CONTINUUM ELECTROMECHANICS GROUP
Department of Electrical Engineering
Massachusetts Institute of Technology
CHARGED DROPLET TECHNOLOGY FOR REKOVAL
OF PARTICIPATES FROM INDUSTRIAL GASES
by
J. R. Melcher and K. S. Sachar
Final Report under Task No. 8
Contract #68-002-0018
August 1, 1971
-------
CHARGED DROPLET TECHNOLOGY FOR RE~'OV AL
OF PARTICULATES FROM INDUSTRIAL GASES
by
J. R. Melcher and K. S. Sachar
Final Report under Task No.8
Contract #68-002-0018
August 1, 1971
Attention:
Robert C. Lorentz
Air Pollution Control Office
411 West Chapel Hill St. Annex
Durham
North Carolina
27701
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I.
II.
III.
IV.
1
TABLE
OF
CONTENTS
Introduction
A.
B.
Background
Outline
Survey and Classification of Devices
A.
B.
Process Functions
Classification of Drop-particle Interactions
Classification of Devices Disclosed in the Patent Literature
C.
D.
Basic Work Generally Relevant to Drop-particle Interactions
Charged Drop Devices Described in the Literature
E.
Simple Models for Classes of Drop-particle Interactions
A. Class I: Inertial Impact Scrubbing
B.
C.
Class II:
Class III:
Electricallv Augmented Impact Scrubbin~
Oppositely Charged Drops and Particles with
No Ambient E
D.
Class IV:
Ambient E. Particles Charges and Drops Initially
Uncharged
E.
Class V:
Hybrid Interactions
Production of Charged Drops
A.
B.
Classification of Particle Production Techniques
Mechanical Atomization
C.
D.
Condensation
Limits on Electrical Charging
E.
F.
Corona Char~ing; Char~ing in the Bulk
Influence Charging
G.
Electrohydrodynamic Spraying
Condensation Charging
H.
V. Comparison of Systen~
VI. Conclusions and Recommendations
Bibliography
Appendix A:
Appendix B:
Charged Particle Collection on Charged Drops in an
Ambient Flow and Field
Drop Electrical Conductivity
Page
2
2
2
4
4
4
18
35
42
48
48
53
56
64
67
68
68
70
73
75
77
78
81
90
91
95
100
106
121
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2
CHARGED DROPLET TECHNOLOGY FOR REMOVAL
OF PARTICULATES FROH INDUSTRIAL r:ASES
by
J. R. Helcher
and
K. S. Sachar
1.
Introduction
A.
Background
Nature gives an example of how drops can scavenge particulate from the
atmosphere.
It is well documented that falling raindrops effectively re-
duce the number density of particulate in the range of I-50 ]..Im[l] ,
Further, the existence of atmospheric electric fields has encouraged in-
vestigation of possible influences of particle and drop charging on the
collection of particulate by the drops [2].
Hence, it is not surprising
that the idea of using electric fields to enhance collection of particu-
late on drons is often suggested as an approach to controlling particle
emissions in industrial gases.
He are concerned with a class of devices that is hybrid between
scrutbers and electrostatic precipitators.
The scrubber makes use of
drops usually moving relative to the particle-laden gas, while the pre-
cipitator depends on electrical forces caused by charginQ the particles
and subjecting them to an electric field.
The contrast between these
conventional devices correctly suggests that there are a number of
basically different mechanisms for collecting the particles on the drops.
B.
Outline
--
The first objective is a revieT;J of \o]hat has been reported through
patents and in the formal literature relating to the use of drops and
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3
electric fields in particulate control.
from "electrically
Devices ranf!e
augmented inertial impact scrubbers" to "electrostatic precipitatorS "lith
pretreated particles".
Some,.]here bet'iJeen is a class of devices w"hich take
unique advantage of the combination of fields and drops.
It is the intent
of the survey given in
SII not only to cite the relevant reported work,
but also to classify the devices according to the type of interaction
between drops and particles, and organize the literature within that frame-
work.
There are many combinations of scrubbers and precipitators that offer
no neu mechanism for removing particles, albeit poSsible im!1rovements in a
technological sense.
Gur approach to the classification emphasizes what
is unique to the use of drops and electric fields in collecting particles:
the interaction between fields-dro!1s and particles.
A second objective, in
sIll, is a sketch of fundamental models appro-
priate to each class of interaction.
The simple models
given in
sIll
serve at least two purposes:
thev further clarifv the basic mechanisms
used for classification in
sII, and by showing parameter dependences,
they make possible comparison of systems in
sV.
The third objective is to place the basic interaction mechanisms in
the context of systems.
Important factors beyond the basic drop-particle
i~teraction are the means bv which drops are formed, charged, and injected,
and means for their removal.
Electric fields have been used in devices
for producin~ char~ed drops, hence the discussion of drop generators is
taken up in a separate section,
slY.
Then comparison between systems
is discussed in
s V.
The fourth objective is an assessment of needed research and an iden-
tification of ?romising types of devices; this is given in
sVI.
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4
II.
Survey and Classi%ication of Devices
A.
Process Functions
A schematic view of the processes called for in an electrostatic-
droplet type of device is sho,Vll in Fig. II-I.
drop production
and charging
drop-particle
interaction
droj) removal
particle
treatment
Fig. II-I
Schematic of processes that must occur in
complete particle removal system
---_.-
The practicality of a device, of course, depends on the ~eans for pro-
clucing and charging the droplets and for charging the gas-entrained par-
ticulate prior to collection of particles on drops.
Also, once collected
on the drops, particles are removed by removing the drops and the provision
for drop collection is also essential.
But the heart of the d~p-particle
approach is in the mechanism by which the particles are collected on the
drops.
In reviewing and classifying devices, we first focus on the inter-
action mechanism.
Distinction betH'een devices in a given class is then
based on methods for prior or subsequent processing of the drops and
particles.
B.
Classj}j._cation o(l!~-P article ---..lnt~.r.~ctions
In the zone of drop-particle interaction, there can be many combina-
tions of droj)-char~e, particle-charfe, and electric field configuration.
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5
The classification given by Table 11-1 makes a compromise between the pro-
liferation of categories that results from a refined view of the interaction
classification in the first place.
and the need for simplification which is the objective of a
A given class is specified by the elec-
mechanism,
trical state of the drops and of the particles, and by whether or not there
is a significant ambient or macroscopic electric field playing a dominant
role.
Eefore discussing the classes of interaction, comments pertaining
to terminology are appropriate.
Ambient Electric Fields: By an "ambient electric field intensity", E, we
mean
one which should be distinguished from the component of electric
field that fluctuates spatially over distances on the order of the inter-
particle or interdrop spacing.
The sketch of Fig. 1I-2a shows a region in
the interaction zone occupied by charged drops and particles.
In general,
these can each be of both polarities.
Gauss' law requires that the total
flux of electric field normal to the surface, S, of a volume V enclosing
some of the drops and particles be equal to the net charge contained
within that volune.
l £oE.nda
S
J PfdV
V
(11.1)
Here, £ =
o
-12 -
8.85 x 10 , n is the unit normal to S, and Pf the net charge
density.
~!ade small enough, V can contain one particle or drop.
As it
in size so as to include more charg,es, it ;s .
~ ~ ev~dent that a part
of the associated electric field v~ries rapidly over a h
c aracteristic
increases
length typified by the distance between particles.
But, as the volume
begins to include many particles, there is a contribut;on
- ~ to the electric
field t[-,at is steady. and that increases in proportion to h
tenet charge
-------
Drop
Unchar~ed
Charged; no
ambient E
Charged, and
aIT'bient I.:
Uncharged
I. Hechanical
scrubbers;
inertial impact
from drop iajec-
tion.
II. Electrical
scrubbin?; ;
inertial impact
through elec-
trical propul-
sion of drops.
/:=0-
.. E
6
Char~ed; No
Ambient E
Charged,
Ambient E
IV. Collection
on half-surface
of polarized drop
havin~ no net
charge.
E
III. Drops having
net charqe col-
lect Darticlesl
havinq; net
opposite charl!e.
~i/
0.....
(j1 -.~ ~ --
/,'_L "-
f
Combination
of II, III and
IV
o
Table II-I
Classification of Particle-Drop
Interaction "fechanisms
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7
+
+
+
+
+
+
+
+
+
+
--
+-
I
r- -- -- -1;
I 6 e 0 E> ,<
I 0@ e e @ -4-\
I ('s on electrodes; (c) ~ield induced hv "spact charge" caused by
net effect of drop and narticle charging; (d) :Jo ambient field. but
microfield due to narticles.
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8
enclosed.
It is this average component of E that we call the "ambient"
E.
There are two ways of producing an ambient E.
Usually, as in a con-
ventional electrostatic precipitator, a voltage is applied to electrodes,
as sketched in Fig. 1I-2b.
Charged particles and drops in the intervening
volume contribute to the field, but often to a negligible degree simply
because they are outnumbered by charges on the walls. The ambient field is
then termed an "imposed field".
If, on the other hands there is enough
net charge in the volume, even with the electrodes grounded, an anmient E
can be generated by virtue of net charge carried by the combination of
drops and particles in the volume.
Such an ambient E Hill be called a
"space charge field", since it arises from the space-average net charge
density in the volume making an appreciable contributiono
The microelectric fields are illustrated hy the extreme depicted in
Fi? TI-2d, Hhere there are as many charges of one sirn as of the other
and no external excitations to induce charges on electrode8.
Then. the
onlv electric fields are at the micro level. because by Gauss' 1mV', any
volume enclosing many particles includes no net charge.
The electrical force on a particle having: charge q is qE.
Hence.
the micro fields represent forces of attraction or repulsion between
neivhborin~ particles, Hhile the macro. or ambient, fields represent
forces tending to carry particles from one macroscopic region of net
charge to another.
In Fig. 1I-2b. the ambient field carries the par-
ticles toward one or the other electrode, ,.!hile in Fig. II-2c, the
ambient field tends to make the positive charge carriers "explode" tOHard
the image charges on the electrodes.
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9
It is, of course, not possible to have even one charge in the interaction
region without having it make a contribution to the electric field.
But
for practical purposes, we distinguish bet~~een interactions that are dom-
inated by the ambient E or by a micro-E.
We will further distinguish be-
tween ambient electric fields generated by external sources applied to
electrodes and those generated by space charge from the drops and particles.
These ambient electric fields are respectively termed "imposed" and "space
charge" electric fields.
Attachment:
The classification pertains to practical mechanisms by which
particles are made to collicle \vi th drops.
The implicit assumption is that
the collision is tantamount to attachment.
Although somewhat conflicting,
v!hat studies there are of attachment bet~veen typical "dust" particles and
water drops tend to support this viev!.
In a revieu of wet scrubbers, Heber
makes the statement (3]:
"If dust ;')articles and vJater droos collide, the
former "viII invariably attach the1'1.selves to the latter".
He goes on to
qualify this statement by distinr,uishing between the manner in which wet-
ting and nonwetting particles adhere to the drop.
The wetted particles
are ingested into the drop volume, while the nonwetting particles tend to
be retained at the surface.
In either case, the particles adhere to the
drops.
~JeLer's e~phatic prediction that industrial particulates are
attached upon collision is at some variance with l'fcCullv' s observations
[1] in v,7hich experiments are cited that shoH nomJettable beads can bounce
off water drops, and ilencc that some collisions ,vith nom-Jetting particles
are not tantamount to attachment.
~ith additives in the water, it appears
that a vlide range of particulate readily attach on collision, at least in
the ahsence of an electrical chargin/l.
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10
But a further question is the possible influence of the electric
charging on attachment.
Here, it is important to define what is meant
by "charging" and the region occupied by the associated electric field.
Hhen ,;ve refer to "charging a drop". we mean that there is a layer of net
charges per unit area at the gas-liquid interface responsible for the dis-
continuity between electric field just outside the water, and the zero
field region inside.
This field is on the order of 106 vIm, and is
limited by electrical breakdown or electrohydrodynamic instability, as
discussed in
5 IV.
It should be distinguished from fields associated with
o
double layers of charge in a zone on tl1e order of 100 A at the drop-gas
interface.
It is this double-layer charge that is closely tied up ~„ith
the theory of ,;vetting.
Fields in the double layer can be far greater
than those possible in the gas phase re?ion outside the drop.
The surface tension is knmm to depend on charging of the double layer,
and if it were such a charging that ,;vas of interest here, then ';7e ,.;'ould
expect that the attachment ';vould depend ('In charging.
By definition,
charging of the double layer, "hid1 can be thought of as a thin capacitor
,vith spherical electrodes in the neighborhood of the dro~ interface, leaves
the drop with no net charge.
The type of charging referred to here leaves
tne drop Hith a net charge, and results in an electric field in the region
exterior to the drop.
This exterior field is far weaker than that in the
double layer, and bence too small to influence the surface tension.
It
has been experimentally verifieo that even vTater-air interfaces which sup-
port monomolecular films have surface tensions that are independent of electric
field up to strengths sufficient to produce electrical breakdo~m [4].
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11
Because \.,1e \Jould expect attachment to be closely related to surface
tension, this finding tends to support the vie'", that there sl10uld be
little effect of the field on the mechanisms of attachment present in the
absence of the fields.
One mechanism by ur,ich the electric field can influence attachment
is through charge exchange upon collision.
TIle drop is relatively highly
conductin~, and depending on their electrical properties, the particles
can acauire the same sign of charge as the drop on collision, and then be
repelled by electrostatic forces.
Some work has been done on the compe-
tition bet'deen these electrostatic forces and forces of adl~sion on solid
surfaces [5].
Also, there are studies of electric field influence on drop-
drop I adhesion" [65]. The evic.ence is that attachment may be a considera-
tion, Lut that the relative merits of usin~ electrical forces for initiating
particle-drop collision can over-rioe the attach~ent question.
That attach-
ment takes place vlith a .wide range of particle types is supported by ex-
periments operated under nractical conditions [7].
The classes outlined in Fig. 11-1 are as follows:
~r~.£.1?__and Par.tjc1es UnchaI_3ed '- no Am-Eient E.
Class I:
Here, there is purely rc.echanical scrubbing "lith no electrical inter-
action.
This class includes venturi and c'Tclone scrubbers.
Particles
are collected on droDs mainly by inertial impact.
Advantage is taken
of the tendency of the particles, by virtue of their inertia, to leave
t~e gas stream and be collected on the drops.
Also included are such
mechanisms as entrainment in the ~"ake of drops woving relative to
the p-as.
[suecially for extremely small particles, further collection
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12
mechanisms are molecular and turbulent diffusion of particles
through boundary layers adjacent to the drop.
In an inertial scrubber, it is the inertial force on a particle
""hich prevents it from "turning the corner" and following the gas
stream around the drop.
Typically, the particle of
radius a,
having relative velocity w and mass densitv p , suffers an accel-
- a
eration on the order w2/R in the neighborhood of a drop, where R
is the drop radius.
Hence, if the gas mass density relative to that
of the particle is ignored, the particle experiences an inertial force
4/3 P 7Ta3(\v2/R).
a
That force is retarded by a viscous drag force
uhich, if represented by Stokes' law,is of the order 67Tl1aH, uhere 11
is the gas viscosity.
The iner.tial impact para~eter [8] is the ratio
of these two forces and must be appreciable compared to unity for the
collection process to be effective.
inertial force
inertial impact parameter = viscous drag
=
2
2 °aa \V
9 Rl1
(1)
Class II:
Drops Ch~r~e~!~rticJes Uncharged,
Ambient E
~-------
In a mechanical scrubber, relative motion between drops and particle-
laden gas is often obtained by injecting the drops at a velocity dif-
fering from that of the gas.
Tilis relative velocity can also be
achieved by charging the drops and subjecting them to an ambient
electric field.
The resultin~ electric force gives a drop motion,
relative to the ~as, that can be used to scrub unchar~ed particles
from the gas.
'lhe advantaf!e of the field-induced scrubbinl:'; is that
the relative velocity does not decay to zero from the point of injec-
tion, but rather reaches a steady value determined bv the hydrodynarric
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13
drag, particle charge and ambient electric field.
Thus, the device
i distance associated with
scaling is altered because the penetrat on
the mechanical scrwJber is no longer a limitation.
The inertial impact ~arameter of Ea. (1) remains appropriate for
the class II interactions, ,lith the relative velocity w determined
oy the balance of electric and viscous forces on the drop.
If we let
the drops be charged to 0 = C'TTazE: E*, ~vhere R is the drop radius, E*
. 0
is a charging field, and C is a geometry factor varying between about
three and 12 depending on the charging method, and again aSSUme Stokes'
drag, in an electric field E, the drop reaches a steady velocity
Ttl =
[(C'TTRZE:OE*)/6'TT~R]E.
Thus, the anpropriate inertial impact para-
meter follows from Eq. (1) as
impact parameter
Z
paCE: E*E
a 0
27 ~z
(2)
electrically induced inertial
=
Class III:
I!!_ol?_~ha!ged~art}_c1es . C1'0rge~,- no ~bien_t E
By contrast with Classes I and II, there is negligible relative ve1o-
city oetween gas and drops in Class III interactions.
Particles are
collected on a charged drop surface by electrical attraction of oppo-
si te charge.
Hence the drop surfaces attract particles much as do the
precipitating electrodes of a conventional electrostatic precipitator.
Fields responsible for collection of particles are largely "micro"
fields.
Clearly, Class III collection dominates if the charge density
of small Darticles is equal and opposite to that of the drops.
Then,
there is no net space charge, hence no ambient field.
Other possibil-
ities
are mixtures of both nositive and negative particles along with
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14
both positive and negative drops, in proportions such that there
is negligible field due to net space charge.
But, from a practical
point of vie,,,, the charge density of the drops could far outweigh
that of the particles and still result in an interaction of essen-
tially the Class III type.
The fundamental collection mechanism is placed in the perspective
of conventional electrostatic precipitators by introducing the fol-
lowing commonly used simplified model of a conventional precipi-
tator [9].
Suppose that a section of a preciDitator havin~ len~th £
prec
collects an appreciable fraction of particles on electrode collect-
iug surfaces used to i~pose an ambient E normal to their surfaces.
The field causes a particle velocity normal to the electrodes w, and
the electrodes are characterized geometrically by a circumference S,
and cross-sectional area perpendicular to the flow, A.
The number of
particles passing a given cross section per second is then UAn, and
that must be on the order of the number per second £
prec.
Sw n
prec
collected
at the Halls.
Hence,
£ S,-l %
prec prec
UA
(3)
For efficient precipitation, the device lenQth, 1, should be large
compared to
£ .
prec
1
Q,
prec
1S H
( prec) > 1
UA
(4 )
Nmv,
consider a len,gth £111 in ~vl-lich a large fraction of the
particles
is collected on drops.
In Eq. (3), the particle collection
surface is £ S, and <;-lith N-per-unit volume of droDs, each of Hhich
prec
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15
has surface area 4'ITR2, this collection area is replaced by
4'ITR2NA9-Ill.
We define CYR
as the number of drop radii by which the
drops are separated on the average, so that N = l/(~R)3, and it
follows that the e~uivalent of Eq. (3) for the drop precipitator is
4'ITR2 AQ,III
----
~3R3
WIll %
UA
(5)
TI1US, for efficient collection of particles on drops, we must have
L/9-II >
I, v7here
L
9-III
L4'ITWIII
u~jR
(6)
TIle necessity for oavin? close packinp, of the drops, or low ais if
they are to compete with the conventional precipitator, is emphasized
by taking the ratio of characteristic collection lengths
Q,III
9-
-prec
a 3RS
R
4 'ITA
w
prec
FIll
(7)
For the drop system to compete favorably, Lq. (7) should give a ratio
large compared to unity.
i~ote that the particle velocities w
prec
wIll at the collecting surfaces are functions of the particle charge
and
~nd electric field intensity at the respective surfaces.
nUA
k
>1
Q,
Free.
Conventional nrecipitator Class III drop "precipitator"
~ig. 11-3 Configurations for comparing conventional
nrecivitator and Class III interactions
-;> \ 0,,* 0
\
nUA J
/ 0 0 0
/
1(, .err I ~
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16
Class IV:Drops Uncharged, Partic1es~harged, Ambj!!~~
Neutral drops introduced into the flowing ?,as and subjected to an
ambient electric field are polarized.
The flux of electric field
lines over an area three times that of the drop cross section is
intercepted by the drop.
Thus, char£ed particles migrating toward the
drop along these lines are intercepted by the drop.
If particles are
charged to only one sign, then thev are initially collected over half
of the drop surface.
If rarticles are charged to both polarities,
then collection takes 1)lace over the ,.,ho1e drop surface.
In the unipolar particle case, the drop collects particles at the
expense of acquiring a net charge, and the field in the drop's vicinity
is altered so as to 1iDit narticle collection.
Because of its result-
ant net charge and the imposed E, drops drift relative to the gas.
Eence,
Class II interactions can come into playas the process pro-
ceeds.
Also, the net charge on a drop can be the basis for subsequent
drop collection using conventional precipitator configurations or
space char~e precipitators.
In the case of bipolar charging of the narticu1ate, it is possible
to have the neutrAl drops collect particles ,vithout significant alter-
ation of the charfe neutrality.
In that case, contribution to the
ambient I.:: from particle charging is also minimized.
Assuming unipolar
charginr- ,
the effective drop-collecting surface is initially 3TIR2, and
~lence the collecting area in a collection length .Q,IV is 3TIR2NAiIV'
Fol10winp arguments similar to those accompanving Eqs. (5)-(7), effec-
tive particle collection on the drops requires that L/.Q,IV >
1, ,.]here
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17
L
Q,IV -
L3TIWIV
U~"R
(8)
Class V:
~brid Interactions_with D~~~nd Particles Cha~and An
Ambient Field
With the combination of ambient electric field and charges of opposite
sign on drops and particles, it is possible to collect particles on the
drops through combinations of the mechanisms included under Classes II,
III, and IV.
In this class, the drops can be charged to differing
signs, as can also the particles.
The ambient electric field is im-
posed by means of external electrodes, or caused by space charge.
For
example, suppose that drops of one sign are mixed with the dusty gas
charged to the orposite sign, and the mixture subjected to an ambient
electric field.
Then, droplets are driven at a relative velocit~T Hith
respect to the gas, so that the inertial iMpact mechanisros of Class II
come into play.
TIle particles also collect on drops through the micro
field interaction of Class III.
Once neutralized by the collection of
oppositely charged particles, ~le drops are the sites of further par-
ticle collection throuvh the mechanisms of Class IV.
Thus, dependin~
on the relative wagnitudes of charpe and electric field, on the size
of the particles and drops, and on the interaction time betHeen the
varticles and drops, all three mechanisms come into play to one
extent or another.
?urtl~r- Tvp~_s_~L- ::>ey_ice_1?- Not--~!~yplving li_asica_!}y ~eH PheE~mena
The classification of drop-particle collection mechanisms emphasizes
tIle interaction, rattler than differences in systems.
It is through these
mechanisms that there is prorrise for making a neH departure in particle
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18
collection technology.
Devices have been proposed that combine drops
and fields for particle collection, but that really do not exploit new
mechanisms which might therefore hold promise for developing a tech-
nology for handling sub-micron particles.
An example is the combination of a scrubber and electrostatic pre-
cipitator into a single volume, where each functions in an essentially
conventional manner.
Reference is made in the following review of the
literature to "miscellaneous" devices that fall into this category-
They
are not regarded as exploiting what is basically new about tne inter-
action of drops and particles in an electric field.
C.
Classification of Devices Disclosed in the Patent Literature
.---
In the summary of patents directly relating to the use of electric
fields and drops for collecting particulate, primary emphasis is given to
the drop-particle interaction.
Also included is a categ~rization of the
method of:
(a) charging particulate, (b) charging and producing drops,
(c) removing drops, and (d) method of creating ambient fields~ if any.
Class I interactions encompass conventional mechanical scrubbing, and are
included in the classification only for purposes of comT'arison.
Hence,
they are not surveyed in the following.
Table 11-2 lists patents des-
cribed in this section.
Table II-2
-"-----, -
Patents~~lating Dir_e_ctly ~~- Llectr2c~11'y-:-1ndyce~.-?llection
~Yar_~cle~~ Drops
Class
Inventor
Patent Ho.
Title
~)a te
--------
----~---~---------
II
WinterTT!ute
1,959,752
Liquid Flushing for Discharge
Electrodes
1934
II
ScllIT'.id
2,962,llS
Apparatus for Separatin? Solid
and Liquid ~articles for
Gases and Vapours
1960
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19
Class Inventor Patent No. Title Date
II !"arks 3,503,704 Method and Apparatus for Suppres-
sing Fumes w/Charged Aerosols 1970
II ;carks 3,520,662 Smokestack Aerosol Gas Puri fie r 1970
III 1.-!agner 1,940,198 Apparatus for Cleaning Gas 1933
III Penney 2,357,354 Electrified Liquid Spray Dust
Precip:itators 1944
III Penney 2,357,355 Electrical Dust Precipitator for
Utilizing Liquid Sprays 1944
III Gilman 2,523,616 Electrostatic Apparatus 1950
III Gilman 2,525,347 Electrostatic Apparatus 1950
III Peterson 2,949,168 Electrical Precipitator Apparatus
of the Liquid Spray Type 1960
III Peterson 3,331,192 Electrical Precipitator Apparatus
of the Liquid Spray Type 1967
III Romell 3,440,799 roas Scrubber 1967
v
Fodson and
Klep!perer
2,615,530
Liquid Cleaned Precipitator
1952
v
::\.ansburg
2,788,031
F.lectrostatic Gas-Treating
Apparatus
1957
v
DeGraaf, Haas
van .Jorsser and
Zaalber~ 2,864,458
Liquid-Electrostatic Precipitation 1958
v
Ziems and
Dbnicke
3,384,446
Apparatus for Disinfecting Gases
1968
-------
Class
Inventor
Patent No.
J'vtiscell.
Buff
1,905,993
l'iiscell.
Vicard
2,983,332
Hiscell.
vHemer
3,221,475
Hiscell.
Vicard
3,363,403
~,fiscell.
Ebert
3,492,790
Hiscell.
Humbert
3,523,407
III* Prentiss 2,758,666
III* Johnstone 2,924,294
lIP'. Silverman 2,992,700
IIP'~* Allemann, l'foore
& Upson 3,218,781
IV*
2,990,912
Cole
20
Title
.-----
------
Treatment of Gases
Process and Apparatus for the
Purification of Gases
Wet Electrostatic Precipitator
Electrostatic Filtering Apparatus
Gas Cleaning Apparatus and ~~ore
Particularly to an Improved
Electrical Precipitator
Method for Electrostatic Pre-
cipitation of Dust Particles
Carbon Black Separation
Apparatus for Cleaning Gases wi~h
Electrostatically C~arged Particles
Electrostatic Air Cleaning Device
and ~~ethod
Electrostatic Apparatus for ~emoval
of Dust Particles from a Gas
Stream
Electrical Precipitator and Char?ed
Particle Collection Structure
Therefor
*
Solid particles used instead of drops
** Drops replaced ~y bubbles
Lla ::?:.
-------
1933
1956
1%3
19fiS
1970
1970
1956
1960
1961
1965
1961
-------
21
Class II:
Elect~}cally Augmented Impact Scrubbinp,
\.Jin termute:
1,959,752
-----
The invention relates to the addition of liquids to a conventional
electrostatic precipitator.
In the configuration described, a sin~le-stage
precipitator of tubular construction is fitted with a water injection system
so that the discharge "Tire (passing down the center of the cylindrical col-
lecting electrode, ~'Thich in this case is at high voltage) is surrounded by a
liquid stream.
Because of the electric stress, this stream breaks up into
drops.
As described, the device operates much like a conventional precipi-
tator with the water electrically made to strike the outer electrode,
and hence clean it.
~o interaction mechanism between drops and particles is
described.
However, we knOT:7 from related work on corona discharges from wet
surfaces [10] that the ~Jire must be the source of both ions and drops having
the same ~olarity.
Thus, the annulus is a region filled by radially expand-
ing ions and drops.
Particles are introduced to the tube structure as in a conventional
precipitator.
Upon entering the field re~ion, the particles aSSUme ~..rhatever
sign of charge is carried by the flux of ions.
Hence, particles and drops
have the same sign, and there is at best a limited tendency of a particle to
be attracted to a drop bec~use of the polarization of the drops in the ambient
field.
(That collection mechanism vJOuld cut off if a drop \lere charged on
formation to the saturation charpE, as discussed in
9 II LA) . Thus, the only
remaining mechanism for electrical augmentation of the particle reT1'oval pro-
cess ty collection on the drops is via inertial impact caused by the relative
velocity betvleen drops and particles traveling radially outward in the imposed
-~' ---~ -----_._--------~
ion impact, but not consequential
pa~ticle interaction
indu~tion and/or ion iwpact
electric precipitation
imposed
particle charginp
to drop-
drop charginp.
drop removal
ambient field
-------
22
electriC field.
Schmid:
2,962,115
------
A problem ,vith centrifugal separators is that, once the particulate
has been forced to the outside wall, it must still be removed from the
device by inertial (8ravitational) settlin?-.
To hasten this process, the
size of the particulate could be increased, possibly by agglomeration.
The
dirty air from one cyclone is passed to another.
Inside the latter are a
pair of parallel plates, with a high voltage ~laced between them.
Charged
~..1ater spray is then introduced bet~Jeen thefT!; tilis is accomnlished by
inducin~ electrodes placed a sligl: t dis tance a'-lay from the nozzles.
The
drops oscillate betHeen the plates, and collect tile uncharf>ed particulate
by inertial impaction.
These drops are heavy enough to fall to the bottom
of t;1e chamber v:here they can be drained awav.
----------
particle charging
drop charginr;
drop removal
ambient field
none
by induction
settling
imposed.
11arks :
3,520,662
-~-
To clean the flo" from a smokestack of particulate and fumes, the gas
is deflected through an annular region containinq an array of small nozzles.
Do~~stream of this is a perforated char gin? electrode.
TIle fluid is drawn
out of the nozzles by the electric field in the form of very fine drops.
Past the charger is a mixing region, where the c1roplets mix Hith the flm!
and pick up the dust and fumes.
Since the walls are grounded, the mist is
space-cllarge deposited there.
:10 provision is made to chan~e the dust.
Another "ay to form the charged drops is to draw fluid through a grounded
porous plug surrounded by a screen set at high volta,17e.
The drops produced
-------
23
are claiT"ed to be aDout the same size as the holes, 1 - 100 ~.
111e inertial
" l"S l"n~_erred from the patent because the drop-narticle
imp8ct interactlon -
interaction is not actually described.
-- -" -- - - ----
~article charfinf-
drop charging
drop removal
alT'bient field
none
by induction
electric precipitation
space charge
;.[arks:
3,503,704
A methoc to cleanse a gas flow of noxious fumes is offeree.
Inside the
channel, an array of capillary tubes is placed across the floF and connected
to ground.
Dmmstream of this is ~ositioned a
-------
24
Class III:
2Epos~tely Cllarged Dr~.s_~nd Particles 'vith Essentially No_Ambj~nt E
Hagner~
1,940,198
Just, presuMably c:lar~ed durin? combustion, is passed through a re~ion
saturated vlith ,,7ater droplets.
The latter are frictionally chaq~ed either in
passing tl1rougll the nozzle or through the air.
Collection of the p8rticulate
uy the droplets then occurs in this mixing rer-:ion, promoted to a large extent
by the turbulence established by the injection of the sprav.
The flmv is next
directed through lmv-terrperature re~:dons vJhich cause the droplets to coalesce.
These larger drops are then removed froM the gas floH by inertial means.
particle chargin~
drop charging
droj) remov8l
ambient field
combustion
frictional
inertial
negligible
Penney:
2,357,354
Dust-laden gas first passes through a tubular electrost~tic ionizing sec-
tion to charge the particulate hy ion iITpact.
Just dmmstreap' from this is an
arra? of nozzles ,'J:tich issue a snray of inductively charged or ion-impact-
chargee! drops.
III experiT"cn ts reported, drops are in the size range of 500 ~m.
"Penney eT!lpllasizes that dro~s must 'ue of sufficient size that they can be easily
removed from the gas.
Drops and particulate have or~osite polarity.
Durinf
passage dmm the channel, the drops scavenge the particulate, until finally
the v are removed.
Suggested means of removal are inertial iJ11pact and other
conventional means.
l'ilis patent not only makes a primary disclosure, but is an inforJ11ative
and useful guide to the desi!!n of the general class of devices.
Penney clearly
recognizes
t:le competition bet'veen the sp8ce-charge-generated ambient field
and the micro ficlcs responsible for the collection of particles on drops.
'~'o alleviate the adverse effect of the space-charge ambient field, particularly
-------
25
in electrical breakdovm, a modification of his device is described in which
an arra:;r of grounded parallel plates are placed just after the high voltage
Their purpose is to keep the
cilarge,
inducing electrodes of the sprayer.
In
3 III-C, we discuss
droplet space charge from growing to discharge levels.
the role of particulate space charl?:8, 1vhich Penney chose to make negligible
cOT:1pared to that of the drops.
Limiting the volume occupiec bv the space charge is necessary if the
ambient field is to be limited.
Equation (11.1) shows that, for a given net
charg:e per unit volume, the greater the volume enclosed, the p:reater the
average electric field intensi~y at the surface of the volume.
The space
charl-!e fields act to promote collection of the drops, but this is tantamount
to removal of the dust only if toe drops have had time to collect the dust.
Space-charge ambient fields also bring into possible play Class II interactions.
particle cLarging
drop chargin~
drop removal
ambient field
Penney =-
2,357,355
ion imnact
ion impact or induction
inertial impact, orecipitator
oresent due to space char?e, but not
hasic to the interaction
The ilprinciples and teacllin~s" of renney's Patent 2,357,354 are basic
to what is disclosed here.
and crop orifices
are described.
particle char~ing
drop charging
dro!, removal
ambient field
Furt;ler Rrran!='eJ'1ents of electrodes, gas stream
ion impact
ion imoact or induction
inertial impact, etc.
inadvertently due to space
char f!e
-------
26
Gilman:
2,523,618
One problem arisin~ in Penney's devices is that water collects on the
high voltage electrode opposite the source of water spray.
The field at
this inducing electrode is sufficient to cause discharge of such a sign that
the drops leaving the nozzle ';iJill be discharged before encounterinp. the charg-ed
dust.
A solution offered is to use tvJO parallel rods as the high-voltage-
inducinf' electrodes, Hi th the rOVJ of nozzles situated between and slightly
above them.
T~ese electrodes ,"ould be slightly tilted, so that any liquid
collecting on them T,'ould run off.
Props ,,'QuId then forro at the lower end,
,.,here the field strength 1;lOuld be the 'peakes t.
These take the place of Pen-
ney's ring inducin~ electrodes.
In addition, a pneuroatic type of sprayer is
described that produces much more highly charVed crops than the other non-
rmeumatic types.
------ ~----- --------
See Penney - 2,357,354
Cill'1an:
2,525,347
-----
i.\s ill his patent 2,523,618, an iP1nroverrent is disclosec on Penney's
devices.
The proble~ is that, in a sprav device with induced charging,
water collects on the hi?h voltaf,e end and discharges.
This results in a loss
of cnarp:e on the esca~in~ drops.
To prevent this, another grounded ring
electrode is added beneath the hip:h voltap;e one, "Tilich tends to pull the drops
and their discharge aHay froI'l the ITIain (lust flm".
-~------
See Penney -
2 , 357 , 351+
Peterson:
2,949,168
This device is similar to Penney's.
The dust and sprav are charged to
onposite polarities bv pRssing t:le resDective flovs through corona discharr-e
rep;ions.
Although the spray is injected transverse to the dust flmJ, a fan
-------
27
at the output of the systeIT1 pulls both the particulate and the drops down-
There is no i~posed ambient electric field in this re~ion,
streJ-tn together.
outer "aIls of tile device are constructed of insulating material.
sine" the
T:1is ,dll be true as long as ,-letting and subsequent fouling of the Halls by
the crops can be prevented.
Collection of the drops is accomplished by
inertial impaction at Jaffle plates placed do-mstream.
The patent pertains
to arrangements of apparatus leading to reliable operation without the neces-
sity for cleaning.
-~--_.-
particle charging
dro? charging
drop removal
ambient field
AlleT1anr., Hoare and Upson:
ion impact
ion impact
inertial impact
negligible
3,218,781
Strictly, the disclosec device does not involve drops, but rather bubbles.
In a sense, it is the Class III type of interaction "turned inside outll. Ion
impact char:>~d particles are entr,qinerl in a gC:tS forced tl-}rough holes in an
insulatinp plate.
A conducting liquid is on the other side of the plate,
and the gas passes
t1-trol1Jh in th_e form of bubbles.
Hence, the charged particles
find ther,1selves ,vi thin Cl Duob12 ane are precipitated on the bubble ,.;alls.
--~--_._----------- -.---
1'1111S, tiley axe tnmsferred to the Fater, and reT'loved.
particle charging
drop charging
"dror reJ11oval.1
ambient field
Peterson:
3,331,192
---
ion impact
induction
(bubbles removed by
none
IIsettlingll)
Aoparatus improvements relatin~ directly to Petersons patent 2,949,168
See also Peterson's patent 3,098,890 for device capable of
are disc-losed.
d . ll"n_uid bet~een two points that ~ust re~ain electr~ca_llv
ductin~ a can uctlnr ~
insulating.
-------
28
Romel1:
3,440,799
---
'l'he main innovation in this device is the use of r:elvin' s influence
machine [13] for both chaqdl1f': the drops and nrovidinp; the hip;h voltage for
the corona source.
The basic interactions seere most similar to Penney's.
Considering the significant emphasis ~iven to problems of foulinp, and main-
tenance of electrical insulation in the region of dirty gas and drops, it is
extremely doubtful that the pro:,osed technique of converting hydrostatic head
into the required high voltage electricity is a practical or appreciable
innovation.
------_._.-
particle charging
drop charging
drop removal
ambient field
ion impact
induction
settlin ~
negliginle
Class IV:
Ambient E \dt:l1_~~rticl~~ Cha]:"ged- but_lJr0J2...s_Ini~iall:LUncharged
----
Tilere do aot appear to be patents that clearly fall in this class.
See
Class V patents for devices tnat probably involve the Class IV collection
under some conditions.
A disclosure
~al~ing
use of solid particles instead
of drops is:
Cole:
2,990,912
---
A two-stage electrostatic precipitator is mace with a conventional
corona source for chaqrinp; particles by ion im]'act.
111e collection section
of the conventional ~recipitator is replaced by a packed bed of spherical
semi-insulatin?, lar?e particles.
Tlle bed is sub.iected to an irmosed electric
field so that the spherical large particles are polarized with positive and
nerative surface char~es, resr,ectively, over half-surfaces.
Jlence, the
sol irl 1anre particles playa role similar to that of the drops in a Class IV
-------
29
type of interaction.
bv contrast ,7ith the drops, the particles of Cole's
invention are fixed in position and packed bet~,reen conducting grids to the
point of sustaining a conduction current.
Class \1:
E~riJrid Inte_ra~tions Fi~l1- HOt!1 Dr_0--E.? and Parti_~les Ci1a~ed in
an Aml}ient "Field
----------~-
liodson &. i(le~E.erer:
2,615,530
After the dust flou is mixed with steam it passes into the ionization
section, ~~ich is cooled by a water jacket.
lhis promotes condensation of
t~e vapor. with the particulate as nuclei.
This effectively increases their
size and allo~.rs a larger amount of char~e to he placed on them.
In the col-
lector, a rod instea~ of a vire
(as in the ionization section) is placed
along the axis.
The outer Hall is ap.ain Hater cooled.
The ; thermal head"
and the electrostatic force act to drive the cnar~ed particulate to the wall.
Hater drops t~lat ~'Jere not ch;:nf.ed in the ionization section experience a dipole
force produced uy the nonuniforn field tendin~ to pull them tmlard the center
conductor,
The relative C1otion '1roduced ~lill enable these uncharged drops
to collect, by means of impaction,otner particulate \vhich may have escaped
c;larging in the ionization section.
Altho'Jf':1 not apP9rentl V reco?'nized by t:lle inventors, those drops arri vin~
in the collector section with less than the saturation charge will collect
-;Jarticle::: throug;l tne Class IV mechanism, thus giving rise to a drop charr;in?
that resul ts both in particle collection and the net charge on the drop neces-
sary f0r conventio~al Jrecipitation.
------- ---- ---.-- --~._-_. ---
particle c~ar~in~
droT) charginp
dror removAl
8J11bient field
ion iT:1pact
dondensation and ion i~pact
electrostatic prcciDitation
ifT'posec
claiMed
-------
30
Ransbur....&.~-
2,788,081
This device is very similar to penney's.
The chargin~ of the dust is
accomplished with a cone-shaped device having a sharp base edge to promote
corona dischar2;e, \,hich presents much less resistance to the flow than an array
of bars.
The droplets are produced and charged by placing a spinning- disk
atomizer at high voltage Hith respect to tile ~rounded Hall.
A relatively
non-conducting fluid is used, so that the pump can be placed at ground.
T~le electric field. present causes the drops to disperse and migrate to the
",alls.
Provision is Made to allow collected liquid to drain away to prevent
the drops there from becoming a source of back ionization.
The transverse motion of the drops across the dust flm, tends to remove
the particulate.
In this case, there is no mixing alonf the flow, where the
d.ust and drops are made to flow t08ether downstream.
The basic collection
process is not specified, but it can be inferred that Class II and III inter-
actions are intended..
Tile spinning- disk used to produce the charged drops
is the main innovation.
~his has been highly successful in the electrostatic
paint sprayin~ application [11,12].
-_._---------
particle charginv
droT) cllaq!ing
drop rewoval
aMbient field
ion irrract
in(~uction
inertial im"1act
irn.nosccl
and electrostatic nrecipitation
DeGraaf et al:
2,864,458
._-
The device descrihed consists of a grounded metal pipe "7ith a discharge
electrode set at hi?!l volta!-!e running dmm its axis.
Beginning j 1.lst above
the ".rire,
and spaced oetv!een it and the outer Hall, is a curtain of ,Tater
emanatinr: from grounded nozzles.
One reason for this arrangement is to pre-
vent discharge from the nozzles.
The closest ~round to the wire is the
curtain.
A snort dis tance do\mstrearn, tile curtain breaks UT' into individual
-------
31
drons.
These are inductively charRed to a polarity opposite from that of
the dust, as a result of the corona.
The electric field causes the dust and
drops to move in o~posite directions - one toward the ~~ire, and the other
tOHard the \-,Tal1.
This encourages mixing and further agglomeration.
The
performanc.e of this scrubber ~']as compared to that of a Vlet Cottrell and
Penney's, and fared much better, especially at hi~h gas velocities.
Note
61at the particles are in competition ~.,ith the ions in discharging the
drops (Class III), and char?ing the drops (Class IV).
Also, the drops are
accelerated relative to the gas, so as to encouraf'e inertial impact of
particles.
------ ----~
aIEbient field
ion impact
induction
inertial impact
Drecipitation
imposed.
and electrostatic
particle charging
drop char~ing
drop removal
Ziems & Bonicke:
3,334,446
-- ------ -----
A I".2c:13.nism for di sinfectin?, a room is described.
l:isinfectant is
sprayed froTn nozzles placed far above the floor and connected to a high
voltave sou~ce.
The charred drops passin(Y into the air Fill tend to collcct
dus, '~jich apparently is natural Iv char~ed.
Through the action of both
f'ravi ty and the elec tric fi~ld ~etvJeen the tOHer and the ground plane, the
elf rt"
draT's
~ill be collected on the floor.
Provision is made to allm., the
drops to be eit~er positively or nepatively charged, depending on whether the
dust is Dre,:ominantly one sifJ:n or the other.
The device might operate in
any or all of t~e classes, dependinQ on the degree of drop charging, the
s trcn",th of ttle iI"'p05e6 field, and the char?;e of the particulate.
The in-
ventors n-ive fe'} clues 2S to the basic -mechanisrr.
-------
32
ambtent field
random "natural"
induction
?,ravitational settling
precipitation
imposed
and electrostatic
particle charging
drop cLlargin8"
drop removal
Clc~ss: rii.~~~llan~us :Fatents -C
-------
:33
\.Jiemer;
3,221,475
The P1a;or innovation in this patent is the use of thermal effects to
augment the formation of pater dro~lets on dust particles.
Incorporated into
tne device is a conventional electrostatic orecinitation system.
Ebert:
3,1~92,790
----
The flain innovation is a systeP1 for rotating the corona charging elec-
trodes so as to dlarge more comoletely the particulate.
The device is essen-
tially a conventional scrubber vlaced in series with a wet-wall precipitator.
Humbert:
3,523,407
Use of liquid additives to precondition particulate before conventional
electrostatic nrecipitation is described as a means of alleviating problems
1;'li th
bigh
resistitivitv particles.
Vicard:
3,363,403
In this version, relating to Patent 2,983,332, vanes arc added to the
venturi tnroat to irpC'rt rotationAl motion to the flm' cOT"oosed of condensed
droplets and particulAte.
This forces the drops to the outside and prevents
t;le system froTT: arcin'!" and aids in the later electrostatic precipitation of
the \.~et particulate, since the outer ~1all is the collecting electrode.
-------
34
Patent~_....::~_sclosinf': Use of Sol~d Pa~tic1es_J.~lste3E_of Dr~
Prentiss:
2,753,666
--.----
Particles are carbon black, charverl by ion imn8ct to differinr siRns
in se~arate re~ions,
or bv means of an ac electric field.
AgglolT'eraU on of
small particles on lar?e ones may be considered as equivalent
to tt1e Cla:;~;
III interaction ~cith one of the carbon blacJ~ families playin8" the role of
the drops.
Johnstone:
2,924,294
---
Solid pellets are char~ed by frictional electrification and used as col~
lection sites for fine pGrticlcs tnrou~h electrustatic attraction,
P011ets
are essentiallv insclatin? and collected in a cyclonc-tyne filter.
Hi th the
uellets ?layln~ the role of charged rlrons o~ insulatinR liquid, the inter~c~ion
would be Class III.
Silverman:
2,992,70-)
-~---
A fluidized Led 0f soliJ insulating particles is charged I~y ~riboelec-
trification".
1~e dirtv gas is apparently naturally cnar?ect, and UDon bein~
fil tered t:lrough tr-,e hed, leave~) "articulRte all the insulatin? nR.rticles of
the [)ed.
The collection process
is of type
Ill, if that explanation is
accepted.
-------
35
J) .
-~:?J.-_c_~lork_~~!,"'2 ;:-al} v ?,~lev_an t!~l?_r~=-"P article In te~ac tions
Oncs it is recoRnized that charge and field effects on narticle inter-
actions are of interest in such \"idely separated areas as meteorology, colloid
cnemis try , 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 fra~ented.
There are a lar~e number of investigations reported
on charge effects in the stability and aging of aerosols [14,15,16,17,18,19].
Other rerorts relate to cloud-drop interactions with ions, particulate,
and dro-f'lets.
An excellent overvie\v of the electrical behavior of aerosols
is given bv Uhitby and Li '-l [20] .
Tlte spectrum of phenomena is, of course,
relevant to the use of drop-pprticle interC!ctions in cleaning incustrial ?ases.
Hm;e-"'2-r, we can avoid becoming overvJhelIT1ed by the lar~e number of para-
meters ;:1;:-;::1 ?rnccss that could be hrou,=ht into ]llav bv recogaizing at the out-
set certain limitations on the systems of interest here.
First, the drops
are probab~v in the ranre of 10 ~.
Penney states that there is little point
in introducing th2 dro?s unless rileY t;,eu,sel ves are easily removed [7], which
tends to place a lOller LOllnd on the size of useful drops.
Ee gives an
example of droj1s in the size ran~e of 0.1 - 0.5 rom, yith 10 ]..lID as a lm.:,er
bound.
Tvpical devices
such
as inertial impact scrubbers, cvc10ne scrubbers
and the like) as well as electrostatic precipitators, begin to have limited
capaoilities as the nartic1e size is rec:1uced 1T'uch be10vl 10 ]..l.
Fence, 1 ~
is ,-:ertain.lv a lOFer- liT':it on the range of drop size of practical interest,
and IJ]..l is likelv to be typical.
-------
36
Second, for industrial applications we are concerned "ith processes
that occur in seconds,ratner than apinp processes that take ndnutes or more
to rrouuce a significant effective change in particle
si.ze.
This is a ma;or
reason for considering inter.qctions between particles and relativelv lar2;e
drops.
A sin~lc collision results in a drastic change in effective size.
In vieu of the relatively lar?:e size of the drops and the submicron size of
particles of interest, ~ve can think of a "sea" of small particles ane reI a-
tively '"ddel v c.ispel"Sed much larger drops.
Figure 11-4 shows the drops,
To!ith radius }~, havin{! average sp.?ci~f all and tie partic'e3 wij 1:1 radius 3.
navin~ average spacin~ a a.
a
In general, the particles can be Lath posi-
tively an~ negatively charger:.
"Cader the assu]'T1Dtion t:lat CL £(- »
I{
a a, a particle can be considered as
a
interactinp: uit:l an .'_sol~ted drop.
ConsidE:L3b 1e literature exi-:: ts for '3 tucii: s
of interactions betl.;een isolated "aropslt 'Ind various t~Tf'eS of
S'targ2d 'PH,ti-
cles.
The rranner in which a particle aCQuires charges froJT1 a 31c:a of ions
in an ambient l~lectri.c fiel
-------
37
..
\J
: ~)
.
;.._---~ 'J ~ /--........
-.---- ~R f'
o .I:~~ (\
"
I.C I ~ ."
I '. )
" t
0 \'
It' ''''
r ~, <'
~ ~ ~
2Q. . -
t ' ('
e .
o
Fi..go II-4 Relatively large and ''lidelv spaced drops fn a "sea"
of particles
1 1 1 j
I
!
~ E
0
,
.
~"Char~e Q
1
1
1 Wo
Fig. II-5
Drop generally havinp. net charge 0 in an ambient
field E , and having velocity Wo relative to the
o
?as.
-------
38
For convenience, consider the drop as fixed with the gas having a
relative velocity H and an aTT'bient field E far from the drop.
o 0
The defi-
nitions of positive flow and field are shrnln in ?ig. 11-5.
The rlrop is
taken as perfectly conducting, since the relaxation time of the Hater is
far shorter than other dynamical times of interest (see Appendix B for a
discussion of this point).
Note that die relative velocity Wo could be
caused 1y the electrical force on the drop due to its charge, Q, and the
ambient field E .
o
Then the relative velocity ~-vo and net drop charge ()
would not be independent quantities.
For the Dresent, think of the state
of the drop in terms of its net ci.1arge Q and t:le ambient field multiplied
by the particle p'obility. O. ;:;nd the relative velocity'" .
o
Sr>ecification
of the first tHO of t)lese quantities gives a point in the (O,bEo) DIane
1 .
S,lOT..ffi ln
Vif'. TI-6.
~le relative velocitv w
. 0
then sDecific3 the location
of the vertical line at b~
o
= TN .
o
T;le figure sUTnTllarizes the manner in which
particles ch2r~e or discharge, ~iven an initial state.
TIle critical charge,
0c' is proportional to Eo
o
c
12m:: p.2r
o 0
~~ile currents i an6 i Are proportional tn ~
1 2
and th2 narticle charge
density, and depend on G itself [see Ecs.
(1\.2). (A.22) and (A.26) J.
~emember that an electrical current is e~uivalent to the deposition
of particles on the drop.
In the Fig. II-h, the :.>articles are assumed
positive.
r:ence,
an~~herc on the surface of the drop that the electric
field is directed inpard, it can collect particles.
The ",,,indo'J" through
which particles can reach the droD is sketched to typify each regime.
As
the cilarp-e chan~es,
so also does the '\lindow".
cor example, su~pose that
I,'.'
.~o
> H ;:mu 2- dror ini_ti91ly has a sufficientl', ne
-------
39
it is
in re;:;ime
(£) of the figure.
Then, it has at first a "vlindow" that
is the Hhole surface and T,Jill collect particles Fith a current i2 until
it has
~jscharged to the critical charfe -Qc' As it continues into regime
(i) Hnere it discharf.'es vlit~1. current il ' the "'-lindow" hep:ins to close
and finally it char~es to +Qc by passing through re[?ime (f).
The drop is
t!len saturated and incapable of collecting more pa-rticles.
It has acquired
a sufficient positive char~e to insure that there are no lines of electric
field intensity directed inward on its surface.
Note that the saturation
char~e 0 is familiar from field charging theory for conventional precip-
- 'c
itators (see, for exaF
-------
40
example, a drop havin~ an initial charge sufficiently positive to place
it in regime (d) will dischar~e
until it reaches an equilibrium somewhere
in
regimes (h) or (.Q,).
If the degree of particle cilarging is symmetric,
then the equilibrium charge will be zero.
That the net electrical current
vanishes as the particle reaches this final state of zero charge does not
mean that the rarticlc current approaches zero; on the contrary, the individ.
ual particle currents from each family of particles remain finite, and the
drop continues to collect particles after it reaches its equilibrium charge.
This state of zero charge collection is one ~ossible basis for Class IV
interactions.
Positivt particles inpact the drory over half of its surface,
while neeative ones impact over the other half.
If the Darticle charging
is symmetric, the net current is zero, and 11ence the cIrop remains in fI. state
of zero net charq;c, even though it continues to collect particles.
One of the main values of the TJhi~rle ano Chalmers analysis is that
it places the role of gas convection
in uerspective.
The theorv is based
on the assuTIption t11at a high Reynolds number laminar flO\J exists around
the drop.
But, because particle conduction to the drop at the interface
is controlled only by the electric field there, the details of the gas
flow have little to do with the collection Drocess.
Only the switching fro~
one collection rep:ime to another is determinec.: by the flov, and that is a
matter of the relative values of bE , the particle velocity relative to the
a .
gas, and "'0 far from the drop.
\.Jith the o!Jjective of re fininv the theory for the collection of
extreI:lely small particles, Zebel [2] has extended the \ITiliPDle and Chalmers
analysis to include a diffusion Lound.qry layer around the draT).
nis analv-
sis arrears to be of value mainly because of the li~ht it sheds on the
nTocesscs by which the particles are actually collected.
'I'he addition of
-------
41
oiffusion to the model allows a prediction of the diffusion boundarv
layer thickness.
But for relatively strong electric forces, the \\Thipple
and Chalrrers picture adeauately predicts the collection rate.
~I)~T us inr
ions, "ott
[23] hIS verified the "hippIe and Chalmers model
of electrical charginp.
hracmer and Johnstone [25] consider the interactions
beth/cen a charp:ed aerosol and a sinple charged or potential-constrained
spherical particle.
T:lei r ~'Tork a180 relates largel~T to an inertialess rep-
resentation of the particle collisions l7ith the spherical collector, but it
includes some numerical re,resentations of the effects of particle inertia.
n,ey 'Tlake the COIT\TT1cnt that, in p-eneral, the effects of inertial i!!!pact and
other Jistin~uishable collection ~echanisms can b2 represented by super-
imposiTl?: collpction efficiencies cOMputed for t'1e T'1echanisms considered
separately.
TI-tis is
an especi;'\lly pood approach if one of the mechanisms
is dominant.
In tlte ove:rvic"T taKen :lere, that vieioJpoint is implicitly taken.
~'J2 ignore
tile c.f'fec.ts of ir,ertir,
and cOI!l?are the electrical collection pro-
cess 'vi ti-, that
c.s.u;.;ed b:r
inertia :1c.tinr in t:le atsence of an electrical
aur,mentation.
Kraemer anG Johnstone a180 consider effects of narticle space charge
on tIle collection process. tut do not include an aI"uient field.
One of
t;,cir inter.qction J'lcchanisrls
w;:ic~ involves the ~utual attraction of
c:larf':ed drop and rarticle c-'1arges of opposite sip:n is identical to the
Class III wc'.ch;:misf'l and malleI.
The "-4~" collection efficiency is con-
sistent ,lith \11ii'ple and Chalmers in the limit of no aIT'hient E.
Eence,
their exreri~ental observations on the collection efficiency of dioctyl
nhtitalate acrosol particles on a sp;lcrical collector are in a?:reement Hith
that mocel, and :~ence lend sunuort to its use.
Their spherical collector,
-------
42
which played the role of the drop and was fixed to a
stinp.er in the
flowing gas, was metal and in the diameter range 1/4 - 7/16 inch.
Complications of self-consistent field and particle charge are addressed
in the theoretical work of Smirnov and Deryagin [26].
These complications.
also included in the theoretical work of Kraemer and Johnstone, represent a
refinement beyond our present needs.
Yue effects of finite particle size
and inertia are brought into the picture in various numerical studies
[27,28,29] aimed at understanding cloud drop-droplet interactions.
Again,
these meteorologically motivated studies are relevant, but bring in cornpli-
cations not of immediate interest here.
Eo
Charged Dro~evices Described in the Literature
Hanson [30,31] and !~rks [32,33] sup,gest 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 of dirty gas.
In either case, their
self-fields are responsible for the collection of the drops and/or particles
on con due ting ~!al15.
The use of space charge to replace one of the elec-
trodes in a conventional nrecipit~tor is an application of charged drop
technology that uses the conventional collection Mechanism.
The objective
is a simplification of systems, or perhaps an improvement in capacity to
handle low-conductivity particles [34].
However, the space-charge type of
drop devices is of interest here, because whether designed to do ~ or not,
it does have the inherent possibility of giving an electrically augmented
collection of particles by the drops.
Marks describes devices in which the entering particles are not in-
tentionally char~ed.
The mechanism hy which they are collected by the
drops before the drops are space-charge-precipitated is not specified.
-------
43
AS pointed out in
9II.C, one possible mechanism is a Class II type of scrub-
bing interaction, "ith the drons moving under the influence of the space-
charge field and collecting particles by inertial impact.
Such a mec!lanism
of collection is possible in the devices described by Hanson as well, althou~h
there the particles have the same si~n of char~e as the drops, hence the
coulombe contribution to the particle-drop interaction tends to obstruct
collection.
Eyraud [35,36] describes t~le use of charged drops for collectinp !';ub-
micron biological narticles.
Lis interaction is one in \.;rhich the drops are
introduced and charged in the imffediate vicinity of a corona wire.
The
arrangement is othe~Tise similar to that of a single-stage tube-type pre-
cipitator.
Again, tile interaction mechanism is not specified.
The author
cites the ease wj tn ~vhich the
drops are re~oved by the precipitator, but
alludes only to the mechanism by whicil the drops pick up the particles (before
being themselves removed) with the staterrent: "Furthermore, each drop plays
the role of a high-voltage electrode for a very limited region of the gas
to be cleaned".
TIlis i~plies the interaction i~ of Class III ty?e.
HOH-
ever, 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 l)y their charging and the imposed electric
field can lead to a Class II type of induced inertial impact scrubbing.
There seems to be remarkably little work reported in the formal litera-
ture
, . ,
Wi11 CD
can serve as a guide to making "efficient use of drops in collecting
particles.
The patent literature of 9 II. C is a considerably better indication
of "That has been accomplislled in this area than is tile formal literature.
Even though considerable progress has been made toward understanding the basic
-------
44
particle-drop iateraction (see 9 II.d), the relAtionship
of these pro-
cesses to practical systems such as those disclosed in the patent litera-
ture is undeveloped.
In many respects, the particle-dro~ interaction
can be regarded as a type of agglomeration akin to that studied recentlv
[37] ~etween large and small solid particles.
To discuss properly the feasibiliv of usin~ drops to collect particu-
late, attention TTlUSt be paie to the charging dynamics itself.
Because the
volume of water introduced is critical to the success of such methods,
complete utilization of the collecting capabilities of the drop is highly
desirable.
These syste~s aspects of usinr charged drons are discussed in
the next section.
:~esults from tile work [25] 'tlidl electricallv-induced
agglomeration between solids will be directly applicable to t~e Class III
interactions and arplicable with some mDdification to tne Class IV inter~
actions.
-------
t
,
. (d) ~(e) y*
, IQcl
t
0
I
I
l .+
1-
t 1
L .+
T 0
1
. (!~) (h) (i)
.
(:1)
Q
t~
_1- (j)
.+
~,
1- 'IX
- lOci
45
(b)
13
(1:)
--.....".--
~"-
particles enter z ~ + 00
(c)
~
.+
1-
2
--....F
narticles enter
z ~ - 00
Fir. rI-() ro~, i ti ve p;;p-ticlc cban'in7 di apr;=tm. Charpinp repimes ctepicteci in
t:1C :>1i1nc of dro1> cbar(7e 11 And mobilitv-field }Jroduct. Pith increasinr
fluid vclncit", the vertical line of rlCT"3rcAtion indicated bv ~l JT10VCS
'0 t',1e riaht. InitiAL chArgcs. indicAted b'I 0, follmv the tra~ectories
:<10',:n un til t;lev rcach a final vrllue pi ven u'1 X. T f there is ~o
::\ilYpin<>. the' findl dnd initiCll clli1rrcs are identical, and are indicater.
, , g. T:\e inserted cliarraT'ls show' the force lines v :t bE.
-------
i:
- i~ 1
i
1 - 10 I
I C
.}..,--
(j) (k) (1)
~ Q9 ~~
(a)
~/
. --7"-~---'
(d)
(g)
\"
.......,,-
rarticles enter at
z-+_oo
./'---
46
(b)
"t
w
(h)
Q
(c)
~
i
2
(f)
IQcl
r
~=J;:'t~bE
) , 0
o
-
(i)
particles
......,..-
enter at z -+ + 00
w~
is moved to the left.
T;'i~. 11-7 :kr-ative particle charf'inr- dia~rajT1. :1ro]1 charpe vs TJ1obilH:v~
field product. Conventions are as in the previous fi2ure. Wi~1
increasin~ fluid velocity, the line of demarcation indicated by
-------
o
(a)
/
(c)
/ (d)
t 0.- i
lficl 1.
2 2 2
(e) (0 (g) (h)
> > 0
. .+ .+ + . 1+ < I 0 <
1.1 + 1.1 1.1 1.2 . 1
. 1- -. Q,
.+ -
1. + i
i 1 1
2 -~-
Q - - - -- ---'- - ..- -- -
. 1 0
-1 (j) (k) -I 1) ~
---J
Q1
+ i+ .. Q2 - -- -
i i+ + i
1 1 .+
1.
1 2 1 .+ .-
I+~ I ; Q > 0 1. + 1.
- 1 < In I 1 1
> 0 > ()
C 2
(m) -IQ ! (0) .+
.+ i+ i+
1.2 c 1.2
2 2
.. . .
w
o
w
o
Fig. II-8
/' I
Drop-charge-imposeci field trajecto'ries for impact charp-inp in
comhinedf1.ux of positive and ne~ative particles
-------
48
III.
Simp~~!~?els for Classes of Drop-Particle Interaction
Before an assessment can be made of the relative merits of a scheme
using electric fields and drops, the scaling of the interaction to a prac-
tical system must be delineated.
It is the purpose of this section to
hir,;hlight the dependence of the various collection mechanisms on systems
design factors.
In the suhsections to follow, only preliminary estimates
are made.
Obviously, anv one of the device classes could involve many pages
of theoretical development and still give only a theory capable of defining
trends and orders of magnitud~.
Our major effort is given to syste~E fac-
tors with Class III interactions, since they appear to hold the most promise
for a new approach.
A.
Class I: Inertial Impact Scrubbinp-
Heber [3] gives a comDrel-tensive reviev of pet scru~)bers.
The scrub-
bing can be i:nplemented by a numJcr
of different mechanis~s.
He cIa ssifies
the processes by waich drors and particles combine as
a)
b)
Direct inertial i~pact collision
Condensation
c)
d)
Diffusion througil a :lour.dar'T laver
Sedimentation effects
If a condensation mechanis~ is used, particles can be first charged and then
serve as nuclei for the drops, or the drons can be first condensed on par-
ticles and then charged.
Then the drops can be orecipitated by using an
electric field.
In either case, the resulting device is a condensation
type scrubber in series with a conventional precipitator.
Any virtues of
the system must be argued by comparing the condensation scrubber to conven-
tional scrubbers.
Devices which use tile condensation mechanism are not
regarded as uniquely involving the drops and fields to provide a collection
-------
49
mechar,ism.
Heber indicates that, within the context of scrubbers, little
is kno\Vll about the condensation type of devices and there is little to sug-
gest that they are co~petitive.
Of the other mechanisms listed, the dominant is usually impact
scrubbing.
As a particle entrained in the ~as approaches a drop with
the relative velocity w , it undergoes an acceleration in trying to follow
the gas streamline.
The resulting inertial force can overcome the viscous
drag and cause collision with the drop.
The impaction parameter K defined
with Eq. (11.1) determines the effective cross section of the drop for col-
lision.
In representing the systems aspect of scrubbers. Calvert [38]
uses the empirical formula
v* 2
~-)
R
1
O~7r
K
-
? 0 a2w
- a
- ----
') R]J
c
(1)
( 1 +
\vhere y* is the radius of the effective co] lection cross section.
If
particles are subwicronic, Vc is the air viscosity diminished oy the
Cunninghanl .,:actor.
The drop is introduced into the flow, perhaps by an
atomizac~on process, and is effective as a collector only 80 long as it
has a rel£tive velocity with respect to the gas.
Because relative motion
is damped ou t b~l the gas. there is a limi tec1 dis tance over ~.,hich the drops
are effective and that distance is a function of the drop size.
A simpli-
fied ve:sion of the systems analysis !:dven by Calvert [ 8] is given here
1;;Titl1 thE: obiective of identifying the essential parameter values.
Host suspect in our simple model is the use of Stokes' dra~ for the
drops, since in many scrubbers the relative velocity can be large.
But,
vith the understanding that the predictions are restricted, the drops
-------
50
initiated into the flow with a relative velocity w obey the equation of
motion
4 3 d,v
3" 'IT~ PR dt + 6'ITjJRw
=
o
(2)
Thus, the relative velocity decays with a time constant
T =
i
2 R2
PR-"
91.1
(3)
and ,ve can think of that time constant as the effective lifetime for particle
collection of the drop.
Tae distance traveled hy the drop relative to the gas durinr. the life-
time given by Eq. (3)
is WT., and hence we can use Eq. (1) to .,rite
].
the volume of the gas "cutout" by tl.e drop, and hence cleaned of particles
as
'lTR2
(1 + G,/Y
4 R3 .
By identifvin? the mass of tile drop, "3 'IT PR' ~n Eq. (4), and dividing it
volume of gas cleaned/drop =
') P2
,-Pp, '
9jJ
w
(4)
out, we obtain an expression for the volume of gas cleaned per unit mass
of ~ater required.
Rw
2
61-1 (1 + a ~7 )
Again, with the understanding that the domain of validity of our model is
Vol. cleaned
--------
mass of Hater
1
(5 )
limited, we can recognize from Eq. (5) that there is an optimum value of
l{
opt
R. given by
2
20 a w
a
----
6.3 1.1
c
(6)
t:,e drop radius,
and if that optirrum values is used, then Eq. (5) becomes
Vol cleaned m3
mass of water kg
=
2 2
W P a
a
--
75 1.1jJ
c
(7)
-------
51
In obtdining Eq. (4), we have ignored the continuous change in relative
velocity by approximating the drop motion 28 being constant throughout a
fini te 'lif,~ ti~e" .
Calvert's more refined development leads to an expres-
sion \vhich is essentially consistent with Eq. (5), provided the device
efficiency is lmv.
l'1ote that the perforTPance of the scrubber, according to the model
developed he~e, does not depend on the particulate loading of the gas.
The volume of gas cleaned per unit mass of water used in no way reflects
the amount of particulate removed.
By contrast, the Class III type of
interactions are characterized in terms of a mass of narticulate removed
per unit volume of water used.
The dramatic dependence of the scrubber
efficiency on drop relative velocity (usually on the order of gas velocity
relative to duct) wand, more imrortant, on particle size, a, is illustrated
by exrressing Eq. (7) as
vol. c12aned - ft3
--------
v,reigilt of Hater - lbs.
=
-2
4.95 x 10
w2a2 [1 + 0.086 ] {a in micron9j.
a w ft/sec.
(8)
Typical values of the volume of air cleaned per unit water used are shmro
in Table III-I
Table III-I
--.--
Volume of Air Cleaned per Unit Weight of Water
in ft3/lb., for Various Particle Radii and Drop
Relative Velocities
<$>
0<.
0.....
..-[t/sec~l~-~~-
1 9.2 x 10-4
0.5
1
5
--------
----------~
X 10-2
5.37 x 10-2
5.37
1.26
126
10
9.2 x 10-2
1.45
1..45
145
537
12,600
100
9.2
-------
52
If the drops' relative velocity does not tend to <,..ro~ then what
limits the amount of gas that can be cleaned by a single drop?
The anS1>Jer
to this question comes from practical limitations on potential differences
that can be used to pull the drop through the gas,
To achieve a ~iven E
within the t!as volume, the voltage must be raised in proDortion to the dis-
tance between electrodes.
Operating voltages ~re limited, probably to
the range of 100 kv (in view of the 'vet environment of the electrodes).
Hence, the electrode spacing is taken here as a limit on the effective path
length of the drops as they pass through the gas.
Thus, instead of Eq. (4),
the gas volume cleaned bv a sin~le drop is the collision cross section mul-
tiplied by the path length,
9-.
Usini< EQ. (1),
vol. cleaned
drop
=
TI(y*)2~ =
TIR 29.
(l+O~:r
(10)
Here, the ir.lpact parameter Ke is based on the electricallv induced drop
velocity given bv Eq. (9):
TF
f\.
e
2
9
r a2 QE
a
RZlJ 6TIlJ
c
(ll)
By dividing (10) ty t~e draD ~ass, ~1e obtain the volume of air cleaned
Der unit mass of water required:
vol. cleaned
mass of water
4p!"R
3 11,
( 1 + -~~ 7 r
(12)
To determine if the electrically augmented scrubbing should be
given
practical consideration, first consider the electrical impact parameters
that can be achieved in practice.
li!hether created hy corona d1arginf. oc r?
influence chaq!.in~, the drop chaq~e is likelv to be on the order of
(I
=
2 'I,
12 TIS !-~. E
o
eU ~
-------
53
using a :elati'le velocity ,oJ =
100 ft/sec., a plant operating at 105 cfm
would require (105/9.2) ~ 104 lb/min. of water to clean O.l-micron particles
and 105/12,600
~ 8 lb/t"'in. of v1ater to clean 5-micron particles.
B.Class II:
Electrically Augmen!~~I~ct Scrubbing
In this class of device, the particles are not charged.
Drops are
given charge, Q, and there is an ambient field, E.
Under the assumption
that dipole moments induced in the particles by the imposed electric field
do not produce a significant interaction with the nonuniform electric
field from the drops, the collection ~echanism is mechanical and is the
same as for the conventional scrubber.
The difference is that the drops
are charged and made to move relative to the ?,as by an electrical force.
As point~d out in J II.E, space-charge fields can also be used to provide
the ambient field.
Vor present considerations, it will be assumed, though,
that E is caused by a voltage, V, applied to external electrodes having
the spacing
Q. .
It does not appear that scaling laY's will differ appre-
ciably if L is developed cv sp~ce charge.
In tne conventional scrubber, there is a limitation on the useful
life of a drop bec~use of the finite penetration distance.
Drops injected
at
a velocity differing from that of the ~as tend to the gas velocity.
In the electricallv augmented device. each drop has a charge 0 which,
because the particles are not chareed and the other drops have the same
charge J can be regarded as constant.
In an electric field E, the drop
experien~es a constant driving force QE, hence tends tmvard a constant
velocitv relative to the gas.
Under the assumption that the QE force is
equilibrated in the steady state bv Stokes' drag, ue have the drift velocity
,,1
QE
6 1T)lF
(9)
-------
54
where E* is a charging fields.
If we take both the i~posed field and the
charging field as being E = E* = 5 x 105 vIm, then Eq. (11)
K
e
=
becomes
4
9
p a 2£ E*E
a 0
~ ~
c
=
2.46 a2[1 + 0.086 ] (a - micron) .
a
(14)
Typical values of the electrical impact parameter are given in Table 111-2
as a function of particle radius.
:~ote that K does not depend on R.
e
Hence, according to Eq. (12), the
cleaning efficiency is inversely proportional to the drop size, R.
Of
course, there is a lower limit on useful drop sizes imposed by the require-
ment that the drops be reIDoved from the gas volume before leaving the device.
For example, suppose that tae drops are iniected across the flow.
They must
traverse the distance ~ between electrodes before being carried by the gas
out of the field rep.ion.
This reauirement is si~ilar to that for particle
collection in a conventional electrostatic precipitator, and places a 10T/7er
limit on 2.. in ttle range of one micron.
Table III-2
Electrical 1npact Parameter K as Function of Particle
kadius. Charp.ing and 1mposedeFields are AssuIDed to be
5 kv/crn.
a- micron
-----
0.1
0.5
1
5
10
K
e
0.046
0.722
2.68
61.5
246
A typical device, using an electrode voltage of 100 kv and an ambient
Evaluation of Eq. (12)
E =
5 lev/em, has electrode spacing
~
0.2 m.
-------
55
t:,c-n .~i\Jes
gas v~. __clea!l~d
Hater ueight
ft3 =
lb
-3
2.4 x 10
R (1 + ~~7)2
(R in meters)
(15)
Typical values from this expression are tabulated in Table 111-3, where use
is "f1ade of K
e
from Table 111-2.
Table 1II-3
----
Gas Volume Cleaned per Water Weight Required in ft3/1b
as Functions of Particle Radius a and Drop Radius R
--- - - ..~~,
.---.~ ..",--.,~._~-~- ..~-
. -'" .L_~' ~--. ---- -"_.- -".r. --.
R
meters 0.1
10-6 9.1
10-5 0.91
10-" 0.091
0.5
1
5
--------
----
62
150
6.2
15
24
-------
56
C.
Class III:
Oppositely Char~ed Drops and Particles with No Ambient E
In terms of the Whipple and Chalmers model of
sII.D, the Class III inter-
actions involve particle collection with bE =
o
0, and hence Q =
c
0; therefore,
interactions fall in domains (j), (k) and (i) of Fip. 11-6.
The drops are
formed and charged in one volume, while the particles are oppositely charged
in another.
As depicted schematically by Fig. II-I, the drops and particles
are then mixed in a separate interaction region.
Note that am ambient field
is probably used to charge both the drops and the particles.
But, in the
much larger interaction region, the ambient field is negligible.
Also, there
can be more than one family of Darticles and of drops.
For example, both
positive and negative particles can be used.
In the following, we consider
only one family of particles and one of drops.
Our objective is to obtain
relationships het'hTeen the efficienc~r of 1:"emoving narticles and residence
time, ~iven syste~s parameters such as drop and particle size, 'vater volume
loading, etc.
Yne theoretical model used here is similar to one developed for the
agglomeration betFeen laqre and sT"'all solid narticles [37].
It is aimed at
determining the residence time, T, required to remove a given fraction of
particulate.
As the drons and particles interact, there is a simultaneous
decay of tile number
densitv, n,
of tile fine particles and of the charge
per drop, 0.
Design of a syste:n for makinz best use of the charged drops
requires that account be taken of the play-off bet~veen a short resilience
time and the requirement for large anounts of Hater.
In fact, a certain
J:1.inimum loading of ~'.Tater is required if an arbitrary fraction of particles
is to be reT"'oved in a single-sta~c device, because the collected ?articles
neutralize the drofJs, and :Icnce nullify the collection mechanism.
Ey
contrast '-lit)) the Class I and II interactions, the. scalinp laws now depend
on the fJarticle loading.
-------
57
Consider the collection process from a frame of reference moving with
the drops.
Because the ambient electric field is negli~ible, we can assume
that the relative velocity w betHeen drops and gas is negligible, and hence
that the residence tiwe of the drops is equivalent to the effective length
of the device divided by the !;>:as velocity.
In re~imes (j), (k) and (£) of Fig. 11-6, the electrical current to
the droD caused by the particle collection is simply
i
2
- nqbE(47fR2)
=
dQ
dt
(16)
,,,here b is the particle mobili tv and () and q are both positive.
Moreover,
the electric field, E, at the surface of the drop is merely that due to
its own charge, and llence Eq. (16) becomes
dO
dt
=
- nobQ
£0
(17)
In this expression, the rleDendent variables are (Q,n).
To obtain a second expression for the decav of the Darticle density
net), ooserve that in a unit volume there are N drops, each collecting one
particle for each charge q collected.
Eence, the rate of decrease of the
Darticle density is simply l'~/n multivlied times i2 from Eq. (16).
Thus,
the particle density equation is
dn
dt
- nbQN
E
a
(18)
L..'1ese last tuo coupled e~uations determine the decay of the charge and
particle densitv. and hence the residence time required to achieve a given
efficiency.
lor design Durposes, it is
convenient to define the following para-
meters:
-------
58
I;; - [Q(O)N 1]
q n(O)
E
T* = 0
bq n (0)
E
Td 0
- bQ(O)N
Collection capacity
(19)
Particle relaxation time
(20)
Drop relaxation time
(21)
where Q(O) and n(O) denote the initial drop charge and particle density.
1~en, in terms of these parameters, solutions to Eqs. (17) and (18) are:
n 1 (1 + 1:.) ~t/T* -1
-- = [- - + e]
n(O) I;; I;;
_L ?;t/T* 1 1 ~t/T*-l
Q(O) e [- - + (1 + --) e ]
S I;;
Also, it follo\'1s from LqS. (17) and (18) that
1 on -.l dQ
fit --
dt rr dt
so that Q and 11 are simply related by
net) (s + 1) Q(t) - l;
n(O) 0(0)
(22)
(23)
(24)
(25)
If
I;; = 0, then nand 0 decay nronortionately.
If l; < 0, then Q decays to
zero before the particle density is reduced to zero, and the system of drops
doe3 not have the capacity to collect all of the particles.
By contrast, if
I;; >
0, then all of the particles can be collected before the drop charge
decays to zero, and there is more th~n sufficent capacity to collect all of
the particles in a sin~le stage.
The only excuse for making I;; > 0 is to
achieve a given efficiency ,,7ith a shorter residence time.
If we define the efficiency of sin~le-stage particle removal as
Eff
=
n(D) - n
n(O)
(26)
then it follows from Eq. (22) that the residence time T required for
-------
1
b
,~
t
"r
-
1'~
.3
2-
o
-1
Pig. III-l
Residence time, T, rcauired to achieve particle removal
efficiences of 90r and 95% as a function of collecting capacity parameter.
- . _u_---+.
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
V1
I..:>
o
J.
:3
~~5
/0
7
4
{;,
2>
9
z.
-------
60
achieving that efficiency is
T -
T* -
.!..,Q,n [(1 - l;; Eff)
r,; L r,; + 1
+ 1 ]
(27)
TIle residence time has been normalized to the particle relaxation time T*
and is plotted as a function of the collection capacity r,; for two efficiencies
in Fig. III-I.
To make use of Eq. (27) or Fig. III-I, soecify the required
efficiency of particle removal and the loadinp. capacity
l;;. Then, the re-
quired residence time is given in units of T*.
Particle charge and mobility in the submicron ranp.e are typified by
values given in Table 111-4. vnere a charging fielrl of 3.6 kv/cm is used.
If He specify the particl~ mass loading, m, in grains/ft3 (here the particles
are assumed to be spherical and to have the ~ass density of ~ater), and the
particle radius is given in microns, then the particle density is
n Uifm3)
=
11 m
5.46 x 10 ::3
a
3
(grains/ft )
(microns)
(28)
Table III-4
- ---------
Submicron [article Char~e and ~fubi1ity and m* (Particles
Charged in a Corona Discharp.e ~ith Field E = 3.6 kv/cm;
see ~ihite [9), 146-147.)
a-~ q b m*
(coulombI';) (~2 /v see) (grain/ft3)
0.1 1.3 x 10-18 1 x 10-7 0.125
0.2 4.0 x 10-18 1.1 X 10-7 0.295
0.3 9.5 x 10-18 1.3x10-7 0.354
0.4 1.7 x 10-17 1.6 X 10-7 0.381
0.5 2.6 x 10-17 1. 9 X 10-7 0.41
0.6 3.7 x 10-17 2.2 x 10-7 0.43
-------
61
Ta-b1e 1II-5
M* as a !unction of Drop and Particle Radius;
mobilities are those of Table 111-4.
R-m a = 0.1 a = 0.3 a = 0.6
10 6 1.39 x 1~=:G~7 x 10-" 6.3 x 10-5
10-5 1.39 x 10-3 1.07 x 10-3 6.3 x 10-"
10-" 1. 39 x 10-2 i 1.07 x 10-2 6.3 x 10-3
I I
10-3 1. 39 x 10.-1 1. 07 x 10-1 I 6.3 x 10-2
I
It follows from Eq. (2')) tbat
m* E: a3
T* m* 0 (29)
~. 10 1 1)
, bq(5.46 x
TI
Values of m*
are 12;i ven in
Table 111-4 for the 0.1 - 0.6 micron radius range
of ~articles (re~emter, charged in a 3.6 kv/cm field).
1Ll us, wi th a mas s
loading of one ~rain/ft3 of one micron diameter particlee (a = 0.5), the
particle relaxation time is
~iven
fro11' Zq.
(29) Hith m~': from Table III-4
as 0.41 seconds.
The drop relaxation time is similarly written in terms of engineering
quantities, by assu~in~ t~at the drops are caarged in a chargin~ field E*
to the value
(\
=
12 TIE p.2 E*
o
(30)
T:1i3 v}ould [)e the case if t;il2 drops Here charged to saturation in a corona
field.
Also, essentially the same type of relationship between applied
field and charge would exist with induction charging of the drops.
The
only difference ,wuld be in a geometric constant, which can be thought of
;lere as absor;Jed into the effective ch.?ndng field.
for purposes of
-------
62
establishing the magnitudes of typical quantities, consider a charging
field of 5 x 105 vim.
Then, if ~,! is the drop mass loading in lb/ft3 , we
can \.Tri te Eq.
(21) as
Td
11* .
M .
H*
R
(7.2 x 104)b
(lb/ft3). ( R in meters)
(31)
Values of H* are tabulated in Table 1II-5, \l7here the particle mobilities
have been used from Table 111-4.
Hate that the collecting capacity is
s =
T*
[-
Td
- 1]
1-1 m*
= (li*) (m)
- 1
(32)
For very small particle loadings, such that s
»
1, the drop relaxa-
tion time typifies the residence time.
TIlis can be seen by taking the limit
of Eqs. (27) and (32) \7here ?;; » 1 .?;; -+ T*/T
T
T-
Ii
1
9,n [ 1 - Eff ]
(33)
The tabulated results give a picture of the critical cesign parameters for
a wide range of svstems para~etcrs.
To illustrate how they can be used,
consider the removal of particle~ characterized by:
particle loading
=
0.1 grains/ft 3
2a
=
0.2 micron
chargin? field
=
3.6
l~ v / cm
FroT'! Table 111-4, it follmvs that m)'~
0.124 grains/ft3.
Pence, using
EC]. (29),
T)'~ =
m*
m
0.124
0.1
1. 24 seconds
(34)
To achieve 95% efficiencv with a residence time of 2.5 seconds, Fig. 111-4
T.-lith T/T* ~
2 shows that
-------
63
c;; =
1.25
(35)
It follows from Eq. (32) that
M
ij*
=
1.82
(36)
From Table 111-5, the water mass loading required is then
1'1
2.5 x 10-~ lb/ft3 for R = 10-6 m
H
=
2.5 x 10-3 lb/ft3 for R = 10-5 m
(37)
This means that, in a plant havinr: a flow rate of 105 cfm, 25 lb/min. of
water
injected in the form of 2-~-diameter drops would be required.
As a rule of thumb in determining effects of collecting capacity, the
charging is proportional to radius, and under the assumption that both
particle and drop charging is accomrlished in fields of the same typical
intensity, tre have Q/q a ~2/a2 . Also, N/n a
a~/~
and hence we can,
under these assumptions, write the loadin~ capacity as
c;;
[QN - 1] =
an
a3
a R3 a
[ RaT ~3 - 1]
v
[~ E.. - 1 1
V R '
a
(38)
,~here VR and Va are the volu~e loadin~ of drops and particles, respectively.
That is, in order to achieve a loading capacity 1:; = 0, the volume ratio of
t,:ater to particles must be eaual to the ratio of the drop radii to the
particle radii.
To achieve an arbitrary efficiency in a single stage, we
fTJust have
c;; > O.
Thus, to obtain a large fractional removal of particles
of 0.1 micron radius using drops of 10 micron radius, the volume of water
~ust exceed that of the particulate bv a factor of approximately 100.
T"is is essential1v Fl-tat has been found ,vith Eq.
(37), since 2.5 x 10-3
10 I ft 3
17.5 -:rrains/ft3 of pater to clean 0.1 grains/ft3 of particles,
-------
64
and vle have taken particles and ,vater drops as having the same I'1ass densities
o
a
and PRo
As a further rule of thumb in determining residence timest Td is a char-
acteristic time if the collection capacity is higl1t and T* is a typical time
if it is in the ran~e 2 - 10
(see Fig. III-I).
D.
Class- n~:~bient Et }'~~ti_cles Charged and :;::'rops--.lEiti~l-L"pncharged
Tne interaction region for this class of devices is one in Hhich the
previously charged particles are mixed with uncharged drops under the in flu-
ence of an amtient electric field.
In terms of the drop charging diagrams
(summarized for positivct for negativet and for both positive and negative
particles by Figs. II-ot 11-7 and 11-8 rcs?ectivelY)t the drop starts out on
the horizontal <'txis t tvhere q =
o.
Because there is initially no net charge
on a drop.tte electric field does not give rise to a relative velocity Wt
and
hence the drop state is on the horizontal axis between either regions
(f) and (i) or (d) and (f) in "Figs. II-6 and II-7 t or in the case of par-
ticles c;lar~ed to th'O di fferent signs t betHeen repions (h) and CO or (e)
and (i) in Fig. 11-8.
The drop charflnr subsequent to mixing wit~ the narticles has many
possibilities t dCDendin? on ti.1e relative numbers of positive and nep.:ative
particles.
rrobably the ~ost practical and certainly the simplest is the
one in ~,!hich the numoer of particles charged positivelv iust eauals that
charged negatively.
Tilen the currents charginp: the dro1"'t depicted in T<'ig.
1I-8t and ~iven by E~s.
(A.29) and (A.2)t are:
.+
11
- i
1
3Tf,;2bnqE
(39)
Thus, the drop charge remains zero as it collects particles.
The number of
..!-
positively charged narticles collected per unit volume is (N/q)i'
1
and an
-------
65
equal number of negatively char~ed particles per unit volume are also col-
Thus, the particle density can be ~vritten as
lected by the drops.
dn
dt
n
TIV
(40)
~1ere the time constant for collection is
TIV
=
1
67TRLbNE
(41)
~~e solution to Eq. (4) is si~~ly
- t/TTV
n = n(O)e
(42)
and hence the efficiency of particle removal for a svstem having the resi-
dence time T can ~e written as
Eff =
1 - e
- TIT
IV
(43)
To determine the ccpendence of the time constant TIV on drop loading,
note that it can be written as
T
IV
21=\.P.?
"
---
9HbE
-5 R
2. 7 x 10 (rID)
R - meters
'1 - lb£ft3
b - m Idec-V
(44)
TYDical values of TIV are ~iven as functions of drop radius Rand lb/ft3
of ";atcr required for removal of tHO sizes of particles in Table 111-6.
~;ote that it is desirable to have as small a drop radius as possible.
Just
how small R can be made, practically, is a matter of the means used to re-
move the drops, once they have been used to collect the particles.
Because
conventional electrostatic nrecipitation techni~ues ~vould probably be used
to remove the dro"!'Js, a drop radius of one micron is a reasonable minimum.
-------
66
If one of the particle families doroinates the other, the collection
of particles on crops and removal of drops to the electrodes could be
combined.
Then, in the process of collecting particles, the drops would
become charged.
Because of the ambient electric field, there would result
a precipitating force tending to collect the drops on the electrodes.
Aho,
snace-charge fields could be used to precipitate the drops, once charged
by the particle collection.
But note that, as the drops pick up speed
relative to the gas, the relative velocity H in the charging diagrams
becomes finite.
In fact, if the char~ing field for the particles is on
the order of the ambient field in the interaction region, the drops have
mobilities larger than those of the p~rticles, bv a :actor R2/a2.
Hence,
the drops cannot reach the critical charge Q ,d thout firs t being limited
- c
by the expansion of the regime (e), in which the orop velocity relative
to the I?;as exceeds that of the particle.
Table 111-6
--_.,----
Collection TIV in Seconds for Class IV Interactions
~.Tith T)ipolar Particles: Ambient E = 5 x 105 vim:
Particle ',fobilities from Table IlI-4.
----~-
------------------
rl (lb 1ft 3)
R = l~ , a = 0.1 ~
R = 5 ~, a = 0.5 ~
-::~:---- -----1-.
-----------"-----,----- ------- ----
I
27.0
71.0
2.70
7.10
10-3
0.27
0.71
-------
67
E.
Class v:
Hybrid Interactions
In hybrid interactions, both the effects of a drop charge and of an
ambient field are significant.
The result is a combination of the Class III
and IV interactions.
Practical systems considerations motivate the use of
a hybrid interaction.
For example, once drops have exhausted their collection
capacity in a Class III interaction, it might be desirable to subject them to
an ambient field.
1Vith unipolar charging of the particles, they would then
recharge while continuin? to collect particles.
Also, they could then be
removed by means of toe imposed electric field.
One of our reasons for introducinp: the charging diagrams of Figs.
11-6-8 is to errphasize tne large number of ,vays in whic~1 a drop can attract
a current of charged particles.
~10 attempt Hill be made to give performance
equations for hybrid systems.
Partly, this is due to the diversity of pos-
sible combinations of field, drop charze, and relative dron velocity.
But
also, we can exnect that, oasicallv, no neH collection phenomena are brought
into Dlav.
-------
68
IV.
Production of Charged-E!oP~
A.
Classific~.!ion of Particle Prod_':!.ction Technique~
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 whicb
a liquid bulk is broken up into drops typically in stages by
first forming liquid sheets or jets or jets that reduce to
drops which in turn subdivide to the required size.
ii) Conden-
sation; a saturated phase is condensed on nuclei leadin~ 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 elf.(~tric Held
and an ion flux from a corona discharge is an example. ii) Charging
at birth.
Condensation on ions is a char~ing mecnanism 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 "splashinglT charg-
inp.; of Lenard and Zelen y is strictly in this category, \.dth the
charging taking place essentially by induction as drops encounter
a metallic or insulating surface.
In the following 9 Band C, we first comment on the alternative means
of mechanically forming drops.
TIlen, 9 D through ~ relate to the charging
techniq ues .
-------
69
Ihe formation of charged drops usually amounts to adding one of the
electrical charging methods to a conventional mechanical process.
Al though
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 thermodynamic.
In the case of influence
charging, no electrical energy is required in principle, and with corona
charging, the process is typically in a region removed from that where the
particles are formed. Hence, the electric field energy does not contribute
in an essential way to the energy supplied to the mechanical drop formation.
The electrohydrodynamic spraying technique for producin~ charged drops
is discussed in 9 G, and does make use of the electric field to form the
drops i::1 a mechanical sense.
Fluid DUMping, atomization, and charging are
accomplished in a single process.
That process can still be categorized
as indicated above.
The drops are formed by atomization and primarily
charged by induction, but the electric field is intimately involved with
both charging and atomization.
The main objective of the following discussion of dro~ production
techniques is to determine the feasibility of usin~ schemes outlined in the
previo~s sections.
Does the particle ?roduction prDblem make the use of
Ci<2lds aIld (lrOpS impractical?
However, the electrohydrodynamic spraying
cntroduces a broader issue.
Is there an electrically driven alternative
~o existing mechanical techniques for atomization?
Even if the drop charg-
Lng is superfluous, an alternative to the extremely inefficient devices
used for atomization would be highly significant.
Our
discussions therefore
beaL on what is known about the efficiency with which current-driven jets
proc:Jce drops.
-------
70
B.
Mechanical Atomization
A general review of conventional means for atomizing liquids into a
gas is given by Perry [38].
It is not appropriate to repeat his review here.
Relevant, however, are the observations that in conventional devices (whether
they make use of liquid ejected under pressure, of rotating members, or of
liquid and gas ejected under pressure), fundamentally the energy required to
form drops of radius R is simply that necessary to make new surface.
To make
a single drop, the energy required is
w
y
4TIR2y
(1)
where
Y is the surface tension.
TIluS, the energy required per unit vol\~e
of the water is
w
y
=
3y
R
2.16 x 10-3 joules
R m3H 0
2
(2)
where R is in meters.
In practice, dominant power losses result from making droDs at a finite
rate.
These are attributable to: i) residual kinetic energy resulting from
dynamic breakup as, for example, that caused by mixin~ with high velocity
air stream, (ii) viscous losses as the water passes from the bulk state to
a system of drops, and iii) ~ump-type losses associated with the production
of hydrodynamic head.
Of these, the Rreatest factor is the second.
In
making l~ drops, it has been estimated to be 105 to 107 times greater than
that theoretically needed to form the new surface in one case study [39].
Calculation of power requirements for atomization can at best be crude.
Atomization devices are diverse in design, and even the laboratory model
designed to simplify correlations with theory shows that practkal atomization
processes are extremely complex.
Perry states of the losses in atomization:
IIThey are generally incalculable, and the power requirement of an atomizing
system must be predicted from experience".
-------
71
Here, t\vO exam~le3 based on data for commercial sprayer nozzles are
used to estahlish order-of-magnitude estimates of energy requirements in
producing drops.
Perry [38] cites data for a hollow-cone pressure nozzle
producing drops with a median radius of 50 ~.
Drops are produced by a single
unit at 0.2 ~al/min using a pressure of 250 lb/in2.
Thus, the power require-
ment for the single unit is 20 watts.
If we assume a spray system comprised
of a plurality of such units, then the power requirement is 100 watts/(gal/min).
It is usual to give power requirements in watts/cfm of gas.
To this end,
recognize that the gal/min of vater required to process 1000 cfm of air using
M lb. H20/ft3 gas is
Gal-H20/min
1000 cfm
120 M
(3)
A typical water loading for drops in this 50~ radius range [see Eq. (37)] is:
:.1 ~
10-2 1b/£t3
or, from Eq. (3~ 1.2 (Gal/min)/lOOO cfm.
Note that relatively large drops have been used so as to be consistent with
the sprayer characteristics.
This rather large water requirement is the
penalty paid for using such large drops.
The power requirement is (1.2)(100)
120 watts/lOOO cfm.
Power requirements for tynical electrostatic precip-
itators are in the ran~e of 30 - 130 watts/1000 cfm (see Ref. [9], page 204).
~~ote that the conventional sprayer considered here produces a wide range of
drop sizes, hence is inherently wasteful of the given water supply.
Drop sizes an order of magnitude smaller than produced by the spray
nozzle just considered are most likely required.
A given mass of these is
certainly produced at considerably greater expense.
Pneumatic nozzles are
more adaptable than pressure types to drop sizes in the micron range.
An
-------
72
example is a sprayer producing 5~ median-radiusdrops [40].
(Sprayer Setup
#lA supplied by Spray Systems Co., 3201 Randolph Street, Bellwood, Illinois).
This device produces 0.5 ga1/hr of drops with the maior portion of the energy
supplied by compressed Ras; 50 psi at 1.13 standard cubic ft/min.
Estimated
power supplied bas(~d on an isothermal expansion of the air [38] is 7 x 104
]'ou1es/1b H O.
, 2
Again, using the case study for Class III devices, Eq. (37),
a typical water loading using R = 5~ is 10-3 lb
lb H 0/sec/1000 cfmo
2
Hence, the required power
H 0/ft3 gas, or 0.0166
2 .
'v
is (7xl04)(0.0166) =
1 kw/1000 cfm !
To accomplish this,
approximately 12 of the sprayeJ!." units
would be required per 1000 cfm of gas processed.
The t\VO examples r resented here only establish the relative significance
of the atomization problem.
Certainly, no suggestion is ~ade that the power
requirement in this l'f!;t example is so high as 1 kw/1000 cfm.
J ,Jr OM thing,
the sprayer systems considered ar,2 not designed for the scale of the vpplica-
tion.
More important, note that the particle loading of 0.1 !?rain/ft3
of
0.2 micron diameter particles is extremely large.
But it should be clear
that atomization of drops is a maior consideration in making the use of drops
as particle collectors feasiole.
In the Class III type of interaction, the
drops play the role of electrodes, and in a sense the capital investment in
an electrode system is offset by the operating cost of making the drops.
Means of atomizing liquid mechanically are extremely diverse.
Spinning
disks and cylinders are often used to induce breakup of the liquid bulk [11,46].
Most of these methods can be used with the charging methods discussed in 9 E
and F to produce charged drops.
In a sense, the hydrodynamic pumping is
supplied in part by the atomizer itself in such devices.
As with the pressure
and pneumatic type nozzles, hydrodynamic losses are the dominant power sink.
-------
73
'~ou,""e.nsation
Clouds-;l ve
an example of droplets formed by condensation of a super-
sat"1:ated vapor,
In fact, the water loading commonly found in clouds of
0.2 -, 1 'f/TT!3 approaches the 10-" Ib/ft3 found in the Class III interactions
~lS
viug efficient collection of O.l~ particles.
Scientifically, a distinction
is ,~~e. 1:et'l.]een the condensation from a vapor phase to a system of droplets,
Eccocdinf to wh=:ther nuclei such as ions or microscopic particles augment
the forme:, don (he terogeneous nucleation), or if the process requires a
ulc::::: veli high supersaturation hecause of the ,ab~ence of nuclei (homogeneous
nuclE &t:ic --d 0
In practice, and ~ost certainly in the environment of a drop
(:olL:t :I.cn ,:;ystem, the heterogeneous condensation is dominant.
Fletcher gives
:i S 'uil- iLrj ;:) I. the
theory involved (Ref. [41], Chapter 3) from a cloud physics
p,:):Lnt (,f v: ew.
;,er:; :c.re
two issues to bp. raised in counection with condensation as a
mEJ::n=t :~SL ; '-0'(
farTling drops.
First, simply as an alternative method for
makiuJ dLl,~', i:::: a condensation method attractive?
If ions are used as
nuel:'. i, ll:lei.e is the possibility of simultaneously providing for not only
the li!C':':'1arical formation, but the charging as well.
,~ ,,:c.2.Ci, i:hE cm1densation nuclei can be the particles to be precipitated.
Th""J, Ul'-:; 'UE'S don is broadened to the viability of a collection system, rather
th'1I! s :irq,-prod'Jcing mechanism.
A collection device might consist of two
s t:> 7<::3
1=: ~:-e first st.s.ge, particles are used as condensation sites.
In
the :3e'2~',-c.,
;:1:e d=-cp-entrained particles are electrically removed, much as
in a cGnvent~onal precipitator.
If the condensation sites are not charged
prior =J t~e drop formation, then charging can be achieved by means of a
corona d:,s Cl9.rge after the condensation is complete.
The device described
by Vic~irC: and classified in 9 III as "}!iscellaneous" is in this cate~ory.
-------
74
As pointed out, Vicard's type of device really does not reveal an
innovation in the use of the electric fields and drops.
The essence of the
process is in the condensation on the particles.
Once enveloped by water,
the particles are collected in a conventional manner, and the mechanism of
bringing particle and drop together is only indirectly related to the elec~
tric field. (Although there is a connection between the charge on nuclei and.
for example, critical condensation radii, particles can act as nuclei, whether
charged or not.)
There are at least two approaches to formin~ drops by condensation.
The first involves processing a major fraction of the stack gas by humidi-
fying (if necessary) and then cooling below the dew point.
The second makes
use of nozzles for the processing of a relatively small volume, perhaps of
steam available from a thermal cycle, with this volume of vapor-entrained
drops injected into the dirty gas [42].
A determination of the feasibility
of usin~ these methods, and particularly the latter, which appears to be the
more practical of the two approaches. requires a knov:ledge of the inciden.
of condensation as well as the growth dynamics, so that drop sizes can be
accounted for.
Condensing methods ~enerally co~e into their own for pro-
ducing extremely fine dro?s; O.l~
or less.
Here, we are interested in
relatively large drops, l~ or greater.
No attempt will be made here to
calculate the energy requirements of condensing methods of drop formation.
-------
75
D.
Limits on Electrical Charging
In all but the Class IV interactions, charged drops are required.
The two main chargin~ mechanisms are discussed in the followin~ two sections.
Both 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" [43], and is given in HKS units by
Q =
"Ray
STI / EyR 3
(4)
where y is the surface tension.
TIlis is one upper Lound on the drop charge
used in the Class II and III interactions.
For water, y =
-2
7.2 x 10 newt/m
and I:q. (4) is conveniently vrritten as
0/.
Qn (couloIT~s) = (2 x 10-S)R 2
~,ay
(5)
where R is in meters.
Similar electromechanical consider8tions place an upper limit on the
electric stress that can be applied to an unchar?ed dror in an initially
uniform electric field ~vithout producing rupture.
Here,
Class IV interactions
are of interes t.
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 [44]:
E
Tay
f£-v.
0.458 -Y- R 2
E
o
(6)
For water drops in air,
Eq. (3)
oecomes
LT (v/m)
av
4.12 X 10'+
IT
(7)
-------
76
Table IV-l
Rayleigh's Limiting Charge QRayt Taylor's Limiting
Electric Field Intensity ET and the Saturation
ay
Char~e as a Function of Drop Radius
R - m
o - coulombs
'Ray
E
Tay
Q at E* = 106 vim
c
---~--
------~--- --
10-6
2 x 10-11i
4.12 x 107
3.34 X 10-16
3.34 x 10-11'
3.34 x 10-12
10-5
6.32 X 10-13
1.3 x 107
10-1i
2 x 10-11
4.12 x 106
10-3
6.32 x 10-10
1. 3 X 106
3.34 X 10-)0
------
---- ----- --------
----------.- ---
In
9 III t for estimating drop charges t ~ve made use of the so turaLion.
charge on a dro!, charged in a field E*:
Q
c
12 TIE P.2E*
o
3.34 x 10-10R2E* {R - rr.eters }
E* - vim
(8)
=
Table IV-1 shows the dependence on drop radius of ~{ayleigh' s limiting charj!e,
of Taylor's limiting electric field intensitYt and the saturation charge
given by Eq. (8).
~~ote
first thatt even under the assumption of a charging
field E* twice as large as that use~ in typical calculations in ~ lIlt the
saturation charp.e is less than Rayleigh's li~it.
liencet there is some 1ee-
~vay on the drop charge that can be used insofar as ~ayleigh' s limit is con-
cerned.
Second, only for the extremely large drops are electric field in ten-
sities required to produce rupture of an uncharged drop within a range where
they mif!ht be encountered in a nractical device.
(The breakdown strength
of drv air betpeen uniform electrodes is about 3 x 106v/m.) Thus t under prac-
tical conditions, either in the Class III or IV interactions, there does not
appear to be any li-nit on the drop charginp: hrou7-ht about by the electrohy-
-------
77
drodynamic instability of the drop.
E.
Corona CharginJ~_; Charging in the Bulk
The conventionallv used theory of "field charging" [9] is a limiting
case of the ,fuipple and Chalmers [22] drop charging picture introduced in
9 II.~.
As a drop or particle passes through the region of a caron dis-
charge, it experiences simultaneously an ambient electric field and an ion
flux.
Hence, the role of the "particles" in the Hhipple and Chalmers
theory is played 0Y ions which typically have mobilities much greater than
those of the particles... on the order of 10-" m2/v-sec.
Hence, under
field conditions practical in a device, the ions move at hundreds of meters
per second, and the relative velocity of the gas can be neglected.
In the
charginr diagrams, thjs means that lo! -+ o.
As sho\--n bv the charr,i'1z, diag-rams of Figs. 11-6, drops or particles
enter ing with no chan~e Q are charged to a limiting "cri tiCR1 H or "satura-
tion" charge given by E'l. (8).
(TI1is charging process caused by particles
or drops collectin~ ions should be distinguished fro~ the one in which
drops collect particles.)
The charging equation for a drop or particle is
d(0/Q )
- c
dt
=
bn.ll.
1'1
4 £
o
, 2
1.1 - o/Q )
, c
(9)
where b. n., and o. are the ion ~obilitv particle density and the charge,
1 -1
respectively.
~hus, the chargin~ rate is governed by the time constant
4£ l'on. q . .
all
E,ecause this quantity does not depend on the nature of the drop
or ~article being chaq>:ed, \/e can conclude that it is typJfied bv charging
time constants in conventionally used corona chargers.
It is well known
that the char~ing time in a conventional precipitator can be made quite short
cor.rra red to typical residence times [9].
Because the well developed theories
-------
78
of particle and drop charging for conventional precipitators are equally
applicable here, further discussion of the corona chargin~ mechanism is
not required.
F.
Influ~nc~ Char.R!ng
A powerful mechanism for charging highlv conductinR drops is influ-
ence or induction charging.
By "highly conducting", ~,!e mean drops vlhich
have electrical relaxation times £0(2 + £!£o)!a short compared to typical
times involved in the drop formation.
As discussed in Appendix B, this
condition is easily met in the use of water, unless the formation time is
extremely short.
Influence, or induction, char~ing is characterized by the configuration
of Fig. IV-I.
~
T
V.
~
t-
1
" ~l--
/~J'- _I
. .....-----
Hater
stream
I - - charged - --
~O~ drops ~O~
1-- -.-r l;_-
I
. I
Or-
f, ,:
r ri-
+-r
I
I
I
I
'"
charging
electrode ring
Fig. IV-l
Induction charging of drops
--.'-----'----- -..
Dro~s are forMed in a nozzle so that they hreak ffivay either from the
conducting nozzle, or from a short jet, under the influence of ~n electric
-------
79
field.
This field is applied bv means of a char~in~ electrode having a
potential V
.. c
one electrode of a capacitor having an applied voltage Vc.
relative to that of the water; thus, as it forms, the drop is
~aximum charge
per drop, Q, is obtained by making the drop break away from the nozzle or
jet as it accrues the maximum charge.
Estimates of the charge/drop attempt to account for the geometry of
the ~vater interface as the drop breaks away.
As a rule of thumb, the charge
is on tae order of the cross-sectional area of the drop, TIR2 multiplied by
E E* where E* is a typical charging 2lectric field intensity.
a '
For example,
if at the instant of breal:ing loose, the drop can he represented as a
sphere on a con~uctln~ plane, then the charge is [45]:
Q
6.56 TIR2E E><
o
(10)
Here, E* is the uniform field irtensity in the absence of the drops, so
the field concentration around th~ drop is accounted for. ~ote that, ~thin
a factor of 2., t~lis expression for t~1e drop C~larfte caused by induction is
the same as elat
oi.ven by
Ea. (8) for corona c~arging.
3y contrast ,Titi1 61e corona method of charging, the induction charger
electrical
in principle, reauires no/~m;er input.
To see this, observe that over the
period of drop charging, the a~ount of energy required from the source V
c
is
Jv cO
c e
(ll)
uhere Q is the charge on the char!!ing electrodc.
e
Because V is constant,
c
the inte~ratjon of Eq.
(lJ) amounts to taking the diffcrence bet~.]een the Q's
e
at the end and beQinning the charr-ing cycle.
Because the drop charf!ing E
-------
80
periodic, the electrode charge at beginning and end of the cycle are the
same, and hence no electrical energy is supplied.
Even though the electrical energy required for the idealized charging
is zero, the losses connected with the influence charger are a major con-
sideration.
As discussed in
911, much of the patent literature pertains
to means for avoiding the fouling of the charging electrode by the drops.
From Fig. IV-I, it is clear that a charged drop will tend toward the charg-
ing electrode.
Invariably, the cbargin~ ring intercepts at least a fraction
of the drops and becowes the seat of electrical activity.
Drops re-emitted
from the charging electrode have a polarity opposite to that from the
nozzle.
In a scheme which depends on having only one sign of drops, this
is a nuisance.
Also, drops formed from the char~ing electrode by electro
hydrodynamic spraying consume power frow the source Vi' ~nd so the ring
capture brings into play electrical losses.
The powerful charging mechanis~ provided by influence charging makes
it an attractive basis for drop charring.
If the configuration can be
properly designed to avoid fouling of electrodes by drops and particles,
the power requirements for drop formation ~re essentially the same as
for a wet scrubber.
The drops are formed mechanically, and charged with
a negligible electrical loss.
In actual devices, it is not always clear whether the charging process
is mainly inductive, or involves corona char~ing caused by ions generated
in the vicinity of the orifice.
But the use of induction charging with
various configurations of atomizing devices is well established [11, 47,
48, 51].
There is little doubt but what the physical principles dominat-
ing this method of producing charged drops are well understood [49].
-------
81
Induction charging is responsible for what is sometimes called "Lenard"
charging [50] of drops, caused as they form from larger drops splashing on
a solid surface.
G.
E1ectrohydrodynamic Spra~nR-
Over the past several decades, with various applications in mind,
inventors have recognized the advantages of using an electric field to atom-
ize liquids [47, 48,63].
Although investigated qualitatively by a number
of researchers [52,53], it is only recently that work has begun to give a
rational description.
Motivation co~es not only from the hope for a more
efficient technique from the standpoint of power requirements, but,at least
for some applications, from the tendency of the drops to be highly charged.
Typical electrohvdrodynamic sprayers are shown in Fig. IV-I.
In (a),
liquid is forced through an orifice much as in an ordinary pressure nozzle,
while in (b) liquid is injected into a mixing region where it is entrained
in the fashion of a pneumatic nozzle.
In both cases, the drops form in the
region of an electric field, acting
either to charge the interface inductive
ly. or if fields are sufficient to produce local electrical breakdown, to
provide for corona charging through the action of an ion flux in the drop
formation region.
As thus far described, each of these devices is simply
a conventional nozzle fitted with a charger as described in previous sec-
tions.
However, in electrohydrodynamic spraying, the field has a radical
effect on the drop formation.
It is helpful to distinguish between two mechanisms by which the
electric stress can contribute to liquid atomization:
i)
The electric field contributes to the stability of the inter-
face.
Just as surface tension is responsible for the breakup
of a laminar jet into drops, the electric field can be the agent
-------
82
of increasing, or the sole
agent of causing, the instability o~:
an interfacial configuration.
Rayleigh's 1imi t on the charge that
can be placed on an isolated drop (see ~ D) is caused by the incip'-
ience of such an electromechanical instability.
o
/////a
. . ~
" A\"p ~orV'<'Ct.tl t:....
C\. V'~ '- ot' 0'''' ""-
~
Ck\r ~ \\ -
\ cl 7 ~ \.) ~:::---
.".. f:~:~_3'~
-r]
( 0..)
( ~
Figure IV-I
Nozzle type electrohydrodynamic
spray configurations
Even a flat interface will "buckle" under a sufficient electl~ic stress.
Typically, the electric field acts normal to the interface, as sketch~d in
Fig. IV-2.
A perturbance on the interface is accompanied by a local field
concentration and an accumulation of surface charge.
The result is Gl',ch
an increase in the local surface traction that the surface deflection is
further increased.
Liquid jets in a radial electric field not only exhijit
an enhanced rate of growth for sausage instabilities associated with t~~
surface tension, but are also unstable in kinking modes [60].
-------
83
ii)
If a mechanism is available to force a current flow through the
liquid, an interface can be subjected to a tangential electric
field as sketched in Fig. IV-3.
With the interface also charged,
there results an electrical shear stress on the interface which
is capable of accelerating and effectively pumping the fluid [61].
T;r/ Illil77!
Figure IV-2
Local interface subject to normal stress
tends to buckle and exhibit instability.
------
The destabilizing effect of (i) alone is enough to have an appreciable
effect on drop production.
However, under practically realizable electric
stresses at atmospheric pressure, the tendency of the field to produce
instability is not sufficient to create single-step processes that change
typical dimensions by orders of magnitude.
For example, even with the help
of a field perpendicular to its surface, under realizable conditions
a jet
breaks up under the action of surface tension into drops that are within an
order of magnitude in diameter of the jet.
Similarly. the direct consequences
-------
84
of instability attributable to normal stresses alone on drop breakup are
fission fragments within an order of magnitude of the same size.
1
J
r-
electric shear rorce
on in terrD.Ce
electric rield associated
with curreLt in licluid
Figure IV-3 Combination or current in liquid and surface
ch~rg~ results in electric shsQr force on inte]~~ce
To account for the drastic changes in size that can be obtained
using electric fields, proper credit must be given to the role played by
the electric shear stresses.
Consider how a detailed investigation has
shown the current-driven jets to produce first, a fine thread of liquid,
and then a spray of charged drops [62,10].
Consider the orifice shown in Fig. IV-4, with a potential difference
applied between the liquid and an electrode structure which might consist
of a ring-shaped electrode, so as to allow for passage of drops (like the
inducer rings in Fig. IV-I).
Without a field, the fluid is supplied with
sufficient rate to produce slow dripping in the range of 1 rom drop radii.
-------
@
( 0..)
85
curren t and
hence electric field
+
t
~
( b)
~? i. .
( ,;
In T,1-~0
- '?':ce of ::1'1. (;l'cctric field, liquid drips from
'--
~. '
. .... .
"rl:lCf; ~t~-...
- r! (, )
, I' "8. rO"':" ',0
-- ':) ..L- ~'J. \
,...!..cll
;,,~~ =.:, to fi..J:;
,-,~c C r:' ..... c r'
d'i. tll
:Cield 2uove
t~;rj: :..~,cl
U~:.'~~'
~(i!
-------
86
As the voltage is raised, with the volume rate of flow kept constant,
the drop rate increases and hence the size of the drops decreases.
This trend continues until a transition is achieved to a regime in which
the dripping is replaced by aperiodic spitting.
Drops are now accompanied
by corona discharge and a spectrum of sizes is produced.
Althou~h the trend with increasing field is still to produce smaller
drops, these are only about a factor of 10 smaller than those that form
in the absence of the field.
As the field is raised still further, a
dramatic switch in the flow configuration is obtained, with the dripping
replaced by a steady stream terminated in a fuzzy region of spray. as
sketched in Fig. IV-4(b).
The liquid narrows to a fine jet which is
steady from orifice to point of breakup.
This stream has been observed
to be as fine as a micron in diameter
[64] .
To understand the current-driven jet, the combined effects of the
shear stress, corona discharge, polarization forces, and of the normal
stress-induced instability must be taken into account.
Observation of
jets in the dark shows that just above the region of spraying, there is a
corona discharge.
Hence, current is carried by the jet from the orifice
to the position at which the electrical breakdown occurs.
This current
insures that the jet interface experiences a tangential electric field.
The interface is also charged.
In the point-to-"plane" configuration,
positive charges generally are distributed along the interface, as sketched.
Hence, there is an electrical shear stress tending to accelerate the stream
and draw it out into toe fine thread.
Further, as long as the jet carries
the current, it can be shown that the field, through the agent of polari-
zation forces, tends to stabilize the stream.
Thus, the natural tendency
-------
87
of :.
E,~tce :enSlon
to cause jet breakup is offset by the field and the
streEJ! ~.::,-~nc.s
to be stable, again as observed.
However, once the stream
narrotvs tc
a sufficiently fine stream that electrical breakdown occurs,
the corona discharge carries away the stabilizing current.
From that
point on, the electric field is normal to the interface and tends to cause
ins tability.
In fact, the conditions for instability are greatly exceeded
and the jet breaks into drops violently.
Because the breakup occurs in a
region occupied by both field and ions from the corona dischar~e, these
drops are highly charged.
In a current-driven jet, the electrical shear stresses act on the
interface and reduce the size of the stream by orders of magnitude before
processes of instability subdivide the stream into drops.
Because these
stresses act on the interface itself, it can be expected that the atomiza-
tioil proces:5 is a more efficient one than that obtained, say, by pushing
the liquid through a risid orifice.
IL recent years, studies have been made of electrohydrodynamic spray-
ing fer its ap~lication to drop production in space propulsion [54, 55, 56,
57,58,59],
Unfortunately. the interest of that work is in drop forma-
tion in vacuum.
As the above description suggests, electrical breakdown
is closely related to the spraying obtained at atmospheric pressure.
In
fact, although not generally given much attention, it is difficult, if not
imp03sible, to obtain electrohydrodynamic sprayin~ under standard conditions
without producing large numbers of ions through attendent corona discharge.
Electrical breakdown may occur prior to the drop formation, but generally
extends throughout the region where the drops break away.
It is essential to recognize that current-driven jets are the source
of both ions ~nd charged drops.
~1at the electrical source must supply
-------
88
power for the ions means that there is an inherent inefficiency.
Further, particles passing through the field region of the jet will be
subject to an ion flux which can result in corona charging to the same
sign as the drops.
Probably the most attractive attribute of the electrical spraying
is the opportunity it gives to avoid use of orifices in forming the drops.
The jets can be formed from a continuous surface, such as a film.
The
generation of audible noise on high voltage transmission lines under foul-
weather conditions is a reminder of this [10].
A film of liquid on a
high voltage cvlindrical electrode is unstable in an electromechanical
sense and forms perturbances on its surface which are the sites of current-
driven jets ... of corona discharge and drops.
If the production of ions
does not present an unreasonable penalty, the wetted electrode has the
advantage of being relatively invulnerable to clogging and deterioration.
In any case, the orifice used with an electrical sprayer can be made much
larger than is typical of a nozzle for producing the same size of drops.
Reported investigations of electrohydrodynarnic spraying give scant
information about electrical power and flow relationships.
Hoburg's work
[10] simulating the spraying from a wetted transmission line is probably
of most direct use in determining the merits of electrical sprayers for
drop formation.
He studied spraying through a 1/8" hole in the wall of a
cylindrical conductor approximately one inch in diameter.
The conductor
was grounded and placed coaxial with a high voltage cylindrical cage.
Unfortunately, although Hoburg's work gives a thorough representation of
the relations between spraying regimes and flow rate, voltage, and current,
-------
89
it does not report the drop size under the spraying conditions.
His drops
were relatively large, probably between 10 and 100 ~.
With the simple
arrangement of coaxial conductors, voltages up to 50 kv were used.
Only
a small fraction of the inter-electrode spacing represented the potential
drop across the liquid stream, hence a large part of the power input was
unnecessarily dissipated in dragging ions across most of the gap.
Even
so, a typical mass of water converted to drops by a single source was
15 cm3/min, with an electrical excitation of 40 kv and 2 x 10-5 amps.
This converts to about 4 x 10-2 (lb/min)/watt.
With a water loading of
2.5 X 10-3 lb/ft3 [Class III loading case study, see Eq. (111.37)], this
amounts to a power requirement of 62.5 watts/lOOO cfm.
Again, we must emphasize that the calculation is at best a rough
indication.
The numbers used are for an apparatus not designed for the
application at hand.
The drops produced were too large and no advantage
was taken of a moving gas to sweep drops from the volume subject to elec-
tric stress.
Flashover caused by the drops in this region places a limit
on how small an electrode-iet spacing can be used, and hence on how much
volta?e is required to achieve the sprayin~.
'k can make the following
observations:
i)
The role of corona discllarge in electrohydrodynamic spraying is
essential at atmospheric pressure, and requires that work done
dL elevated pressures or in vacuum be viewed with circumspection,
Especially as regards the efficiency of the atomizing process.
ii) TI1e electrical stresses do offer an alternative to producing charged
(::rops in the 1- 50~ range with improved efficiency and simplicity
i~ tne apparatus.
Presently, inadequate information is available
to make an enr,ineering evaluation, but such a study would be
relatively strai?htforward.
-------
90
H.
Condensation Charging
Condensation methods both of forming and charging drops can be divided
into the two categories for condensation methods in general, suggested in
~ C...(low velocity-high volume, and high velocity-low volume).
Methods
of charging extremely small drops by condensation on ions are a standard
part of aerosol technology [66].
More recent work has been directed
toward condensation charging in nozzles, usually in the vicinity of a
shock [63,70,71,72.73].
Processes have been demonstrated experimentally
in which drops are so efficient in condensing on ions created by a corona
source that virtually all of the corona current is carried away by the
charged drops [68].
Generally, these condensation devices involve high
concentrations of energy and generate submicron drops.
Primary interest
here is in the generation of relatively large drops; hence, no attempt
is made to assess the viability of these techniques in transforming large
amounts of water into the form of drops.
-------
91
v.
Comparison of Svstems
-~----_.~-
Classes I and II
-----
Generally, devices using drops and fields are in competition with
scrubbers and electrostatic precipitators of conventional design.
But,
because the Class I and II type of interactions are closely related, a com-
varison between these systems is particularly meaningful.
Here, the question
is:
in a system already involving the use of injected water for collecting
particles, is the additional technology introduced by the requirement for
particle charging and c~eating an awbient E offset by the improvement in
performance?
One way to measure performance is in terms of water usage.
TablesIII-l and 111-3 indicate the volume of gas cleaned per pound of
water required in devices which utilize conventional scrubbin~ and elec-
trically induced scrubbing, respectively. It appears t~at the electrical
scrubber competes favorably with mechanical Bcrubbers operating at injection
velocities on the order of If) ft/s~c or less.
Clearly, the electrical pro-
cess is at the ?reatest advantage in collecting the smallest uarticles.
For
example, it see~s that, by using one-micron particles, the electrical device
can do as well as the mechanical scrubber using an injection velocity of
100 ft/sec.
Pe can ccnclude that, in the submicron collection, the Class II
interactions are viable, but not ovenvhelmingly 80.
Further comparison of
the t~vo svstems must be based on energy requirements.
Mechanical losses
in the high-velocity conventional scrubber are a major consideration.
But
on the ot:1er hand, the Class II interactions require an aMbient field.
2encc,
tr1e interaction volume must be filled with high volta~e electrodes
fittecl for collectin~ ancl injecting the drops.
"Pov!er requireMents are the
-------
92
major drawback of the mechanical scrubber in the collection of submicron
sized particles.
Reliability and systems complexity resulting from having
not only the ~.,ater injection and removal equipment, but also the high-
voltage electrodes in a hostile environment, is the principal disadvantage
of the electrical Class II scrubber.
Classes III and IV
A comparison of performance in removing 0.2 micron diameter particles
by Class III and IV interactions can be made using results summarized by Eqs.
(111.34 - 111.37) and Table (111-6).
Pith water loading in the neighborhood
-4 3
of 10 1b/ft, both interactions give reasonable efficiencies for removing
0.2 micron particles \lith residence times of a feu seconds.
The Class III
and IV systems will generally have performance characteristics in the same
range, if the charge induced on the poles of the drop surface by the imposed
field in the Class IV interaction is on the order of that caused by the net
c:1arge in the Class III interaction.
For the Class III interactions:
(a)
The interaction volume rec)uires no ambient E, rlence is simply a
mixing region devoid of electrodes and not involved with electrical insu1a-
tion problems in an environment filled by drops and particles.
(b)
Pmvever,
tne loading of drops is critical if high efficiency is
to be achieved in a single stage.
If the loadin~ capacity defined by Eq.
(111-19) does not exceed zero, hi~h efficiency is impossible, no matter
what the residence time.
For the Class IV interactions:
(a)
No drop charging is required.
Further, with bipolar charging of
the particles, the effective lifetime of a drop is not 1imite0 by the charge
collection.
-------
93
(b) Howevert the interaction region must be filled by an ambient
electric fieldt although the electrodes used to impose that field need
not be used to inject or collect the dropst hence need not be fitted with
hydraulic equipment.
Classes III and lY Compared to Conventional Precipitator
The models used in 9 III indicate that the water requirement for the
electrical collection processes is not unreasonable; orders of magnitude
more water are required in a conventional scrubber.
Renee, the question of
viability for the devices basec on Class III and IV interactions is asked
by making comparisons with conventional electrostatic precipitators.
A fair
comparison gives the conventional precipitator the option of a wet wall,
since the use of drops implies vyet valls sOI!'ewhere t in any case.
Hence,
care must be taken in ar~uing that the drop devices are at an advantage in
solving the re-entrainment problem [see Ref. 34, p. 311].
The residence time for hi~h efficiency in a conventional precipitator
is of tlle order
T
prec
3~
Sv~
prec
3r
2bE
(1)
where we aSSume tu1ular electrodes of radius r.
Pere, vJe have made L/U
from [C]. (11-4) three times A/S,., to gl..ve
prec approximately 95% efficiency
wi th an exponential decay 1m,;.
to Eq. (1).
Also, wprec = bE in going from Eq. (11-4)
For 0.2 micron-diarlcter particles, ,Je use b from Table 111-4
r = 20 cm. and E =
5 x 105 l~v / cU'. to ob tain a residence time from Eq. (1)
This is compar2ble with 2.5 seconds for the case study of
of six seconds.
[CJs. (III-34 - 37).
This latter time constant is achieved with a relatively
modes t 'Ja ter loading.
-------
94
There is a major difference between the Class III type of interaction
and that conventionally used in precipitators.
Performance of the drop
Class III devices is strongly influenced by particle loading.
Such devices
would be compromised in fine particle efficiency by the existence of a sig-
nificant population of large particles.
All particles tend to neutralize
the drops and limit their effective collection time.
If a spectrum of particles is present, it may be best to have a
"topping" precipitator to eliminate the largest particles first.
The advan-
ta~e of the Class III interaction i3 that, in achieving the residence time
required for removal of extremely fine particles, the interaction region E
simply free space.
Hence, much greater residence times can be contemplated
in systems that can practically remove particles in sizes well under 0.1
micron.
The Class IV interactions require systems of electrodes.
However,
because the drops do not need to be charged, it appears t:lat such inter-
actions should be considered Hherever wet -'NaIl electrostatic precipitators
appear attrative.
-------
95
VI.
Conclusions and Recommendations
-----
It is clearly evident fro~ information available in the literature,
from patents and from calculations presented here, that the practical use
of ciroDs and electric fields for the collection of submicron particles is
feasible.
It is also clear tnat fields and drops do not represent a panacea.
Calculations, and what few quantitative results are available do not sug-
gest orders-of-magnitude improve~ent in device performance.
Drop-field devices involve a superposition of the technologies of wet
scrubbers and electrostatic precipitators.
With the complications come
additional degrees of flexibility.
For examole, drop loading becomes an
alternative to device length in improving performance.
However, improve-
ments tend to be offset bv a consi~erable additional device complexity.
This report cannot answer the final question of ~hether or not the com-
plications are worth the improveT"ent; that will depend intimately on the
specific application and tie particul2rs of the configuration.
It is important to recognize that one capability of the drop-type
devices is not shared bv the conventional precipitator.
The drop devices,
like their scrubber relatives, can remove gases as well as particulate.
(lfurks' [**] primary intent is to provide removal of gaseous materials,
not oarticles.)
Each of the electrical interactions described here has
the ca?abilitv of simultaneously actin~ as a gas and particle scrubber.
Because of differences between Class II and Classes III and IV interactions
relative to the p,as, these can be expected to have differing performance
characteristics in the removal of gases.
Because the drop-type devices
can compete, performancewise, ,"ith conventional orecipitators, it is clear
-~--~----
[**] see Table 11-2
-------
96
that further preliminary work is called for in determining the characteristics
of such devices acting as combine gas and particle scrubbers.
As illustrated by ~ III, performance is determined by the collective
interactions of drops and particles.
It is ,lell known that "real" hydrody-
namic effects are a dominating influence in conventional precipitators.
There, the distance between electrodes is great enough that v]e can think of
the particles as entrained in a turbulent gas core, and migrating to the
electrodes across boundary layers.
Althou~h we are certainly justified in
thinking of the drop surface as a conventional collecting electrode, there
is no analogy to the relative gas flo~.
According to whether the drops are
in Class II or Classes III. and IV, there mayor may not be a velocity rela-
tive to the gas.
In either case, tte scale of the turbulence relative to
the typical collectin~ surface dimension has changed completely.
There is
a lack of experi~ental work aimed at giving supoort to ouantitative des-
criptions of the collective particle interactions with entrained drops.
II next logicC'1 ster tnward device desi?n with confidence is exoeriments
usin~ drops in the Class II, III and IV interactions.
Of these, the most
i~portant seems to be the Class III interactions.
A necessary next step in refinin~ comparisons bet"een field-drop
devices and conventional ones is the identification of specific applications
that provide a context for a complete systems design.
Only in this ~vay is
it possible to compare alternatives meaningfullv.
So f~r as we can tell,
drop-field type devices have not been investigated for lar?e-scale applica-
tions.
Yet it is to large systems, perhaps with a need for collectin?
gaseous effluent also, that the Class III type interaction would seem to
have the ~ost to offer.
-------
97
Questions that must next be answered are these:
a)
What confidence can we have in the models given in 9 III for particle
collection on drops through the agency of an electric field?
Here,
the need is for experiments that place the particle and drop popula-
tions and charges under control and allow for measurements resolved
in space and time.
The need is for the collection performance
measurements of the system
of drops and particles under realistic
flow condi tions .
The models have already been given considerable
support for collection on isolated drops.
b)
What are the implications of thermodynamic effects in the face of
evaporation?
What is the lifetime of drops under practical industrial
conditions?
What are the relative merits of using a thermal source
of energy to make drops by one of the condensation mechanisms cited
in
9 IV C?
c)
Penney emphasizes the necessity of recognizing the implications of
space charge effects for device scalin?
Included in the Class III
interactions are collection on bipolar charged drops, or systems of
heterogeneously d!arged drops.
The use of such techniques for
eliminating space charge effects as tile devices are scaled up in
size requires careful investigation of the implications for the
collection properties of the system, under (a) above.
A specific
example of heterogeneous charging, used to prevent electrical break-
do,m limitations as the scale is increased, is shown in the hybrid
system of Fig. VI-I.
Space char~e problems are avoided in the Class
III interaction using drops charged to only one sign by making the
collection capacity ~ on the order of zero.
This generally leads
to operation with a relatively low water requirement loading and
long residence times.
For example, for 95% efficiency, the residence
time at ~ = 0 is about 20 Ld'
-------
98
Dirty !::3.8 vri th
--/
bi~ol&r ch~rged purti~le8
~
c
o
D
o ,)
<1 e> ()
charged
----
:==:1
---..
"
#
~ c3
11 !3' 0 ,,:J
!) "" 0,..,
t:'J 0: .:>~ <:),,;
c ~J C" ,J.(.'f 0 ';:J
19 I
Q .;
; ... ~ ~
("J C) r..
o
<. ,"
I!' .... II> ~
0. ..,. ~
t> .... ."
(> 4
()
;4
o f,)
(!
Q c
()
c
~
(I
~
..
tJ
C' r 1,:"' ~ negatively charged
o ,(' 0 (\ drops
0 [I l' ..:!
iJ .p
t.:' (1
~
:=JjJ
.~
.. ,
t') tt r! " ':1
J.;I ,1 r1
J.
1< fl
" :>
~.
o
J
'} <' ~-")
tI "...'
<'I
P
~
Q
f' /:1
(')
.)
..J
.:.1
u
rJ
..
..'I
.;,
....-..
()
t)' (J
11 a /~
.-.... (" I 0 ()
-==:J 6 II' :J {'I <:"
. oJ i!J J cJ tJ C
0 .c
---fiiJ'- .:> ."~ d "
(1 0
o
"
()
neu tl'2.l dro 1)8
!!
~
Fig. VI-l
Drops are charged to alternate polarities in
neighboring regions with a buffer region between of
uncharged drops.
The charged regions collect particles by
the Class III mechanism, while the uncharged drops are in
the ambient field generated by the space charge from the
charged drops, and therefore collect particles by the
Class IV mechanism.
-------
99
d)
The necessity for having a viable large-scale scheme for making
drops has been shown to be an important consideration.
Further
studies should be made of current-driven jets as the basis for
electrohydrodynamic spraying to determine the power requirements
and particle production capabilities, using apparatus simple and
rugged
enough in design to be used in a large-scale system.
e)
Further consideration should be given to designs exploiting the
dual capability of the drop systems to remove both particulate
and noxious gases.
As shown in this study, there is a consider-
able disparity between the liquid loading associated with the
scrubber-like devices and the Class III and IV precipitator-like
devices.
Is there a range of loadings in which a device operates
efficiently in both modes?
-------
100
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-------
106
Appendix A : Charged Particle Collection on Charged Drop in Ambient Flow
and Field (Adapted from book, Electrohydrodynamics, by J. R.
t~lcher, to be published by M.I.T. Press).
~fuipple and Chalmers [22] use an imposed field and 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 Hme. Horeault-Hanot [21].
This latter work did not include
the hydrodynamic effect of the strea~ing neutral gas.
Because the particle
inertia is ignored, the model developed here for collection of charged par-
ticles on a drop is essentially the SRme as these ion-impact models.
A schematic view of the physical situation is depicted bv Fig.
A-I
wherein the pRrticle is viewed as fixed in the frame of reference, and hence
the neutral gas streams relative to the drop with a velocity w .
o
The imposed
field, like the imposed flow, is uniform at infinity with the amplitude Eo'
also shown in Fig. t-l .
In the followinf" Eo will be considered positive or
negative, with the positive directions as defined by the figure.
Ob;ectives in the following derivations are to determine the rate of
charging of the particle, given its initial charge, and to find the final
charge established after the drop has been falling through the particle flux for
a long period of time.
To look ahead, the desired information is summarized
in a plot like that given by Fig. 11-6
Coordinates are the instantaneous
drop charge, Q~ and the field-induced velocity. Eo.
Given that the charge
on the drop and field
are represented by some point in the plane, the ques-
tions we ask are:
\-That, then, is the rate of charging of the particle?
filld what is the trajectory followed in this plane, endin? at a final equi-
librium charge?
-------
107
1 1 1 1
E
o
1 1 1 1
y
1/1
w
o
z
Pie. A-I
Spherical concluctinp drop in iMposed electric field
and f1011 that Are uni for~ at infinity. Eo and "'0 are
positive if directed a3 shown;in f'eneral, the electric field
in tens i tv E
. 0
can be either positive or nepative.
-------
108
At the outset, we draw attention to parameters which will be found use-
ful throughout.
Regimes of charging are demarked by the critical charge
Qc
= 12 TIE R2E
o 0
(A. 1)
which can be positive or negative, depending on the sign of E .
o
Rates of
cllarging will be characterized by the currents
1+
TIR2b+ P:t Eo
(A. 2)
which are also determined in sign by E .
o
The magnitudes of the positive
and negative particle charge densities are
P+ respectively. at infinity.
That the charging rate is to be calculated infers that the particle
motions are not in the steady state.
We assume that transit times through
several drop radii R are short compared to charging times of interest, and
hence, at any instant take the drop charge, Q, as a known constant, which
then makes a contribution to the instantaneous electric field intensity
imposed throughout.
TIle particle is taken as perfectly conducting, hence
the potential and electric field intensity follow from well known solutions.
The imposed electric field intensity is therefore
3
E = - V~= { E (2R
o r3
Q } i R3
+ 1) cos ~ + 4TIE r2 r + {Eo(~
o
1) sin~}iw .
(A.3)
A stream function for the electric field intensity can be defined as
E
2 R 1 r 2 2
= - E R [- + -(-) ] sin ~ +
o r 2 R
Q co~
4TI E
a
(A.4)
where
E
1
- Vx[ie r sin ~
l:]
It v.rill be evident shortly that the particular details of the velocity
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109
distribution are surprisingly unireportant.
He could use potential flow, but
here we follmv Whipple and Chalmers [22] and use lOH Reynolds number flow.
Thus, it is possible to make both components of velocity at the spherical sur~
face vanish.
In terms of the stream function, the boundary condition at
infinity is
~ = l w (r sin ~)2.
2 0
In fact, the stream function is readily
available in the literature.
~
"', R2
o
2
2
[(!.) - (!)]
R r
. 2 ,"
sln 'I'
(A. 5)
where
v =
1
- V x[i8 r sin ~
~ ]
(A. 6 )
The mobility, bi' is taken as constant.
Hence we are dealing with a
system of charged particles with the charge-per-particle a constant.
~
dt
+
Vo}i
= 0 :
a = :t o.
'1
(A. 7)
The neutral fluid mn be taken as having a knO\ffi velocity; in addition,
how'ever, ~,Te reQuire that it he incompressible, so that
V.v = O.
If space
charge effects \Jere important, f;auss' law v,TQuld also relate the local net
char~e density to the electric field intensity.
But, in our approximation,
t~e electric field intensity. like the velocity of the neutral fluid, is
solenoidal:
V.£ = O.
Pith these assmT',ptions, substitution of Eq. (A.6)
into (A.7) gives a simnle expression for the transoort of each charge density
dp.
1
at
+ (v:t b.noVo.
1 '1
o
(A. 8)
Thus, the only coupling bet~een the particles occurs because of alterations
in the iT:lposed fields due to t:1e charging of boundaries.
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110
Equation (A.8) can be integrated with complete generality using the
method of characteristics.
The equations reduce to
dp. = 0
1
dr
on -
dt
V :t bi E
(A.9)
That is, the charge density of each species of particle 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 imposed boundary conditions on the ilth species, wherever
n. (v :t b. E) < 0
1
(A. 10 )
,.,here n is taken as positive if directed out of the volume of interest.
At
points on the surface other than those that satisfy Eq. (A.lO), 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.
Motions in the face of a r.iven flow can be described ,.,ith considerable
generality for those problems in which stream functions can be defined for
both the electric field intensity and the velocity of the fluid, so as to
insure that both E and v are solenoidal.
TI1ese functions are given by Eqs.
(A.4) and (A.5).
The functions L: and If have the simple physical interpre-
tation of bein~ the flux of the electric field intensity of fluid velocity
throurh an open surface, S.
\-lith t11e stream functions given, the lines of constant charge density
given by Eq. (A.9) take the form
dr -1 ~1jJ (:t b L: + '„)
- r 2 sin 1jJ
dt
d1jJ 1 ~r (:t bE + '„)
r"dt r sin 1jJ
(A .11a)
(A.llb)
-------
111
A complete solution can now be obtained by combining this pair of equations.
:fultiplication of (A.llb) by dr/d1)l and equating that expression to Eq. (A.lla)
multiplied by r gives the exact differential:
d(:t bL + '„)
o
(A.l2)
provided E and '„ are independent of time.
Here, our fundamental assumption
of quasi-steady particle motions must be invoked.
He will be interested in
non-steady phenomena.
To integrate particle equations of motion, as we have
in writing Eq. (A.12), we require that the particles have essentially the
same field and flow distribution throughout their motions in the volume of
interest.
In that sense, the motions are steady.
But the particle transit
times are likely to be brief compared to a dynamical time of interest (per-
haps that required for a surface upon which the particles impinge to change,
and hence change the electric field intensitv si~nificantly).
Thus, over
a longer time scale, the flow and field distribution, hence the stream
functions, may be functions of time.
In summary, EI"J.
(A.l2) shows that the
charge densitv of a piven species is constant along constant stream function
lines
p.
1
constant on
:t b.E +
1
'„ = constant
(A. 13)
Given I:qs. (A.4) and (:\.5), the characteristic lines are determined by
substitutinp into (~.ll) to get
:;:: [B: + l(-E-) 2] sin2 \1, :t
r 2 R r
3Q
o
'c
cos 1)1
1 '
-------
113
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, we have the possibility of particle migration.
At the drop
surface, the velocity norMal to the surface is zero, hence the force lines
degenerate to ~ b+E.
This greatly simplifies the charging process, because
we can now use the electric field intensity given by Ea. (A.3) to decide
whether or not a given point on the particle surface can accept charge.
Evaluation of (A.3) shows that force lines are directed into the particle
surface wherever
E > o. 1/J < 1/J < iT (A.17
o < ,
c
E < 0 0 < 1/J < 1/J (A.17b)
> ;
o c
with the upper and lower inequalities indicating positive and negative
particles.
The critical angle 1/J deMarking re~ions of inward and outward
c
force lines follows from Eq. (A.3) as satisfying
cos 1/J =
c
-~
Qc
(A.18)
where 0 is given by Eq. (A. I).
'c
A graphical representation of what has been determined is ~iven by the
direction of incident force lines on the particle surfaces sketched in
Fig. .f1. -2.
1Jhere directed im'lard, these force lines indicate a possible
particle current.
\,fuether or not the current is finite depends on whether
the given force line originates on the boundary at infinity.
In any case,
if the force line is directed outward, we can be assured that there is no
charging current to the particle, and so ~1ithout further derivations,
vle
know that rerimes (a), (b) and (c) for the positive particles and (i) ,(k) and
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112
Theupper and lower signs, respectively, refer to positive and negative particles
and C is a constant which determines the particular characteristic line.
Just what constant char~e density should be associated with each of these
lines is determined by a sin?le boundary condition iMposed wherever the line
"enters" the volume of interest at a point satisfying the condition
n. rv :!: b E] < 0
:!:
(A.1S)
Here, n is tai H .
o
Othen7ise, the charge
density is imposed as z ~ + 00 because the positive narticles enter from below.
Thus, the char~e-imposed field plane divides into two regimes, as shown by
t~e notations at the hottom of Fig. 11-6 .
-------
114
(1) for the negative particles give no charging current;from Eq. (A.16) the
particle charge remains at whatever its initial value within the regime was.
Re~imes (f) and (i) for Positive Particles: (b) and (g) for Negative Particles
We nmV' characterize each regime shown in Figs. ll- 6 and 11-7.
Upper and lower
signs respectively will be used to refer to the positive and negative ion
cases.
The characteristic line terminating at the critical angle on the particle
surface reaches the z + - 00 surface at the radius y* shown in the respective
regimes in Figs .II-6 and II-7
Particles entering within that radius strike
the surface of the drop within the range of angles vlherein the drop can
accept particles.
Hence, to compute the instantaneous drop charging cur-
rent, we can simply find this radius y* 8nd compute the total current pas-
sing within that radius at z + - 00.
The particular line is defined by Eq.
(A.14) evaluated at the critical anele, and on the particle surface:
\)J = 1)1 , r = P..
c
Thus, the constant is eVC'lluated to be
c
= :t i[l + (g )2 ]
cc
(A.19)
To find y*, vle now take the limit of Eq. (A.14) using the constant of (A.19)
to determine that
T v
(y*) (1 + 0)
- h E
:t 0
2
3P2 [1 - ~ ]
(lc
(A.20)
Our proble~ is particularly simple because the particle flux is constant, so
the current passing through the surface with radius y* is simnlv the product
of the current density and the circurnscrihed area
+
i-
1
2
:t 0:1: (:tb:tEo - HO)1T(Y*)
(A.21)
Nmv, if we combine Eqs. (L'\. 20) and (A. 21), ,-]e arrive at
-------
115
+
r
1
31:1:(1
n 2
~)
Q
c
a 2
= :I: 311:1:1 (1 + lOci)
(A. 22)
1~e second equality is written by recognizing the si~1 of Eo in the respective
regimes.
Tole conclude that in the positive particle regimes (f) and (i), the charg-
ing current is nositive, tending to increase the particle charge until
:It
reac~es the limiting value Q =
IQcl
Charging trajectories are shm.m in
the figures, ,vith i the rate of charging, whether the initial particle
1
charzc is "ithin the respective regimes or the chaq~e passes from another
regime into one of these regimes, and then passes on to its final value,
10c I.
For cxamnle, in the case of the positive particle charging, we will soon
find that a particle charges at one rate in regime (1) and then, on reaching
regime (i), assumes the charginr rAte given by E0. (A.22), 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.II-6
and II-7
are
the force line ratterns, and the critical angles defining those portions of
the drop over ",hich conduction can occur.
As a drop charges and then passes
from rerime (i) to (f), and finall" to the boundary between regimes (f) and
(c) in the positive particle case, we see that the anple over which the drop
can accept charge decreases from a ~aximum of 2TI to TI at 0 = 0, and finally
to zero vThen n =
I () I.
c
It is the closing of this IIvlindow" through vlhich
chaq~e can be accepted to trle particle surface l;Jhich is the essence of the
charging process.
-------
116
~gimes (d) and (g) for Positive Particles; (f) and (i) for Negative Particles
These regimes are analogous to the four just discussed except that the ions
enter at z -+ 00, rather than at z -+ - 00.
The derivation is therefore as just
described except that the limiting form of (A.14) is taken as ~ -+ 0, with C
again
given by Eq. (A.19) to obtain
2 - ~Yo
(y*)(l + bE)
:t 0
=
3R2 (1 + 9-) 2
Qc
(A.23)
TIlen, the particle currents can be evaluated as
+
i-
I
o 2
31:t (1 + 0-)
'c
=
+ Q 2
311:t1 (1 + IQcl )
(A. 24)
As would be expected on physical grounds, the positive particle case gives
charging currents and final drop charges in regi~e8 (d) and (g), which are
the same as those in (f) and (i).
Similar remarks apply in the negative
particle charging case.
Certainly, if the fluid velocity is zero, the
charging conditions must be the same, whether the electric field is posi-
tive or nega~ive; we ~ust have symmetry about the ~ axis.
Regimes (i)_~nd (k) fo~ositi~e Particles; (b) and (c) for Ne~at~vc Particles:
For these rCRiNes, the tot31 surface of the drop can accept particles.
The
radius for the circular cross section of particles reaching the surface of
the drop from z -+ 00 is deter~ined bv the line intersectinp the drop surface
at
1jJ =
TT.
This line is defined bv evaluating Fq. (1\.14) at r = R, 11J = TT
to obtain
C
+ 3Q
o
c
(A.25)
Then, if the limit is taken r -+ 00, IjJ -+ 0
of Ea. (A.14), v* is obtained and
the current can be cvaluated as
-------
117
+
i-
1
~ P+( ~b+E + w )n(y*)2
- - 0 0
121 I:t I
IQcl
Q
(A.26)
note that in the positive particle regimes, Q is negative, so our result
indicates that the particle charges at this rate until it leaves the res-
pective regimes when the charge 0
- I Qc I .
Regime (1) for Positive P~rticles; (a) for Negative Particles:
tion here is similar to that for the previous cases, except that particles
The situa-
enter at z ~ - 00, so the appropriate constant for the critical characteristic
lines g;iven by EfJ. (1,.14) evaluated at r = R, y= n , is the negative of Eq.
(1\.25) .
The limit of that equation given at r ~ 00, W ~ n
gives y* and
evaluation of the current gives a value identical to that found with
Eq.
(A.26).
In terms of vip.:. 11-6
for ))osi ti ve particles, \-Te have found
that in the rer,ime (1), where the initial charge is ne~ative, the charging
current is positive, and tends to reduce the T1la?llitude of the particle
charge until it enters re~iMe (i). ~\'here its rate of charging shifts to i
1
and it continues to acauire positive charge until it reaches the final value
10 I indicated on the dia~raM.
c
Rel\_irre- (e), rositiy~ rartic1~s~_e~ime__(h), i'1r:y,ative Particles:
In regimes
(e) and (h) for either sign of particles, the windoF through vJhich the drop
can accept a particle flux is on the oD;"Iosite side from the incident particles.
Tl1is ;?:ives the opportunitv for force lines terminatin? within the windmv
throufh \'lhich the drop can accept particles to ori~inate on the drop itself.
In t;lat case, the chaq>e density on the characteris tic line is zero, since
tile crop surface is incapable of providin~ particles.
10 determine tile particle char2c thatiust prevents force lines ori~dn-
atin\! at z -+ 00
from terrrinatin8" on the particle surface, follow a lines from
t:le z- axis "here t:le drops enter at infinity back to the drop surface.
That
line has a constant determined bv evaluating Eq. (A.14) with W = 0
-------
118
c
=
+]Q
Qc
(A.27)
Now, if we evaluate (A.14) using the constant of Eq. (A.27) and r = R, we
achieve an expression for the angular position at which that characteristic
line meets the drop surface
3 . ,,,
"2 S1.n 'I'
30
-'- (cos 1./J - 1)
Qc
(A. 28)
Note that the quantity on the right is always negative if Q/Qc is positive,
as it is in regimes (e) for the positive particles and (h) for the negative.
[Remember that Q can be positive or negative, according to the sign of Eo,
c
as expressed by Eq. (A. I).]
We conclude that in regime (e) for the positive
particles and (h) for the negative, the rate of charging vanishes; the drop
remains at its initinl charge.
Regirn~<.E2 for Positive. Particles; (e) for Negative Parti~les:
In these
regimes, Q/O
'c
is negative and Eq. (A.28) gives an angle at which the charac-
teristic line along the z- axis meets the particle surface.
To compute the
rate of charging, we do not require the solution to this equation, because
a circular area of incidence for particles at z + 00 is then determined by
the characteristic line reaching the drop at ili = TI .
Actually, no ne~.7 cal-
culation is necessary because that radius is the same as that found for
regime (k) for the positive particles and (b) for the negative,
so v.Te can
+
conclude immediately that the charging current is i; , as given by Eq. (A.26).
Drops in these regimes discharj?e until they reach the charge zero.
~.foreover ,
we can now see that, 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 laH through regimes (h) for the positive par-
ticles and (e) for the negative until the drop reaches zero charge.
-------
119
Positiv~ a~_d ;;erative Particles Simultaneously:
Implicit to our imposed
fields and flou approximation is the non-interaction of pC!rticle species
except throu~lcharges on the drop surface,
If both positive and negative
particles are present si~ultancously, the drop charging is characterized
by sirrply superimposing the results summarized with Figs. 11-6 and 11-7 .
The
diagrams are especially helpful in this regard, in that the charging current
for anv given imposed field and drop charge is obtained as the superposition
of the respective charging currents.
Practically, the diap,rams are super-
imposed 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 respective currents at the
~d ven poin t to find the total charging current.
Charging trajectories are sumnarized for the combined positive and neg-
ative particle configuration by Fi~. 11-8 .
Each of the 16 ref-imes shown is
just the superposition of two regimes from figs. 11-6 and 11-7.
For example,
regime (c) in T<'ig. 11-8 has tile charginf- current ~vhich is the sum of those for
regime (b) of Fig.II-b ana regime (c) of Fig. 11-7
Note that this partic-
ular regime cilaracterizes all of those in the tOD and hottom rmY's in Fig. 11-8
in t;lat onlv on~ of the particle species is conducted to the particle,
',;hile the ot:ler is totally repelled.
In regimes (~). (1), (e) and (i), the rate of charging is
. .+ + .
1 = 1 1
1 1
311+1
(1 - I ~c I ) 2 - 3 I 1- k 1 + + ) 2
I'cl
(A.29)
The pC1rticle charf"es tOFard that v.qlue of ~ that makes the current given
1Jv Ef). (L\.29) vanish.
So the final cllarpe, whicll we call here 0 'is the
'1
solution to the C]uadr,qtic exnression of (1\.29) set eaual to zero:
-------
120
Q
(11+1 )
TCI+l
IQcl
(II I .
Itt-~
[(.~ ,\2
11-1 + 'l
(~- ,~
11-1 7
-J
(A.30)
Here, one root is extraneous because it corresponds to a value of Ql >IQcl.
As summarized in the figure, the dron charge is positive if the positive
particle current exceeds the negative particle current, and vice versa.
It is clearer froM Eq. (A.29) than from (A.30) that, if the positive and
negative particle current densities are equal, the final particle charge
vanishes.
-------
121
Af'pendix 13:
Jrop Electrical Conductivity
~fanv of the theoretical discussions of mechanisms by ,vI-dch "drops"
collect particles ,dth the help of an electric field represent the "drop"
as having a dielectric constant £ and being electrically insulating.
For
almost all applications, the droD should be regarded as perfectly conduct-
ing, especially if it is water.
fortunate1v, £ is sufficiently high in
water that little error is committed in using the field distribution pre-
dicted, assuming t~-,e concluctivitv is zero.
10 see how the electricrtl conductivitv a of the collecting particles
comes into play, consider the typical situation of fig. B-1 in which an
unc!larp"cd drop arrives in a region ,,'here the electric field in initially
uniform.
In the frame of the drop, the field is essentially "turned on"
uhen t = ('.
o
f - \
t=o
t; '770
"Figure B-1
~ith tne aanlication of ~le electric field, there is at first a field
in t;le interior of the GrOD, llence a current density J must exist there
?,iven
by .J =
en: .
As a result, nositive surface charges accumulate on half
of the drop eo.u8l in nunuer to the negative charges that accumulate over
tite ot!ler 'lal f.
~'ese charres build up until the electric field is excluded
frOTf. t:w voluTJ;c of the ciroD: tllat is, until the drop achieves the field
-------
122
configuration of a perfect conductor.
TIle process of charge relaxation is
exponential, \.ith time constant
T
E (2 + ~)
o Eo
a
In tap water, where a is tvpically 1 wl0/m and E ~ 80 E , this time constant
o
is approximately 10-9
sees.
'fust processes of interest take longer than
this, hence we are justified in regardin~ the drop as perfectly conducting.
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