions at which the output of the amplifier vanishes.
These are given in Fig. 5.5.5. Except for effects reflecting the turbulence
it can be argued from several points of view that the frequency measured by
any stationary observer downstream is the same as the excitation frequency.
, ^u ± 5 V ± 10 V ± 20 V ± 100 V
zo (cmT\
v (m/sec) 43X 43 \ 43 43>
) 4.0 j 3.8 ) 4.0 ) 4.4
33> 33.5v 337 327
) 4.4 ) 4.4 \ 4.0 } 4.4
'' 59.S 2*i/ 71 /
22'. 22.5 23'
6.
} 6.2 \ 6.2 \ 6.4
i.57 7.0/ 77
Fig. 5.5.5 Positions 90° out of phase with voltage applied to charging
bars for f - 20 Hz and the implied velocities
Thus, since the distance between the measured nulls is half of the spatial
162
-------
Sec. 5.5.2
wavelength, the velocity of the drops can be calculated from
v - fXd (1)
where X^ ±s the wavelength of the signal measured by the probe and f the fre-
quency of the signal applied to the charging bars. From the data it is
evident that over most of the channel length the drops are moving at a
relatively constant velocity
v - (20 Hz) (0.2m) - Am/sec (2)
It is also noteworthy that this velocity does not change even when the
charging voltage is increased sufficiently to result in the self-precipitation
of the majority of drops.
Since the drops eventually move at a constant speed, their speed
should correspond to that of the gas, U. As a check on whether the measured
evolution is reasonable, the equation of motion for a single drop is solved
dt TgR sR 9n
(3)
* '
where v is the drop velocity and U the gas velocity. Since the gas velocity
is much larger than the settling velocity of the drop, gravitational effects
are ignored. The solutions for the drop velocity and position are
v . (VQ - U) esR + U (4)
z - T8R(vQ - U)(l - e~t/TsR) + Ut (5)
After a time corresponding to 2T _, the calculated drop velocity decreases
from lOm/sec to 4.8m/sec, just about its terminal value. This position can
163
-------
Sec. 5.5.2
be calculated to be about 10cm downstream of the generator, and corresponds
quite well with positions beyond which the probe Indicates a constant drop
velocity.
This agreement between observation and the extremely simple model
represented by Eq. (3) Is somewhat misleading. In fact, the drops interact
aerodynamlcally with each other, and the drag on a drop is only approximately
equivalent to that on an isolated sphere, as pictured by the time constant
T ... Because of these interactions, drops assume a spectrum of velocities
SK
as the stream develops into a turbulent jet. Those that move most slowly
are expected to be selectively precipitated to the walls, either through
turbulent diffusion or self-precipitation.
Because of the complexity of the turbulent jet fluid mechanics,
independent measurements are made of the velocity of the gas in the return
channels, and hence the average gas velocity in this interaction channel.
Two techniques are used. First a hot-wire anemometer, inserted in the upper
section of the return channel, indicates a velocity of 0.7m/sec, independent
of the voltage applied to the charging bars. In another experiment the time
required for an aerosol front injected into the bottom of the side channel
to flow to the top is measured. This interval indicates a speed of
approximately 1.3m/sec. A gas velocity of Im/sec in the return channels
would imply an average gas velocity of 2m/sec in the central section. This
is in contrast with the 4m/sec drop "terminal" velocity measured.
There are at least two possible inferences to be made from this disparity.
First, if the drops and gas move in essential synchronism through the lower
part of the interaction channel, then it is clear that there must be a
profile across the channel that peaks at the center (where the drops are
164
-------
Sec. 5.5.3
initially more concentrated and the velocity is of the order of 4-5m/sec) and
is depressed at the channel edges. Second, there is the possibility that
there is a slip between drops and gas. But this latter conjecture Is negated
by the observed essentially constant velocity established for the drops by
the time they near the lower extremity of the interaction channel. Hence,
the evidence is that the drops and gas tend to move together with a profile
which is dominated by the center half of the channel cross-section. It is
remarkable that even as the drops are charged, and hence their trajectories
radically influenced over much of the interaction channel, the mean gas
velocity remains essentially invarient.
Visual examination of the flow in the return channel, using puffs of
aerosol for visualization, reveals a uniform profile. Hence, the velocities
measured in those regions correspond to the average velocities. As a check,
the distance over which the profile of the flow in those regions is transformed
from a uniform one at the inlet to a fully developed Poiseuille one corresponds
to the distance z, required for laminar boundary layers to grow from each wall
to the center of the channel (Schichting, 1960)
Us2
z. - 0.04 7^7- (6)
d (n/p)
_2 _5 2
for s - 2.54 x 10 m, U - Im/sec, ri/p - 1.5 x 10 m /sec, z, - 1.7m.
Since the channel length is approximately 0.5m, at the position where the
anemometer is inserted, the profile would still be rather flat there.
5.5.3 Measurements of Self-Precipitation of Charged Drops
If both charging bars are set at a certain d-c voltage, the drops
produced are monocharged, and the current intercepted by the current probe
is
165
-------
Sec. 5.5.3
Ip(z) - N(z)Qv(z)Ap (7)
where A is the area of the probe. The drop concentration and velocity are
averages across the channel. If the above equation is normalized to its
value at some reference position z downstream, then
Ip(z) - N(z)v(z)/N(zr)v(zr) (8)
Figure 5.5.6 summarizes the measured spatial decay of the probe current for
seven charging voltages. These currents have been normalized to their values
near the entrance of the middle section. There the drops travel in twin
sheets, and the probe collects all of the drops passing along its length.
It is evident that diffusive effects play a dominant role in determining
the loss of drops from the system at low voltages since for V < 20 volts
the curves overlap. For voltages greater than 50 volts, electrostatic
precipitation becomes the more significant removal mechanism.
The low voltage decay characteristic can be used to obtain an estimate
of Au, the fluctuating velocity of the large scale eddies. Since the electrostatic
effects are unimportant for these low charging levels, the drop loss can
be accounted for by turbulent diffusion alone. If the region is assumed to '
be uniformly mixed, the drop conservation for an incremental length Az and
width w of the channel can be written, using Eq. (5.2.4) for the particle
flux-density to the walls, as
Uws[N(z + Az) - N(z)] - -2(NAU)wAz (9)
In the limit Az •*• 0,
f.-f^H 00,
and
166
-------
Sec. 5.5.3
VD- volts
• 5
0 10
X 20
0 50
A 100
0 150
0
10
20
z
(cm)
30
40
50
I T
t / I
0 0.2 0.4 0.6 0.8 1.0
I (z ) - microamps
0.060
0.105
0.170
0.460
0.800
0.900
200 1.000
Fig. 5.5.6 Spatial decay of probe current normalized to value at z - z -
llcm, where z is the position of the probe relative to charging
bars
1L. e T. o =HL
N e ' T ~ 2AU
o
(ID
From the experiment
* 30cm -*• AU = 15cm/sec
(12)
167
-------
Sec. 5.5.3
If the reference position is selected far enough downstream so that
the drop velocity from that point onwards can be considered constant, the
normalized current of Eq. (8) can be equated to the normalized particle
concentration N(z)/N(zr). The evolution of monocharged drops entrained in
a well-mixed channel flow is given by Eq. (5.2.11), which can be used to
evaluate Eq. (8). Thus, the dependence of probe current on position is
(13)
z - z eQU
- " *(V,zy ; 4R(V'zr} " N(z)Q(V)B(V)
r
The droplet charge density at the reference position can be calculated from
the probe current measured there. Since the velocity is known, and the
mobility, B, determinable from the charging curve, all parameters necessary
for the evaluation of the decay length for a given applied voltage are
available.
If the reference position is taken as 16cm downstream of the bars, the
decay lengths corresponding to a drop velocity of Am/sec and the measured
probe currents for the different charging voltages can be determined. These
can then be used to find the normalized position, JE', of each measuring
point corresponding to the various voltages. If the measured values of the
normalized current, I , are plotted against their distance downstream of the
reference point, normalized to the decay length appropriate for each charging
voltage, and if electrical precipitation is the only removal process present,
the data should lie on the curve given by Eq. (13) and shown as the solid
curve in Fig. 5.5.7. Other removal processes will result in the droplet
168
-------
Sec. 5.5.3
i («•)
• SO volti
-f 100 volt*
Q 130 volt*
O 200 »ole»
10
Fig. 5.5.7 Decay of current to probe normalized to value z • 16cm
downstream of charging bars, beyond which drop velocity is
constant (4m/sec). Downstream position z is normalized to
decay length appropriate to particular charging voltage. Note
that as voltage is raised decay rate approaches that predicted
by theory assuming dominance of electric self-precipitation
concentration being attenuated more rapidly than the above relation would
predict. From Fig. 5.5.7 it is evident that for voltages greater than 50
volts, the early portion of the decay corresponds to the purely electrostatic
model. As expected, once the droplet population has been significantly
diminished, diffusive effects become more Important. Thus, at the positions
further downstream, the droplet attenuation is greater than predicted for
electrical self-precipitation alone. Agreement of the self-precipitation
theory and measurements is quite good once the charging voltage exceeds
150 volts.
For diagnostic purposes using a fixed probe, it is useful to recognize
Che dependence of probe current on charging voltage that is implied by Eqs.
169
-------
Sec. 5.6
(7), (8) and (13). These combine to give
r R
where the characteristic charge
£oU67rnR (15)
QR ~ V (z-z )N(z)
is the drop charge at which the probe current would peak if N(z ) were
maintained constant independent of Q. That is, at a fixed location z, the
probe current I at first increases in proportion to the charging voltage,
and then as the self-precipitation comes into play, peaks out and finally
decreases in inverse proportion to the charging voltage. This characteristic
is clearly evident in the measurements of probe current as a function of
charging voltage shown in Fig. 5.5.8. Also as expected from Eqs. (14) and
(15), the peak occurs at lower and lower values of V as the distance down-
stream is increased. Actually, N(z ) is itself a function of the charging
so that corrections should be made in evaluating Eq. (15) as a function of
9 3
Q. But, taking as an average value N(z)=5xlO drops/m inferred from
the probe current measured at z =• llcm. and with V = 100 volts, the peaks
in the curves of Fig. 5.5.8 are predicted by Eq. (15) (using the charging
characteristic of Fig.5.4.5 to relate V to Q ) to occur at 64, 51, 40 and
34 volts for the Increasingly greater values of z. As would be expected,
the agreement is good for the probe measurement taken furthest downstream.
5.6 Experimental Investigation of Self-Discharge of Blcharged Drops
One of the objectives in experimentally investigating the dynamics
of systems of bicharged drops alone has been accomplished in Sec. 5.5.
170
-------
Sec. 5.6
0.3 -
0.2 _
0.1 ~
0
0
50
100
150
200
Fig. 5.5.8 Measured drop-probe current as function of V (which is
proportional to the drop charge Q) at four different positions
z from charging bars
With bicharging, the development of the turbulent jet in the interaction
channel of the system shown in Fig. 5.5.1 is much the same as with no
charging. The spreading of the neutral bicharged beam is qualitatively
independent of charging, and measurements of circulation velocity in the
return channels indicate a gas velocity essentially independent of charging.
171
-------
Sec. 5.6.1
5.6.2
Hence, for the purposes of representing the fluid mechanics in the next
chapter, the results of Sec. 5.5 are sufficient.
The second objective of establishing some confidence in the self-
discharge theory discussed in Sec. 5.3 is pursued in the remainder of this
section with the drop-jet injected into an essentially open region. This
permits photographing the drops without the intervention of the wetted walls
which make observation at best difficult in the enclosed system.
5.6.1 Experimental Apparatus
The drop generator is again as described in Sec. 5.4.2 with the
inducer bar voltages at opposite polarity and adjusted to produce drops
of the same magnitude of charge. The drop stream is directed downward
into an essentially open region, as shown in Fig. 5.6.1. To discern be-
tween the discharged drops and those that remain charged at a given
distance z from the drop generator, a pair of electrodes are used as a
precipltator to deflect the charged drops. For the potentials positive as
shown in Fig. 5.6.1, positive drops are induced by the left bar, and if
these remain charged upon reaching the analyzer at the position z, they are
deflected to the right. The opposite is true of drops with charges induced
by the right electrode. Of course, after about 20cm of travel, the initially
sheet-like streams have developed into a turbulent jet and it is from this
point on that interest is focused.
5.6.2 Measurement of Drop Velocity
By making use of the analyzer electrodes as a field detector and
exciting the inducer bars with 60Hz alternating voltage, it is easy to
obtain a measure of the drop velocity as a function of distance from the
drop generator. The system is as shown in Fig. 5.6.1 except that Instead
172
-------
Sec. 5.6.2
\
Fig. 5.6.1 Bicharged drop stream with variable position analyzer to deflect
drops that remain charged at a given position z Dimensions in cm.
of the voltage source V , there is an oscilloscope. Also, the inducer bars
are connected to the same a-c source so that the drop stream evolves as a
traveling-wave of space charge. As this charge passes between the electrodes,
charge induced on the left electrode results in a current which is measured
173
-------
(a)
(b)
(c)
Fig. 5.6.2 Bicharged drop jet in configuration of Fig. 5.6.1. (a) V «0 and
Vp-0.
With VD»500V and Vp=6kV, (b) z
3.5cm, (c) z =7.25 cm, (d) z - 11 ^ Note
increase in discharged drops as analyzer field is imposed increasingly furth
downstream.
-------
Sec. 5.6.3
by the oscilloscope. Measurement of positions z at which the signal changes
its phase by 180° gives the half-wavelengths along the stream. Hence, the
drop velocity at that position is v = fX , where f = 60 H . Typical drop
velocities measured in this way for the unconfined drop-stream are shown in
Table 5.6.1.
Table 5.6.1 Typical Drop Velocity as a Function of z as Measured by
Observing Phase of Traveling Charge Wave
z - cm v - m/sec
16 9.7
24 7.8
31 8.9
37 6.7
43 6.5
Hence, the drops are ejected at about lOm/sec, and in the unconfined
configuration, continually transfer momentum to the surrounding air as
they slow to 6.5m/sec near the bottom of the test range.
5.6.3 Drop Discharge Process
The jet of drops and entrained air is shown in Fig. 5.6.2. With no
voltage V applied to the analyzer and no charge inducing voltage V , the
drop jet appears as shown in Fig. 5.6.2a. At increasingly greater distances
z from the inducer bars, the sequence of pictures then shows the effect of
simultaneously charging the drops to V = 500 volts and imposing an analyzer
field with V - 6kV. The self-discharge of the two families of drops is
evident from the photographs. At the first position, where the top edges
175
-------
Sec. 5.6.3
of the analyzer plates are 3.5cm below the inducer bars, essentially all of
the drops remain charged, as is evident from their being deflected by the
imposed analyzer field. By the time the drops reach the second position,
where z - 7.25cm, a neutral beam is formed, which is undeflected by the
analyzer. This beam has increased still more at the expense of the charged
drops by the time drops reach the third position, where z - llcm.
Over the length shown, the jet makes a transition over the first 5-10cm
from a highly ordered pair of oppositely charged drop sheets to a turbulent
jet. From the last two pictures, it is evident that the discharge process
does in fact go forward in the turbulent flow region. Qualitatively, the
discharge process occurs as expected. However, closer scrutiny shows that
the discharge rate is slower than expected from Eq. (5.3.21) with K* - 2.
Based on the width of the jet entering the analyzer in Fig. 5.6.2c, the
—9 3
total drop density is 3 x 10 drops/m . Using the charge and mobility
extrapolated from Fig. 5.4.5, TR - 5.5 x 10~ sec and £R - 0.5cm. This is
to be compared to £R - 3-4cm Inferred from the last two photographs and
Eq. (5.3.21) by taking N/NQ ~ 1/2, z - (11-7.25)cm and NQ defined as the
number density at z - 7.25cm. Thus, the experimental evidence is that in
the turbulent jet, the drops discharge each other at a rate 6-8 times more
slowly than would be expected from the model leading to Eq. (5.3.21).
Considered as a pair of oppositely charged sheets, so that the drops
experience an essentially uniform electric field, but nevertheless are
retarded by the viscous drag of an isolated sphere, the sheets would be
attracted to each other within a distance of 0.2mm from the charging section.
Considered as isolated pairs of drops having the initial spacing of 1.6mm
between the sheets, the drops should neutralize each other within 3.7cm,
176
-------
Sec. 5.6.3
A
according to the two drop model of Sec. 5.3.1 (C - 4.7 x 10 , T_ » 0.6 sec,
R
_3
T _ • 7 x 10 sec). It is clear from the pictures that the drops survive
SK
retaining their initial charge, to a distance of several centimeters. Beyond
this distance, the turbulent regime prevails.
The spreading of the deflected drops might be interpreted as an
indication that the drops are not uniform in size or in charge. In fact,
they are extremely uniform in both, and the spreading is a portent of the
electrohydrodynamic instability that characterizes the transition from the
highly ordered drop beam to the turbulent jet. A pair of charged sheets of
drops are unstable, in the sense that the sheets tend to buckle, some drops
moving inward and some outward under the influence of the self consistent
self-fields. Ignoring the viscous drag, the rate of growth of this Instability
can be shown to be
J8irR3pe
, 2 ° CD
NoQ k
where N° is the surface number density of drops in a sheet and k is the
wavenumber of the instability wavelength in the z direction. Taking k - 2ir/X
o
as the fastest growing wavelength where X is the distance in the z direction
8
between drops, (the shortest distance consistent with the continuum model
s —11 2
used to derive Eq. (1)), N » 6 x 10 drops/m and Q and M consistent with
the drop size and charging voltage, the rate of growth of this instability
is predicted by Eq. (1) to e-fold in the distance 2.5mm. Noise initiated
at the drop generator excites this instability, which then apparently
amplifies into the distribution of particles seen when the analyzer field
is applied.
177
-------
Sec. 6.1
6 Scrubbing and Precipitation of Charged Submicron Aerosols by Charged
Supermicron Drops
6.1 Objectives
Three mechanisms for removal of submicron particulate by means of
fields associated with charged drops are explored theoretically and experi-
mentally in this chapter. In two of these, the CDS-I and CDS-II configurations,
the particulate is collected by the drops. First, unipolar drops (of one
sign) are used to collect submicron particles (of the opposite sign), and then
bicharged drops, injected with net space charge neutrality, are used to
collect charged particulate. In the third mechanism, the CDF configuration,
drops and particulate are charged to the same sign, and hence the particulate
is collected on the walls, much as in a conventional imposed field precipitator
or in a space charge precipitator. The basic difference comes from the life-
time of the charged drops.
To develop a model for the CDS types of interactions it is first
necessary to have a theory for the process through which the charged drops
collect the charged particulate. To this end, Sec. 6.2 develops theories
appropriate when the fields dominate in the collection process in two
aerodynamic extremes, where the flow is laminar and where it is completely
turbulent. For the most practical situations, these theories point at
essentially the same collection rate. The remainder of the sections
devoted to developing models, Sees. 6.3-6.6, combine the constituents of
the three systems to obtain the cleaning performance as a function of basic
parameters. Fundamentally, these systems involve five time constants: three
times connected with the charged drops and particles, Tfl, TR and TC, which
represent phenomena having an effect in accordance with their relation to two
178
-------
Sec. 6.2.1
more times, the gas residence time and the drop residence time. Experiments
are correlated with these models in Sees. 6.7-6.9. The main products of
this chapter are models, supported and qualified by experimental correlations,
that can be used to scale and optimize the CDS-I, CDS-II and CDF configurations.
6.2 Models for Particle Collection on Isolated Drops
6.2.1 Laminar Theory of Whipple and Chalmers
Whipple and Chalmers (1944) use an imposed field and laminar flow
model to predict the charging of water drops as they fall through positive,
negative, and both positive and negative ions. Their theories cover the
results given earlier by Pauthenier and Mme. Moreault-Hanot (1932). This
latter work, which is the basis for the theory of impact (field) charging
as used in precipitator design (see Sec. 5.4.4), did not include the aero-
dynamic effect of the streaming neutral gas. Because the particle inertia
is ignored, the model developed here for collection of charged particles
on a charged drop moving relative to a laminar gas is essentially the same
as these ion-impact models.
A schematic view of the physical situation is depicted by Fig. 6.2.1
wherein the particle is viewed as fixed in the frame of reference, and
hence the neutral gas streams relative to the drop with a velocity WQ.
The imposed field, like the relative flow, is uniform at infinity with
the amplitude E which is defined as positive if directed as shown in
Fig. 6.2.1.
Objectives in the following derivations are to determine the rate of
charging and hence particle collection of the drop, given its initial charge,
and to find the final charge established. Regimes of charging are demarked
by the critical charge
179
-------
Sec. 6.2.1
Charge Q
Fig. 6.2.1 Spherical conducting drop in imposed electric field EQ and
relative flow w that are uniform at inifinity. E and v are
o o o
positive if directed as shown; in general, the electric field
intensity E can be either positive or negative
Q - 12ire R*E
xc o o
(1)
which can be positive or negative, depending on the sign of EQ. Rates of
charging are characterized by the currents
I± -
(2)
also determined in sign by E . The magnitudes of the positive and
180
-------
Sec. 6.2.1
negative particle charge densities are n+q+p+ respectively, at infinity.
That the charging rate is to be calculated infers that the particle
motions are not in the steady state. However, if transit times through
several drop radii R are short compared to charging times of interest, then
the drop charge, Q,and its associated field can be regarded as constant
throughout the transit. The drop is well represented as perfectly conducting,
hence the potential and electric field intensity follow from well known
solutions (in spherical coordinates (r, 6, ).)
3 3
E - - V - {E (-^ + 1) cose + Q z> I + {E (\ - 1) sin6} I.
o j
-------
Sec. 6.2.1
±a readily available in the literature.
w R 2 3 i
21 VT>/ 9*I»' •> ^J •**•" ** \5)
K f. K. i. r
where
Equations 4.4.5 (with diffusion and space charge negligible) and 4.4.6
define the particle motions. They are equivalent to
dn - 0 on -^ " v ± b.¥ (7)
± at i
That is, the particle density of each species is constant along given force
lines in (r,t) space. If we are interested in determining the charge
distribution within a volume enclosed by the surface S, then it is appropriate
to impose boundary conditions on the i'th species, wherever
n • ( v ± bjl) < 0 (8)
where n is taken as positive if directed out of the volume of interest. At
points on the surface other than those that satisfy Eq. (8), a boundary
condition cannot be imposed. These observations, although seemingly obvious
in the transient problem, are crucial to making sense out of quasi-steady
motions.
With the stream functions given, the lines of constant charge density
given by Eq. (7) take the form
- (tbz + f) (9)
r2 sine 3e
182
-------
Sec. 6.2.1
Multiplication of Eq. (10) by dr/d6 and equating that expression to Eq. (9)
multiplied by r gives the exact differential
d(±bZ + *) - 0 (11)
provided £ and Y are independent of time. Here, the fundamental assumption
of quasi-steady particle motions must be invoked. To integrate particle
equations of motion in this way particles must see essentially the
same field and flow distribution throughout their motions through the volume
of interest. But the particle transit times are likely to be brief compared
to the time required for particles to charge the drop and hence change the
electric field intensity significantly. Thus, over a longer time scale, the
flow and field distribution, hence the stream functions, are functions of
time. In summary, Eq. (11) shows that the charge density of a given species
is constant along constant stream function lines
n+ « constant on ±b+I -f ¥ - constant (12)
Given Eqs. (4) and (5), the characteristic lines are determined by
substituting into (11) to get
The upper and lower signs, respectively, refer to positive and negative par-
ticles and C is a constant which determines the particular characteristic line.
183
-------
Sec. 6.2.1
Just what constant charge density should be associated with each of these
lines is determined by a single boundary condition imposed wherever the line
"enters" the volume of interest at a point satisfying Eq. (8). Here, ti is
outward at infinity and inward on the spherical surface of the drop.
In terms of parameters now introduced, the object is to obtain the
net instantaneous electrical current to the drop i+(Q, E , w , n.q., n q ).
With the imposed field, velocity and charge densities held fixed, this
expression then serves to give the rate of drop charging as
The rates of particle collection are then i./'U. an<* "*•_/ w . Otherwise
the charge density is imposed as z •* + °° because the positive particles enter
from below. Thus, the charge-imposed field plane divides into two regimes
b,Eo J 0.
Lines of force v ±b+E originating on the spherical surface carry zero
charge density. At those points on the surface where the force lines are
into the drop, there is the possibility of particle migration. At the drop
surface, the velocity normal to the surface is zero, hence the force lines
184
-------
Sec. 6.2.1
(a)
Fig. 6.2.2 Positive particle charging diagram. Charging regimes depicted in
the plane of drop charge Q and mobility-field product b.E . With
increasing fluid velocity, the vertical line of demarcation indicated
by W moves to the right. Initial charges, indicated by Q , follow
the trajectories shown until they reach a final value given by X* If
there is no charging, the final and initial charges are identical, and
indicated by ® . The inserted diagrams show the force lines v ±b+E,
-------
Sec. 6.2.1
Fig. 6.2.3 Negative particle charging diagram. Conventions are as in the previous
figure. With increasing fluid velocity, the line of demarcation indicate
by v moves to the left
186
-------
Sec. 6.2.1
degenerate to ±b+E. This greatly simplifies the charging process, because
the electric field intensity given by Eq. (3) can be used to decide
whether or not a given point on the particle surface can accept charge.
Evaluation shows that force lines are directed into the particle surface
wherever
Eo < ° ' 6
-------
Sec. 6.2.1
Regimes (f) and (i) for Positive Particles; (b) and (g) for Negative
Particles To continue the characterization of each regime shown in
Figs. 6.2.2 and 6.2.3, upper and lower signs respectively will be used to
refer to the positive and negative particle cases.
The characteristic line terminating at the critical angle on the drop
surface reaches the z •*• - °° surface at the radius y* shown in the respective
regimes in the figures. Particles entering within that radius strike the
surface of the drop within the range of angles wherein the drop can accept
particles. Hence, to compute the instantaneous drop charging current, simply
find this radius y* and compute the total current passing within that radius
at z -». _ oo. xhe particular line is defined by Eq. (13) evaluated at the
critical angle, and on the particle surface: 6 - 6c, r - R. Thus, the constant
is evaluated to be
C - ± |[1 + (£-)2] (18)
x
To find y*, take the limit of Eq. (13) using the constant of Eq. (18)
to determine that
w
(y*)2 (1 + ^1") - 3R2[l - 3-]2 (19)
The problem is particularly simple because the particle flux at infinity
is uniform, so the current passing through the surface with radius y* is
simply the product of the current density and the circumscribed area
(20)
The combination of Eqs. (19) and (20) is
188
-------
Sec. 6.2.1
The second equality is written by recognizing the sign of E in the res-
pective regimes.
In the positive particle regimes (£) and (i), the charging current is
positive, tending to increase the particle charge until it reaches the
limiting value Q - |Q |. Charging trajectories are shown in the figures,
with i, the rate of charging, whether the initial drop charge is within
the respective regimes or the charge passes from another regime iato one of
these regimes, and then passes on to its final value, JQ |. For example,
in the case of the positive particle charging, it will be shown that a
particle charges at one rate in regime (1) and then, on reaching regime (i),
assumes the charging rate given by Eq. (21), which it obeys until the charge
reaches a final value on the boundary between regimes (f) and (c).
Also summarized in the charge field plots of Figs. 6.2.2 and 6.2.3
are the force line patterns, and the critical angles defining those portions
of the drop over which conduction can occur. As a drop charges and then
passes from regime (i) to (f), and finally to the boundary between regimes
(f) and (c) in the positive particle case, the angle over which the drop
can accept particles decreases from a maximum of 2ir to TT at Q » 0, and
finally to zero when Q - JQ |. It is the closing of this "window" through
which charge can be accepted to the particle surface which is the essence
of the collection process.
Regimes (d) and (g) for Positive Particles; (f) and (i) for Negative
Particles These regimes are analogous to the four just discussed except
that the particles enter at z •+ °°, rather than at z •*• - °°. The derivation
is therefore as just described except that the limiting form of (13) is taken
as 6 -»• 0, with C again given by Eq. (18) to obtain
189
-------
Sec. 6.2.1
(22)
Then, the particle currents can be evaluated as
i*.- 3I+(l+§-)2-± SllJU+ir-r)2 (23)
xc ixci
As would be expected on physical grounds, the positive particle case gives
charging currents and final drop charges in regimes (d) and (g) which are
the same as those in (£) and (i).
Regimes (J) and (k) for Positive Particles; (b) and (c) for Negative
Particles For these regimes, the total surface of the drop can accept
particles. The radius for the circular cross section of particles reaching
the surface of the drop from z •»• °° is determined by the line intersecting
the drop surface at 6 - ir. This line is defined by evaluating Eq. (13)
at r - R, 6 - IT to obtain
C - + (24)
x
Then, if the limit is taken r * °°, 6 •* 0 of Eq. (13), y* is obtained and
the current can be evaluated as
- ±n±q±(±b±Eo + woWy*)2 - - Q (25)
Note that in the positive particle regimes, Q is negative, so the result
indicates that the particle charges at this rate until it leaves the res-
pective regimes when the charge Q » - |Qj.
Regime (1) for Positive Particles; (a) for Negative Particles The
situation here is similar to that for the previous cases, except that
190
-------
Sec. 6.2.1
particles enter at z -*•-», so the appropriate constant for the critical
characteristic lines given by Eq. (13) evaluated at r - R, 6 - TT, is the
negative of Eq. (24). The limit of that equation given as r •*• «, 8 -»• ir
gives y* and evaluation of the current gives a value identical to that found
with Eq. (25). In regime (1), for positive particles, where the initial
charge is negative, the charging current is positive, and tends to reduce
the magnitude of the drop charge until it enters regime (1) , where its
rate of charging shifts to i, and it continues to acquire positive charge
until it reaches the final value JQ | indicated on the diagram.
Regime (e), Positive Particles; Regime (h), Negative Particles In
regimes (e) and (h) for either sign of particles, the window through which
the drop can accept a particle flux is on the opposite side from the in-
cident particles. Typical force lines are drawn in Fig. 6.2.4. Force lines
terminating within the window through which the drop can accept particles
can originate on the drop Itself. In that case, the charge density on the
characteristic line is zero, since the drop surface is incapable of providing
particles.
To determine the particle charge that just prevents force lines origin-
ating at z •»• °° from terminating on the particle surface, follow a line from
the z-axis where the drops enter at infinity back to the drop surface. That
line has a constant determined by evaluating Eq. (13) with 9-0
C - ± (26)
x
Now, if Eq. (13) is evaluated using this constant, and r « R, an expression
is found for the angular position at which that characteristic line meets
the drop surface
191
-------
Sec. 6.2.1
Fig. 6.2.4 Force lines In detail for regimes (e) for the positive Ions and
(h) for the negative Ions. Here, all of the force lines terminating
on the particle, also originate on the particle; hence, there Is
no charging. For the case shown, w « ±2bE , Q • ±Q /2
o o c
(27)
sine - (cos6 - 1)
Note that the quantity on the right is always negative if Q/Q is positive,
as it is in regimes (e) for the positive particles and (h) for the negative.
Thus, in regime (e) for the positive particles and (h) for the negative, the
rate of charging vanishes and the drop remains at Its initial charge.
Regime (h) for Positive Particles; (e) for Negative Particles ln these
192
-------
Sec. 6.2.2
regimes, Q/Qc is negative and Eq. (27) gives an angle at which the charac-
teristic line along the z-axis meets the particle surface. Typical force
lines are shown in Fig. 6.2.5. To compute the rate of charging, the
solution to this equation is not required because a circular area of in-
cidence for particles at z •*• °° is then determined by the characteristic
line reaching the drop at 6 » IT. Actually, no new calculation is necessary
because that radius is the same as that found for regime (k) for the
positive particles and (b) for the negative. The charging current is i~, as
given by Eq. (25). Drops in these regimes discharge until they reach the
charge zero. Moreover, if the initial drop charges place the drop in regimes
(k) for the positive particles or (b) for the negative particles, the rate
of discharge follows the same law through regimes (h) for the positive par-
ticles and (e) for the negative until the drop reaches zero charge.
Positive and Negative Particles Simultaneously If both positive and
negative particles are present simultaneously, the drop charging is
characterized by simply superimposing the results summarized with Figs.
6.2.2 and 6.2.3. The diagrams are especially helpful in this regard, in that
the charging current for any given imposed field and drop charge is obtained
as the superposition of the respective charging currents. Practically, the
diagrams are superimposed with their origins (marked 0) coincident. A
given point in either plane then specifies the charge and field experienced
by both families of charges. This justifies merely superimposing the res-
pective currents at the given point to find the total charging current.
6.2.2 Collection With Complete Turbulent Mixing
The laminar flow picture of the collection process relates to the
actual electromechanics of the particle migrations in a practical scrubber
193
-------
Sec. 6.2.2
Fig. 6.2.5 Regimes (h) for the positive ion and (e) for the negative.
Some of the force lines extend to where the charge enters.
wo " * 2b±V Q " ± Qc/2
configuration in much the same way that laminar models for the conventional
ESP represent the collection process in a real device. As in an industrial
scale ESP, turbulent flow characterizes the fluid mechanics of the drops in-
jected into the gas, and the resulting mixing dominates in determining the
distribution of particles among the drops.
One way to see that the turbulent diffusion must have a dominant effect
is to evaluate the characteristic time for the fine scale turbulent diffusion.
From Eq. (5.3.2), this time is of the order
(28)
3 \ Y
where 3 is of order unity and the large scale energy dissipation density
194
-------
Sec. 6.2.2
YT is given by Eq. (5.3.3). For the turbulent jet described in Chap. 5 and
used in the experiments of Sees. 6.7-6.9, YT ^ 10 , and hence the characteristic
_2
time for turbulent diffusion is of the order 10 sees.
This time is to be compared to the time typically required for particles
to be collected on the drops. The results of this section support the
simple model introduced in Sec. 2.4 which argues that this collection time
is of the order
Tc - (29)
—4 3 —7
Typically, NQ * 10 coul/m and b - 10 m/sec/V/m, and hence T - 1 sec.
It can be inferred from the fact that T « T that until the particles
are in the immediate vicinity of a drop, their density is essentially
determined by the fluid mechanics. Locally, the turbulent diffusion tends
to make the distribution of particles uniform between the drops.
By complete mixing, it is meant that the particle density over a
surface very nearly coinciding with that of the drop is uniform. In this
extreme, which represents the most optimistic picture of the electrically
induced scrubbing, the rate of collection is easily calculated. The current
normal to the drop surface has only an electrical component which is evaluated
using Eq. (6.2.3) for E (r » R). This calculation must be carried out taking
care to recognize that there is a collection of positively charged particles
only over that part of the drop surface where E < 0, and of negative par-
ticles where Ey > 0. The characterization of the possible collection regimes
summarized by Figs. 6.2.2 and 6.2.3 is again helpful. Now however it is only
necessary to distinguish three regimes. The first of these is Q < - |Q |
1 " - n+V+E * »da " ~V*+b+ i E • nda (30)
195
-------
Sec. 6.2.2
From Gauss' Law, the integral over the surface enclosing the drop is Q/e and hence
?~ " 4 ; Gl " ~n+b+ 4- for Q < - I JQ | is similar with negatively charged particulate
rather than positively charged particulate collection.
i - - n_q_b_ - - i~ ; Gl - n_b_ - f or Q > |q |
o o
(32)
In the third regime where - |QC| < Q < |Qj both positive and negative par-
ticles contribute
i- ij+i-- 3{|l+|(l-^-j-)2- |lj
-------
Sec. 6.2.2
Surface collecting positive particles .+
Surface collecting negative particles
Fig. 6.2.6 Charging trajectories for a drop having total charge Q in an
ambient field E as it collects positive and negative particles
with complete mixing. 0 indicates initial charge while x indicates
final state
of Q follow by solving Eq. (14) with i - i*. When Q reaches - |Q |, the
current shifts to Eq. (33) and the charging continues until Q reaches a value
197
-------
Sec. 6.3
such that i - 0. Solution of Eq. (33) shows that this happens when Q - Q
where
(35)
The largest possible value to which the drop can charge is therefore JQ |,
and is obtained in the limit where there are no negative particles (I_ •*• 0).
In the opposite limit of no positive particles, the drop never changes its
original charge and the rate of particle collection is zero.
The difference between the laminar and turbulent models comes down
to there being an effect of the mean relative velocity WQ for laminar flow,
but not for the turbulent mixing model. As far as the charging currents are
concerned, the combination of Figs. 6.2.2 and 6.2.3 to give a total charging
diagram is in the limit WQ •* 0, the same as Fig. 6.2.6. The turbulent mixing
model is, by contrast with the laminar model, not restricted to having a
colinear relative flow and ambient electric field.
6.3 Multipass Systems
Regardless of the specific geometry, the collection system involves
a residence time for the gas that must be distinguished from that for the
drops. The effective lifetime of the drops is necessarily on the order of
T . For efficient cleaning, the gas residence time must be at least on the
R
order of TC. This means that the drop residence time must be made considerably
shorter than the gas residence time.
If drops are simply sprayed into a cleaning volume through which the
198
-------
Sec. 6.3
particle ladden gas is passed, it is clear that the gas must undergo internal
circulation on one scale or another. Unless provision is made to control
the flow pattern, the specific circulation pattern is likely to be extremely
complex.
The system shown in Fig. 6.3.1 both illustrates what is involved in
modeling the system as a whole and shows how relative control over the flow
pattern is achieved in the experiments to be described in Sees. 6.7-6.9.
The drop stream enters at the top and is removed by inertial impact at the
bottom after passing down the center through the interaction channel. The
aerosol is introduced at the top with volume rate of flow F. and number
in
density n. . The drops entrain the gas carrying it down the center section.
Because the gas residence time is much longer than that of the drops, most
of the gas recirculates in the return sections with a volume rate of flow
F™ essentially half that through the center section, F.. Some gas is
removed at the bottom entraining the particle density n . The mean gas
velocities in the central and return section are respectively defined as
U and U while the mean drop velocity is U.
In the Interaction channel and in the return channels, there are one-
pass particle removal efficiencies respectively defined as
n2 " ^(Ol (2)
Conservation of the gas in the volume where the gas is injected, the inter-
199
-------
Sec. 6.3
n
in
7
in
n
but
out
Depth w
V V
n0(0)
MO)
Fr V
V V
n2(0)
Fig. 6.3.1 Schematic cross-sectional view of cleaning volume. Drops are
injected at top to form turbulent jet that drives gas downward
in the central interaction region. Drops are removed by impactlon
at the bottom, while the baffles provide a controlled recirculation
of gas and particles.
200
-------
Sec. 6.A
action channel originates and the return channels terminate requires that
Fl - 2F2 + Fin <3>
Conservation of particles in this same region makes a further requirement
on the system
ninFin + 2F2n2<*> ' nl(0)Fl
Finally, under the assumption that complete mixing of the gas occurs at the
outlet region,
- B2(0) - nout (5)
Given the one-pass efficiencies and F. » F. , these last three expressions
combine to give the efficiency of the overall system.
n fc F.
out m in
n.
*1 * "1"2
In making quantitative use of this expression, remember that n, and n2 are
themselves somewhat dependent on the concentration level so that as written
the expression is not explicit in n /n. . In the form of Eq. (6), however,
the one pass efficiency is clearly seen to be multiplied by F. /F., which is
the reciprocal of the number of times that the gas passes through the inter-
action channel during one gas residence time.
6.4 Model for Scrubbing With Unipolar Drops and Particles of Opposite
Sign (CDS-I)
The most important point to be made in writing the equations for the
evolution of drops and particles as they pass through the interaction
201
-------
Sec. 6.4
channel is that over the entire volume the drop charge Q exceeds the critical
charge Q . This can be established by using the induction charger model
of Sec. 5.4.2 (Eq. (5.4.18)) to represent the charge at the point of injection
Q - eh (1)
where (X h) is the effective area projected by one drop in the charging field
s
E_j. If the drop charge is conserved, Gauss' Law requires that the electric
field at the wall of the channel also be essentially EQ. It is at the outer
periphery of the channel that the space charge field is greatest, and hence
Q is greatest. So, at worst,
X h
5_ > _§ _ (2)
02 '
4c 12irir
-4 -4 -5
Using numbers Xg - 1.84 x 10 , h - 4.96 x 10 and R - 2.5 x 10 from
Sec. 5.4.2, it follows that Q/Qc > 3.9. Self-precipitation of drops leads
to a lesser electric field at the channel walls, and hence an even larger
value of Q/Q . The tendency of the drops to be neutralized by the particles
does decrease Q, but the space charge field and hence Q are proportionately
decreased. Slowing of the drops tends to make the total charge/unit length
in the channel about twice that in the charger section, but this is not
sufficient to negate the inequality Q > Q .
This means that the rate at which the drop charge changes is given by
+
12 " -n+b+q±Q/e and the rate at which particles are collected by a drop is
given by G^ • in+b+^- (Eqs. (6.2.31) and (6.2.32)). Note that these rates
~ ~ o
are predicted by either the laminar or the turbulent theory. The latter
theory, however, is based on the more physical model and has the advantage
of being strictly applicable to the case at hand where the ambient field and
202
-------
Sec. 6.4
mean relative flow are perpendicular.
With the drop-particle interaction terms so simply represented,
determining the evolution through the channel is a matter of extending models
tested in Chaps. 4 and 5. For convenience, take the drops as negative and
particles as positive in the following. First, drop conservation is represented
using the same model as in Sec. 5.2.2, but leaving the electric field at the
wall, EW, for the moment unspecified
dN . -
dz 6TrnKU(s/2) * '
Here U is the mean drop velocity. In recognition that there is no precipitation
if the space charge of the particles dominates and E is in fact outward, the
step function u,(-E ) is unity if E < 0 and is zero if E > 0.
Conservation of drop charge is represented by
£ - «£ -
That the particles acquired by the drops are lost from the particle continuum
is now included in a conservation of particles equation similar to that
developed in Sec. 6.2.2, with the addition of a loss term (G N)
dn.-nbSN bnV-l(V ,.,
dz eoUg- (s/2)Ug C5)
Here, U is the mean gas velocity. Finally, Gauss* Law requires that
o
E - (nq - NQ)|— (6)
/e
These last four equations, which involve the unknowns N,n,E and Q,
203
-------
Sec. 6.4
determine the one-pass efficiency r\^. By setting Q » 0, Eqs. (5) and (6)
determine the self-precipitation efficiency n2 in the return channels.
Hence, the system efficiency of Eq. (6.3.6) is evaluated.
The solution of Eqs. (3) - (6) is easily carried out numerically.
However, considerably more insight can be obtained by making two approximations
that are likely to hold in any practical system, and give an adequate accuracy
in interpreting experimental results in Sec. 6.7.
First, as can be seen by taking n as fixed in Eq. (4) and solving for
the decay of Q with distance through the interaction channel, it is seen that
drops tend to lose charge with a decay length £ - T U, where T is based on
a a a
n evaluated at the entrance to the interaction channel. This length is very
long compared to 1. Hence, the drop charge Q can be taken as essentially
constant, and Eq. (4) ignored.
Second, NQ » nq, which is an approximation that is good once the drops
are given a modest amount of charge, but is not true with no charging. The
effect of this approximation is to relegate the self-precipitation to the
return channels. In fact, at low charging levels there is some self-precipitation
in the interaction channel. However, because the gas residence time in the
return channels is twice that in the interaction channel, this approximation
is acceptable.
Because E is determined by NQ alone, Eqs. (3) and (6) determine N(z).
The drop self -precipitation is not influenced by the particles and hence these
equations reduce to Eq. (5.2.10) with a solution given by Eq. (5.2.11). This
result makes it possible to in turn evaluate Eq. (5), which becomes
dn . -nbQN(O)
dl „ ' R ' N(0)QB
€ U (1
o g
204
-------
Sec. 6.4
The solution of this equation, evaluated at z « i, gives the one-pass
efficiency defined by Eq. (6.3.1);
K
(8)
where
e U
o =
N(0)Qb
For a system that is prescribed in every way except the degree to
which the drops are charged, it is now possible to ask what value of Q gives
the best one-pass efficiency.. ..gives the least value of ru? To this end
Eq. (8) is written with Q expressed explicitly.
Q 2-5*
n " [1 + ( ] Q
where
Qd =
81
0 ., ^
QR-\| JLN(O)
The minimum is then found with Q
and with that optimum charge the one-pass efficiency is
(ID
205
-------
Sec. 6.4
This result serves notice that the degree to which the drops are charged is
not the primary limitation on a well designed system. In view of the peak
in probe current shown in Fig. 5.5.8, that the (Q) depends on the drops
alone comes as no surprise. Using as numbers typical of Sec. 6.7, N(0) •
2 x 109drops/m3, R - 2.5 x 10^ and I - 0.56m and Q - 3 x 10~ coul.
This charge is obtained with an inducer bar voltage V_ « 75 volts (Fig.
5.4.5). It is easily possible to raise the value of Q to at least 4 times
this level with the induction system for charging described in Sec. 5.4.2.
The return channel one-pass efficiency ru» defined by Eq. (6.3.2),
follows by solving Eqs. (5) and (6) with Q • 0, to give
n2 - [1 + r . i. i _ U2>
Finally, Eqs. (9) and (12) can be used to evaluate the overall
efficiency of the system, Eq. (6.3.6). With care taken to recognize that
n2(0) - n , it follows that
in
where
- - Bf + ><*f > + cf
_ai (1 _ j _ '1 in
A 1 ?.,_
c = _ (
* ~ i ^ F
f * rl
eoug2
£ai = nlnbq
206
-------
Sec. 6.5
The approximations Implicit to Eq. (13) are most justified in the
drop-charge range where the one-pass efficiency is optimal. Some error
results at the charging extremes. If there is little charge on the drops,
then the dominant particle removal mechanism in even the central region is
self-precipitation. The expression for r\- should then be replaced by
Eq. (12) with n2(0) •*• n^O). This should have the effect of causing the
measured particle concentration at low levels of drop charge to be lower
than predicted by Eq. (13). For very high levels of drop charge, the drop
self-precipitation distance &R is small compared with the channel length i.
Then, the self-field of the particles can again come into play. This would
be a large effect in the experiments of Sec. 6.7 if it were not for the fact
that the particle charge density in the Interaction channel is essentially
that at the outlet. Hence, because the system removes about 95% of the
particles at high drop-charge levels, the effect tends to be small.
6.5 Model for Scrubbing With Bicharged Drops and Charged Particles (CDS-II)
To avoid generation of space-charge fields by the drops, equal
concentrations N(0) of positive and of negative drops are injected into the
interaction channel. The charged particles can then be Injected with unipolar
charging of either polarity or bicharged. With bipolar charging, there is
electrically induced scrubbing by only half of the drops and in addition the
possibility of space charge precipitation due to the self-fields from the
particles. With bicharged particles, space charge neutrality is preserved,
and both drop species are active in the scrubbing. However, rather than a
self-precipitation characterized by Tfl, there is a aelf-agglomeration
characterized by the same time constant. Instead of being a removal of
the particles to the walls, the consequence is a discharge among the particles
207
-------
Sec. 6.5
that renders them inaccessable to the charged drop scrubbing.
A detailed model paralleling that represented by Eqs. (6. 43) -(6. 46)
for the CDS-I interaction would recognize effects of the particle space
charge, if any, and of the self discharge if the drops are bi charged.
Because the particle density is suppressed to the point of being unappreciable
on the time scale of the drop residence time, in this section it is assumed
at the outset that these particle-field effects can be ignored. The drop
densities of positive and negative species are defined as N+ and N respectively
and are the same. Hence, each Is represented by N+ » N_ = N. In the following,
if N is taken as N+, then n = n-. With fields from the particles ignored,
the drops evolve in the same self-discharge process investigated in Sec. 5.3.2
XT i e u
N o =
~
i j. i_ ' R ~ K'N(0)QB
i.
R
where K1 is 2 if the drops are taken as behaving analogously to a system of
bicharged particles, and is 3 according to the extension of the Harper model.
Unless fields induced by unipolar particle charging are extremely large
(much larger than in the experiments of Sec. 6.8) the drop charge |Q| > |q I
thus justifying representing the rate of collection of one sign of aerosol
o
by the opposite sign of drops by NG^particles/m /sec) , where G. is given
by Eq. (31) or (32). Thus, the decay of one species of particle is in
accordance with
dn _ nbQ N(0)
"* "
where Eq. (1) has been used for N(z).
208
-------
Sec. 6.6
Equation (2) is the same as Eq. (6.4.7), found for the CDS-I interaction,
except that K1 appears in 4R, (U •* U/K' in AR). Because N is half of the
total drop density injected, if K1 - 2, it is evident that the only effect
of changing from CDS-I to a CDS-II system is to increase AC by a factor of .
two. If K' - 2, the effect on AR of halving the drop density is exactly
compensated by the factor K1. Hence, Eq. (6.4.13) evaluated using the
CDS-I parameters predicts the particle collection for the system provided
that £ is doubled. According to this model, the collection is expected to
peak-out at the same drop-charging voltage but the fraction of particles
removed should be less than in the comparable CDS-I system.
6.6 Model for Precipitation by Unipolar Drops and Particles of the Same
Polarity (CDP)
The specific model of this section and the correlating experiment of
Sec. 6.9 in which the drops and particles carry unipolar charge of the same
clarity help to emphasize the ubiquity of the fundamental time constants.
the drops repel the particles, but collectively induce a sufficient space
charge field to drive the particles to the walls. In practical systems, the
alls are washed by the self-precipitating drops. Hence, the device has many
Of the features of a wet-wall precipitator.
As in Sec. 6.4, general equations for the evolution of drops and
rticles would include effects of particle space charge. For the present
urposes, the approximation is made at the outset that |NQ| » nq, so that
he drop dynamics are in essence determined without a coupling to the
articles. Thus, the self-precipitation of the drops is described by Eq. (5.2.11),
gives N(z).
The precipitation of particles in the field caused by the self-precipitating
209
-------
Sec. 6.7.1
drops is found by writing a conservation of particles equation for an in
cremental volume having length Az and the cross-section of the channel.
With drops and particles both positive,
swU .JnCz + Az) - n(z)] - -2nbEw wAz (1)
Here, the field at the wall induced by the drops is
W
O
so that in the limit Az -»• 0 and with the substitution of Eq. (5.2.11) for
N(z),
dn _ nbQ N(0) . , _ £oU
" ' * -
dZ U 1£0 1 4- — R ~ N(0>QB
This expression for the particle density decay through the channel is the
same as found in Sec. 6.4.2 for the CDS-I interaction, Eq. (6.4.7). Hence,
for this physically very different system, the one-pass efficiency is the
same as for the CDS-I systems and the collection for the total CDF system
is as given by Eq. (6.4.13).
6.7 Experiments with Unipolar Drops and Particles of Opposite Sign
6.7.1 Experimental System
A schematic diagram of the complete system is given in Fig. 6.7.1.
All components, except the channel, are described in previous chapters.
The drops are injected from above, pass between the inducing bars, and
then enter the central channel. The aerosol is injected through manifolds
located beneath each bar. The drops are impacted at the bottom of the
channel, hence experience just one pass through the system. The gas is
210
-------
Sec. 6.7.2
drawn off at the bottom at a rate slightly greater than is supplied with the
aerosol. The balance is drawn in through leaks in the system in the vicinity
of the plugs inserted between the charging bars and droplet generator.
Corrections are made in correlating experiments with theories to account for
this disparity between inflow and outflow.
Condensation
Aeroaol
Generator
I
Charger
0) Q
"Owl"
V
I—-i
J
Analyzer
Inducing B*r«
Feedback t*i|lon>
Scrubbing Region
Extinction Cell*
ansducer and
iflce Plate
Fig. 6.7.1 Drop-particle interaction experiment showing system for controlled
generation of charged particles and measurement of essential parameters
6.7.2 Experimental Diagnostics
The operating conditions for the experiment are summarized in Table 6.7.1.
The angular positions of reds in the "Owl" are: 6 . » 50°, 103°. Hence,
from Fig. 4.5.2 the radius of the aerosol particles follows from a - 2rra/X - 3.2,
A , - 0.629ym to be a « 0.32ym.
red
211
-------
Sec. 6.7.2
Table 6.7.1 Operating conditions for drop-particle experiments
Aerosol Generator:
a. 5% DOP Solution
b. Heating Tape Voltage - 70 volts
c. Pressure of Prepurified Nitrogen - 15 psig
Aerosol Flow Rate - 5.1 liters/min.
Charger:
a. Corona Voltage - +8 kV
b. Corona Current - +3 yA
c. Accelerating Nitrogen Flow Rate - 1.3 liters/min
Flows:
—4 3
a. Output Flow Rate Through Aspirator (Fout>-1.37 x 10 m /sec
/ 1
b. Input Flow Rate (Fin) - 1.08 x 10~ m /sec
Droplet Generator:
a. Pressure to Water Reservoir - 15 psig
b. Frequency of Orifice Plate Transducer - 54 kHz
c. Droplet Generation Rate - 2.76 x 10 drops/sec
Channel
a. Length (Si) - 0.565 m
_2
b. Width (s) - 2.54 x 10 m
c. Drop Velocity (U) - 4m/sec
d. Gas Velocity (Ugl> - 2m/sec
e. Gas Velocity (U .) - Im/sec
f. w » 15cm
212
-------
Sec. 6.7.2
The self-precipitation and saturation currents measured using the analyzer
of Sec. 4.7.2 determine the charge density and mobility to be b = 2.5 x 10 m/sec/V/m
-4 3
and nq - 0.67 x 10 coul/m respectively.
In order to evaluate the charge density that actually can be considered
to enter the channel, this density must be corrected for impaction of the
aerosol onto the droplets immediately below the point of injection and for
the dilution that occurs because the flow drawn out by the aspirator exceeds
that supplied with the aerosol. This is done by performing a measurement
with the aerosol and the drops uncharged. In this case the ratio of ouput-
to-input concentrations is found to be nout/nln * 0.59. Measurement of
inlet and outlet gas volume rates of flow shows that 21% of the decrease in
exit particle density is due to dilution and 25% is due to inertial impaction.
Most of the leakage is at the inlet, justifying the correction of nln to
account for both effects. In all of the following discussion, n is taken
as the corrected value.
Because the drops make a transition from a confined beam to a turbulent
jet, there is some ambiguity in specifying N(0). In the correlations of this
9 3
chapter, N(0) » x/Uws • 1.77 x 10 drops/m , where x, the rate at which
drops are produced by the generator, is the number of orifices multiplied by
the acoustic frequency.
The particle concentrations n. and n . are obtained from extinction
in out
measurements performed on flows sampled from different points in the system.
The approximate form of the extinction law, Eq. (4.5.5) is used, Although
the amount of beam attenuation is sufficient to cause some error in its
applications, this is considered to be less than that resulting from the
application of Eq. (4.5.4) 1(0) - I(L) and 1(0) are measured directly.
213
-------
Sec. 6.7.3
To obtain I(L) would require subtraction of these quantities, one of which,
1(0), is known less accurately than the other.
6.7.3 Scrubbing Efficiency
A plot of Eq. (13) for these experimental conditions is shown in
Fig. 6.7.2. The measurement at VD - 0, which reflects the self-precipitation
alone, confirms the particle self-precipitation model for the side channels.
Although this process also occurs in the central section, the particle
velocity is twice as large there. Thus, most of the period required for
a particle to make a complete circuit is accounted for by the time it spends
traveling up the sides. In addition, if the interval that a system of
monocharged particles spends is sufficient to cause significant self-precipitation,
then the increase in particle removal resulting from even a doubling of the
residence time is relatively small. The drop voltage at which the collection
process peaks (between 30 and 50 volts) corresponds with the expected range
of Q . (Eq. (10)) and reflects the loss of drops through self-precipitation*
O.JO
O.M
o.ie
•.OS
to
100
-210
MO
Fig. 6.7.2 Calculated and measured collection of positively charged aerosol
particles upon negatively charged drops as a function of drop charging
voltage
214
-------
Sec. 6.8
The smaller than expected rate at which n k/n. decreases at low levels of
out in
drop charge can be accounted for by the self-precipitation in that region.
Until the charge density of the drops exceeds that of the particles, the
Increased collection by the drops tends to be counterbalanced by a loss of
the particle self-precipitation mechanism.
6.8 Experiments With Bicharged Drops and Charged Particles
Experimentally, the alteration from a monocharged drop to a blcharged
drop system is accomplished by applying a positive voltage to one charging bar
and a negative voltage to the other. The variation of drop charge with
voltage is assumed to be identical to that given in Fig. 5.A.4. In practice,
the positive voltage is adjusted to the indicated value, and the negative one
then Increased until a probe inserted into the drop stream indicates no net
current. Probably due to geometric asymmetry, the positive voltage tends
to create more highly charged drops. For example, in order to achieve charge
neutrality at v& - 4-250 V, Vfc had to be adjusted to -190 V. The theoretical
predictions are based on the higher value of VD. The structure of the bi-
charged drop beam differs considerably from the monocharged one. Whereas
the spread of the beam in the latter case increases with drop charging, in
the former case, the beam appears essentially similar to the uncharged one
for voltages as high as ±300 volts. (See Sees. 5.5 and 5.6). The operating
conditions cited in Sec. 6.7 also apply to this experiment.
Equation(6.4.13), normalized, as described in Sec. 6.7 to the corrected
inlet particle density, is plotted in Fig. 6.8.1. A comparison of the
theoretical models for CDS-I and CDS-II interactions afforded from Figs. 6.7.2
and 6.8.1 shows the effect of doubling AC. The fraction of particles removed
as a result of charging the drops is reduced. According to the model, which
215
-------
Sec. 6.8
is based on taking K' - 2, the optimum charge level is the same as for the
CDS-I interaction.
Of the three collection processes investigated experimentally in this
chapter, the CDS-II collection, is the least well understood. The process
does appear to be characterized by &c and &_. However, as a comparison of
model and experimental results in Fig. 6.8.1 shows, the collection tends to
increase less vapidly with voltage than predicted, and does not tend to peak
out as expected, but rather tends toward an asymptote. This latter fact
reflects the observation from Sec. 5.6 that the self-discharge process goes
on more slowly than expected from a theoretical model which takes K1 - 2
(as is assumed in the model for Fig. 6.8.1).
O.JO
O.IJ
O.JO
O.IJ
_out
•i.
O.OJ
10
JO
M
40
too
100
JOO
V_- volt*
D
Fig. 6.8.1 For bicharged drops, calculated and measured efficiencies for
collection of positively charged aerosol particles
216
-------
Sec. 6.9
6.10
6.9 Experiments With Unipolar Drops and Particles of the Same Polarity (CDP)
With the important modification of having drops and particles charged
to the same polarity, the experiment of this section is much the same as the
CDS-I experiment of Sec. 6.7. The theoretical curve shown in Fig. 6.9.1 is
based on the results of Sec. 6.6, which show that collection is expected to
be the same as in the CDS-I experiment. The differences between the theoretical
curves shown in Figs. 6.9.1 and 6.7.2 reflect the experimental variations in
measured parameters used as inputs to the calculations. The major uncertainty
is in the measured correction factor. As described previously, this number
is evaluated by measuring the efficiency of the system when both the drops and
the particles are uncharged. The densities of the particles are sufficiently
large to cause I(L) and 1(0) - I(L) to be on the same order. Thus, the
unapproximated extinction formula (Eq. (4.5.4)) is appropriate. However,
evaluation of I(L) from the measurements requires subtraction of two close
numbers, and, as is evidenced by the variation for otherwise identical
systems, is a source of uncertainty.
Two observations can be made on the basis of these experiments
and the interpretation afforded by the underlying model. The optimum
collection occurs in essentially the same range as for the CDS-I con-
figuration and in roughly the range expected from the theoretical model.
The maximum removal Is about the same as for the CDS-I configuration and
essentially what is predicted using the simple model.
6.10 Summary of Measured Efficiencies
The experimental results of the last three sections are representative
of several experimental runs in each of the classes of operation. The data
presented accurately reflect the trends and magnitudes. Because each of the
217
-------
Sec. 6.10
0.30
0.25
0.20
0.15
0.10
o.os
I
I
I
I
-45-
1
300
0 10 20 30 40 50 Vg- volti 100 ISO 200 .250
Fig. 6.9.1 Theoretical and measured particle collection for drop-precipi-
tation of positively charged aerosol particles by positively
charged drops as a function of drop charging voltage
runs involves re-establishing the flow and aerosol charging conditions there
is some variation in the experimental conditions. This is reflected in parameters
used in the calculation and accounts for the small differences between the
theoretical and between the experimental V « 0 collection in the respective
curves of the preceding sections.
The block diagram of Fig. 6.10.1 helps in summarizing the performance
of the overall system, considered as a collection device. The dilution of
the gas at the inlet due to leakage must be removed from an efficiency
ascribed to the device. Thus, the particle density n at the inlet, where
the volume rate of flow is F , is corrected to give the effective particle
density n1 to the device as a whoie
IN.
in
F
- 0.79
(1)
in ilution
out
218
-------
Sec. 6.10
The inertial scrubbing occurs primarily in the zone at the inlet of the
experiment prior to entering the mixing zone at the entrance to the interaction
channel. The collection attributed to inertial scrubbing is measured by
determining noufc with q » 0 and VD - 0 and is summarized in Table 6.10.1.
Table 6.10.1 Efficiency of System as a Whole
CDS-I CDS-II CDP
(q - 0, VD - 0)
INS 25*
(q, v - o)
87%
INS + SCP
INS + SCP + ( > 95%
25% 25%
86.5% 85%
92% 95%
The additional effect of charging the particles with the drops injected but
with no charging is then represented by the efficiency
n!N
Ef f iciency - 1 - - 1 - _ . Q>75
nin n!N i
(2)
With n /n taken from Figs. 6.7.2, 6.8.1 and 6.9.1 respectively, the overall
out in
efficiencies found from Eq. (2) are as summarized in Table 6.10.1. Finally,
with the drops charged, the overall efficiencies under optimal conditions are
similarly computed from the data and Eq. (2), and are summarized in the table.
The electrical augmentation of the device is evident from the table.
219
-------
Sec. 6.10
In the absence of particle and drop charging, it functions as an inertial
scrubber. The space charge precipitation mechanism accounting for the
collection with V - 0 would be absent in the limit of an infinitely dilute
particle concentration. The collection mechanisms associated with the drop
charging would then be dominant. The table emphasizes once again that the
three charged drop configurations result in essentially the same efficiency.
dilution
1
n1 F
IN out
<»'„)
Inertial
Scrubbing
n. F
in out
Electrically
Induced
Removal
n F
out out
(nout>
Fig. 6.10.1 Stages of concentration attenuation through system as a whole
Efficiencies of Table 6.10.1 are (1 - n ut/n'IN) *n percent
220
-------
Sec. 7.1
7 Summary
7.1 State of Fundamentals
The basic laws of collection for submicron particle control devices
are developed in Chaps. 4-6 in a sequence of interrelated models and supporting
experiments. What can be concluded with the hindsight of these chapters is
that the overview of conventional, self-precipitation, self agglomeration and
charged drop systems given in Chap. 2 does in fact place the alternative
approaches in perspective. Thus, Chap. 2 should be regarded as part of this
summary. The hierarchy of electromechanical time-constants T , T , t is
c* C Ix
clearly basic to models that predict the performance of the SCP, SAG, CDS-I,
CDS-II and GDP configurations. In those situations where the drop charge Q
exceeds in magnitude the critical charge Q (a condition that is most probable
in a practical system in either the CDS-I or CDS-II configurations) experimental
evidence supports the use of the simple rates deduced in Sec. 6.2.2 for
electrically dominated collection. The role of turbulent mixing, which is
basic to this model, should be incorporated into thinking about practical
charged drop collection systems. That the way in which a given drop "sees"
the surrounding sea of particles is poorly pictured in terms of deterministic
laminar trajectories is perhaps best emphasized by simply observing that in
the experiments of Chap. 6 the average slip velocity between drops and gas
is 2m/sec, while even at the drop surface the velocity of a submicron particle
is only of the order of 5cm/sec.
What is found in Chap. 5 concerning the self-discharge of bicharged drops
taken together with the collection performance of the bicharged drop system
found in Sec. 6.8 tends to support the view that the most poorly understood
aspect of any of the systems is the self-discharge of the drops. This process
221
-------
Sec. 7.1
seems to go forward somewhat more slowly than expected. The characteristic
time can be taken as perhaps 4TR rather than T_. (The coefficient K' - 0.5
rather than 2 or 3 In the model for the one-pass efficiency.) The observed
reduced rate of self-discharge in the bicharged system gives some impetus
to preferring the CDS-II configuration in practical applications and future
developments.
On the basis of the experience obtained here, it is clear that a more
refined picture of the drop-particle interactions could be obtained by
supressing the role of self-precipitation. In an Improved experiment,
the efficiency would be measured by more sensitive mass monitoring equipment
which would permit operation at a reduced particle density n. . Thus, the
masking effects of the self-precipitation in the feedback loops would be
largely eliminated. Effectively, this would mean that the particle removals
shown in Figs. 6.7.2, 6.8.1 and 6.9.1 would start at unity when V - 0 and
approach the curves shown by the time V_ is on the order of 50 to 100 volts.
Such experiments would be justified if a critical measure of the drop
collection rate under actual flow and field conditions were called for.
By including effects of particle inertia, or "near-field" image forces
and the like, it is possible to add tentative refinements of the electrical
collection rate model emphasized here. Given a two-particle calculation that
promises radical Improvements in scrubbing.efficiency if the drops and particles
are oppositely charged, two facts supported by every finding in this work should
be kept firmly in view. First, the effect of the field is extremely unlikely
to be larger than the rate actually used in most of the modeling of Chap. 6
222
-------
Sec. 7.2
and corroborated by the experiments there as well. The turbulent mixing model
pictures the drop as acting much like the electrode in an ESP, with the
effective collection field at the surface of the drop where it is most intense,
and the particle density supplied by the turbulent diffusion right up to that
surface. Second, the collective interactions of the drops must be included,
or the fundamental limitations on the device will not be perceived.
7.2 Charged Drop Devices Compared to Conventional Devices
The beauty of devices making use of charged drops is undoubtedly in
the eyes of the user. When Penney did his early work he probably had in mind
making a viable competitor for the conventional electrostatic precipitator.
When he obtained particle removal efficiencies in the CDS-I configuration of
less than 50% to him it was a disappointment. But from the point of view of
wet-scrubber technology, Penny's findings were more impressive and Pilat's
recent experiments in the CDS-I mode are even encouraging. He found an
improvement in scrubber performance for 1.05ym particles from 69% with no
charging to 94% with charging. Are these experimental results consistent
with the fundamentals developed here? Given that the scaling laws implied by
these fundamentals are correct, is there a future for the charged drop family
of devices?
Rough estimates of Pilat's experimental parameters can be made if it
is assumed that the drops have an average velocity of 5m/sec through the active
volume. The parameters shown in Table 7.2.1 are only rough averages, since
both particles and drops are polydisperse, and flow parameters are not reported.
223
-------
Sec. 7.2
Table 7.2.1 Estimates of Average Parameters in Pilat1s CDS-I Experiments
a ^ 5 x 10~ m
n ^ 6.7 x 101:Lparticles/m
q ^ 2.8 x 10~17coul/particle
b ^ 1.5 x 10~7(m/sec)/(V/m)
R ~ 2.5 x 10~5m
N ^ 109drops/m3
Q ^ 3.7 x 10~1Acoul/drop
B ^ 4 x 10"6(m/sec)/(V/m)
It follows from these parameters that
,,-2
T ^3.3 sees. ; T * 1.6 sec ; T • 6 x 10 sec
A C K
(i)
These times are to be compared to a gas residence time of 7 sec and a drop
residence time of perhaps 1/4 sec. Thus, because the gas residence time is
longer than T , appreciable space-charge precipitation is to be expected with
the particles charged but the drops uncharged. Although not formally reported
this SCP contribution is confirmed by Pilat. The particle collection, characterized
by TC relative to the 7 sec gas residence time, is such that charging the drops
should result in an additional increase in efficiency as Indeed it did. Finally
the drop residence time is about 4 times TR. This is corroborated by the
observation that the drops appear to "stiffen" when they are charged. Insofar
as experimental conditions can be pinned down, the results reported by Pilat
are therefore in accord with the models developed here.
What is evident from all available studies is that drop and particle
charging can dramatically improve the performance of the inertial scrubber in
the submicron range. Improvements in performance summarized in Table 6.10.1
are from 25% for the inertial scrubbing alone to 95Z with particles and drops
charged.
224
-------
Sec. 7.2
That it makes little difference whether the drops and particles have
opposite signs, the same signs, or there is a mixture of both positive and
negative drops, points to the fact that "scrubber"is a misleading term for the
charged drop devices. What is called a charged drop scrubber really has the
same characteristics in the limit of electrically dominated collection as the
charged drop precipitator. This fact makes it natural to return to Penny's
original point of view. What is the position of the charged drop devices in
a picture that includes the conventional electrostatic precipitator? The
charged drop precipitator is, after all, an electrostatic precipitator with
half the electrodes replaced by the mobile drops. Taken together, these
observations-make it clear that the charged drop devices are extremely un-
likely to outperform the electrostatic precipitator in terms of residence
time needed for gas cleaning.
Fundamentally, the only way that the gas residence time can be reduced
is to increase the collection surface area per unit volume. Comparison of a
drop system, having drops of radius R separated by an average distance of a
radii, to a conventional precipitator having circular cylindrical electrodes
of radius r, shows that for the drop device to have the shorter residence time
for cleaning (Eq. (2.5.12))
1
a < (f)3 (3)
With r • 10cm and R » 25um, this means that the drops must be packed less
than 16 radii between centers. In the experiments of Chap. 6, for comparison,
a ^ 30. By designing a counterflow of particles and drops it is possible to
make a system having a greater drop density but not charge density. Here again
is that limitation, represented by TR, unique to the charged drop devices.
225
-------
Sec. 7.3
Given a packing satisfying Eq. (3), the drops might just as well be
left uncharged and an ambient electric field used to Induce charges of
opposite sign over hemispheres of the collection sites, as in the EFB and
EPS configurations discussed in Sec. 2.5. Then TR is not a limiting time
constant.
If the residence time is the dominant criterion for the viability of
a submicron particle control system, then the EFB and EPB configurations
have great promise. In these systems, the drops are most likely to be re-
placed by solid collection sites. As pointed out in Sec. 2.5, dramatic
improvements can be made in the residence time for cleaning using this class
of devices. Recent work confirms this prognosis and in fact corroborates
the turbulent mixing collection model developed in Sec. 6.2 (Zahedi and
Melcher, 1974).
7.3 Practical Application
The question of whether or not there is a practical position for
devices making use of charged drops, and hence incentive for technical
developments, is relatively easy to answer. If there is a practical place
for wet inertial scrubbers, then there is one for the charged drop devices as
well.
Valid applications for the charged drop devices tend to spring from
domains in which the wet scrubber is viable. The wet-scrubber has a position
In air pollution control because its use tends to be intensive in operating
costs while relatively low in capital investment. This is by contrast with
the typical industrial scale electrostatic precipitator. Certainly, if a
wet scrubber is marginally competitive because it lacks desired performance
in the submicron range, the electrical augmentation is highly attractive.
226
-------
Sec. 7.3
Hybrid scrubbers, designed to remove gaseous effluents as well as efficiently
control submicron particulate, especially deserve development. What is ob-
tained by charging the drops and particles is a class of devices with the
capital investment and operating cost profile of the wet scrubber but a
particle removal efficiency approaching that of the electrostatic precipitator.
227
-------
Sec. 7.4
7.4 Summary of Calculations Estimating CDS-I, CDS-II and CDP Performance
The models developed in Sees. 6.3 through 6.6 are intended not only
to support the experiments of Chap. 6, but to serve as a guide in scaling and
designing practical devices. Summarized in this section is the procedure by
which these results can be applied.
It is assumed that the system as a whole has the multipass configuration
of Fig. 6.3.1 wherein
3
n. » the number density of particles to be removed (#/m )
in
3
F. * the volume rate of flow of polluted gas (m /sec)
in
i " the length of the region over which gas and drops interact (m)
To be practical, particles circulate with the gas through return paths also
of length I so that the gas passes through the droplet jet region many times,
To a first approximation the volume rate of gas flow in the interaction region,
F, , is the average drop velocity U multiplied by the drop-jet cross-sectional
area. (In the System described in Chap. 6, the gas velocity U . is half the
drop velocity.)
For optimal removal of particles in the Interaction region, drops
should be charged to the value (Eq. (10) of Sec. 6.4)
where
—5 2
n • viscosity of air (2 x 10 nt-sec/m at room temperature)
R - droplet radius (m)
U - mean drop velocity (m/sec)
N(0) - droplet number density at entrance to interaction region
Methods of charging the drops are discussed in Sec. 5.4. In terms of these
parameters, the optimum particle removal in one pass is given by
228
-------
Sec. 7.4
where
Qd E 6TmRb(p- ) (6)
and b is the mobility of the particles entering with density n. . These
in
particles have been previously charged, probably by conventional ion impact
in a corona discharge region as discussed in Sec. 5.4.4.
In the limit where the particle density n is low enough that self-
precipitation is negligible, (&««,. = EQU 2/n. bq) the CDS-I, CDS-II
and CDP devices then have the particle removal efficiency
Efficiency 5 1 - ^Hfe - 1 - ^ . ty"** (7)
-
If self-precipitation effects cannot be ignored (i on the order of I .), then
al
Eq. (13) of Sec. 6.4 can be evaluated to determine n /n. and hence the
out in
efficiency.
229
-------
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234
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GLOSSARY OF SYMBOLS
A gas flow cross-section
A, light beam area
A radius of sphere of influence beyond which turbulent diffusion
o
dominates electrical attraction
A probe area
A overall cross- sectional area of device
sy s t
a radius of particle to be collected
a,, Debye length
db
a radius of sphere of influence beyond which diffusion dominates
o
electrical attraction
B drop mobility
B* see Eq. (6.4.13)
b,b, ,b particle mobility
b. ion mobility
C defined following Eq. (11) of Sec. 5.3.1
C' see Eq. (6.4.13)
C ,C,,C charging capacitances (see Eq. (17) of Sec. 5.4.2)
a D m
C coefficient of contraction
c
CD coefficient of discharge
c jet radius
D defined with Eq. (22) of Sec. 4.3.2
D_,D,,D Brownian diffusion coefficient
a T —
D_, large scale turbulent diffusion coefficient
D fine scale turbulent diffusion coefficient
d spacing of drop sheet and charging bar
235
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d orifice diameter
o
E charging electric field intensity
c
E ambient electric field intensity
o
E /E incident and scattered optical electric field intensity
. s o
1 electric field intensity transverse to flow direction
T
E Taylor limit on electric field that an uncharged drop can sustain
tay
E electric field intensity at electrode or wall
w
—19
e 1.6 x 10 coulomb (electronic charge)
F volume rate of flow of gas
Fdilution v°lume rate of flow of gas leakage
F.,F9 gas volume rates of flow in central and return sections
F ,F volume rates of flow into and out of device
in' out
f frequency
f frequency beyond which liquid jet is stable
c
f frequency of maximum growth-rate on liquid jet
m
G ,G rate of particle collection by single particle
h spacing of jets within drop sheet
I+ see Eq. (2) of Sec. 6.2.1
I,I.,I. light intensity
I electrical drop current
I saturation current
sat
i,i,,i? electrical current
K inertial impact parameter
s
—23
k Boltzman ciefficient, 1.381 x 10 m-nt/deg C
k optical wave number 2WA.
236
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L length
H length
£ particle self-precipitation length
8i
I particle self-discharge length
o
I drop self-precipitation length
K
Si- turbulent diffusion length for drops
H large scale eddy size
I. Brownian diffusion length
M total drop mass
m mass
N number density of drops
n number density of particles
n. ion density
n. inlet particle density
in
n1,... effective particle density into device
IN
n. index of refraction
n initial particle density
n outlet particle density
out
Q ,Q, drop charge
a b
Q saturation charge by ion impact
c
Q see Eq. (9) of Sec. 6.4
Q drop charge for achieving optimum efficiency
Q.. see Eq. (15) of Sec. 5.5.3
K
Q Rayleigh limit on charge of an isolated drop
Ql/2 charge on hemisphere of polarized collection site
q»q+tq_ ion or particle charge
R radius of drop
Ry Reynolds number
23.7
-------
r radial position coordinate
r position of particle
r mean spacing of particles
o
S precipitation perimeter
S, ,S scattering functions
1 2
s electrode spacing
T absolute temperature
t time
U mean gas velocity
U ,,U mean gas flow in central and return sections of multi-pass system
gl g2
U jet velocity
S
it ( ) step function, having value 0 and 1 for argument negative and
positive respectively
V applied voltage
V active volume of collection device
V voltage of charger bars
V voltage at which analyzer current saturates
8& t
V gas velocity
v ,v. charging bar voltages
a D
w width of interaction volume
w relative gas velocity
w ambient relative gas velocity
o
x coordinate
y radius of collection cross-section
z position coordinate
z. growth distance for laminar boundary layer
238
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a mean distance between centers of spherical particles on drops
normalized to particle or drop radius
a. particle circumference normalized to wavelength of light
F particle current density
F_ electrically induced particle flux
Ci
I" turbulent particle flux
y surface tension
Y,Y total particle flux
YT large-scale turbulent energy dissipation density
AU large-scale turbulent fluctuation velocity
6 spacial growth rate of sausage instability on liquid jet
6 see Eq. (6) of Sec. 5.4.2
e permittivity
e 8.854 x 10 farads/meter
o
D gas viscosity
D,,ru single pass particle collection ratios
n gas viscosity corrected by Cunningham factor
c
n water viscosity
8
9 critical angle for charging (see Eq. (17) of Sec. 6.2.1)
c
6, acceptance angle of optical detector
9 . angle of observation for red Tyndall spectra
X mean free path
X, wavelength of charge-wave on drops
X-,X ,X wavelength of light
* r g
X wavelength of jet Instability
£ relative distance between particles and drops
£ ,£_ absolute positions of particles and drops
fl K
239
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E initial spacing of particles and drops
0
p mass density of gas
p particle charge densities
p mass density of particle to be collected
a
p mass density of drop
R
p liquid jet mass density
s
I "stream-function" for solenoidal electric field intensity
a ohmic electrical conductivity
T collision time (general)
T self-discharge on self-precipitation time of particles
a
T. characteristic time for collection by particles polarized by ambient
electric field (bed particles)
T collection time of particles on oppositely charged drops or time
for precipitation of particles due to space charge of drops
c
T typical particle collection time due to Brownian diffusion
dc
T_, characteristic time for instability of drop sheet
EH
T characteristic time for collection in electrostatic precipitator
pc
T_ drop self-discharge or self-precipitation time
R
TD liquid charge relaxation time
Re
T average residence time of gas
res
T characteristic time for inertlal impact scrubbing
sc
T drop scrubbing lifetime
SR
T turbulent eddy characteristic time
T fine scale turbulent diffusion time
4>,9 angular coordinate
41 , rate of particle collection per unit volume
¥ stream function for gas flow
u) angular frequency
240
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-650/2-74-075
2.
3. RECIPIENT'S ACCESSION»NO.
«. TITLE AND SUBTITLE
Charged Droplet Scrubbing of Submicron Particulate
B. REPORT DATE
August 1974
B. PERFORMING ORGANIZATION CODE
r. AUTHOR(S)
J.R. Melcher and K.S. Sachar
B. PERFORMING ORGANIZATION REPORT NO.
OR4AM4ZATIOM MAMt AMD AOONIM
10. PftOOMAM ELIMINT NO..
Massachusetts Institute of Technology
Department of Electrical Engineering
Cambridge, Massachusetts 02139
1AB012; ROAP 21ADL-003
11. CONTRACT/GRANT NO.
68-02-0250
12. SPONSORING AGENCY NAME ANO ADDRESS
EPA, Office of Research and Development
NERC-RTP, Control Systems Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
16. SUPPLEMENTARY NOTES
re.ABSTRACT Tne report gjves results of an investigation of the collection of charged
submicron particles, through a sequence of interrelated experiments and theoretical
models: by oppositely charged supermicron drops; by bicharged drops; and by drops
charged to the same polarity as the particles. It provides experimentally verified
laws of collection for a system with different effective drop and gas residence times.
The report shows, experimentally and through theoretical models, that all three of
the above configurations have the same collection characteristics. Charging of the
drops in any of these cases: results in dramatically improved efficiency, compared
to inertial scrubbers; and approaches the efficiency of high-efficiency electrostatic
precipitators. For example, in experiments typical of each configuration, inertial
scrubbing by 50 jum water drops of 0. 6 /jm DOP aerosol particles gives 25% effic-
iency; self-precipitation of the particles with charging (but without charging of the
drops) results in 85-87% efficiency; and drop and particle charging (regardless of
configuration) results in 92-95% efficiency. Charged-drop scrubbers and precipitators
have the operating cost and capital investment profiles of wet scrubbers, and
submicron particle removal efficiencies approaching those of high-efficiency electro-
static precipitato*s.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Air Pollution
Scrubbers
Washing
Charging
Drops (Liquids)
Experimentation
Mathematical Models
Electrostatic Precip-
itators
Air Pollution Control
Stationary Sources
Charged Droplets
Submicron
Inertial Scrubbers
Particulate
13B, 12A
07A
13H
07D
14B
18. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (ThisReport)
Unclassified
21. NO. OF PAGES
258
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
CPA Form 2220-1 (9-73)
241
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