ELSEVIER
PowderTechnology86 (1996)41-67
Charge distribution and state of agglomeration after tribocharging fine
p'miculate materials
K. Sch~nert, K. Eichas, F. Niermfller
Institarf~r AuJbereiarng, Univemtdt Clmrslhul-Zellerfefd.D~3867a Cfaasrkal-Zelterfeld. Germany
Received21 March1995;revised19July 1995
Abstract
Particle reixtarcsof different noncouductivc:"~ciesneedto be treated in a tribochargingunit so that theycanbe separatedin an electrostatic
field. Such u unit producesan aerosolwith panicles earryingdifferentpositive and negativecharges. An efficientseparationdemandshigh
charges; however,high chargessupportagglomerationand agglomeratesworsenthe separationprocess.This problemleasbeon studi~ using
quartz/calcite mixturesin the size range 20-200 tira usinga vibrationchamberand a brushaerosolgeneratoras tM:trilx)dtatgingunit 11~
particle chargesvary over a wide range up to almost the theoretical maximumvalue, Tim charge distributiondepends on the particle size,
mixture ratio arid atmospherichumidity such that the median value decteasosas the particles becomesmaller, the humidity rises and tim
fraction in the mixtureincreases.Accordingto Coehn's mIe, quartz carries mainlynegativeand calcite mainly[msiti'cecbarg'eLElectnx~.tatic
agglomeratescontainiag particlesabove 10 p,ra can be brokendownby the Con]ombicfarce in the field,but agglomerateswith tinct"particles
have to be destroyed before enteringthe sepa~tor. The most effective methodis to use a high air velocity inside a slit nozzle. Even a feed
with highlycharged mierofineparticlescould be deglomeratedcompletely.
geywords: Electrostaticsgparatlon;Paniclecharging;Deglonmratioa
1. Introduction
Particle mixtures of different noncnnducfive species need
to be treated in a tribocharging unit so that they can be separated in an electrostatic field. The particle charges differ with
resp*et to polarity and charge density. The particle stream is
split into a positive and a negative product leaving the field
near the electrodes. Also, so-calledmiddlings can be obtained
that contain particles of low charge. The field is usually oriente,d horizontally and the particle stream is fed from the top.
The particles should not meet the electrodes and be deposited
on them, as otherwise sparking effects could be caused. The
application of these free-fall separators is limited to particle
sizes between 50-100/.Lm and several millimeters. The lower
limit is due to agglomeration effects and particle deposition
on the electrodes; the upper limit follows from an insufficient
residence time owing to the fast seuling velocity, Big installations of free-full separators are successfully used for proeessiag salt minerals [ 1]. The first investigations on particle
tribocharging were published by Szantho in 1939 [21, and
extensive work was done by Carta and his group during the
1980s (see, for example. Refs, [31 and [4]).
Extending the application of this separation method into
the particle range below 100 #m requires the production of
0032-5910196/$15.00 © 1996EIs~vi*rScience$.A.Alltightsmsm'~ml
$8DlO032-591 O(95 )03036-9
an aerosol with charged particles that feeds into a scpm'ator.
A new type of such a separator, called a triboelectfic drum
separator, was developed recently and invostigated [5,6]; see
Fig. I. The species are separated in the gap I~tstama two
rotating polycarbonate drums. Two imbedded electrodes
build up a high dectrostatic field, The charged particles are
deposited onto the drums, transported to the back and
removed there from the drums by an electric force caused by
oppositely charged back electrodes and bmsbes. A slightly
modified brush aerosol generator [71 is used for tribucl~glag and is mounted above tim separator. Binary mixtur~ of
quartz, calcite, flnorspar, barite and anthrucit, have successfully ~ e n separated in the size range l-t00 p,m. Recoveries
and purifies above 90% could be achieved in one step.
Detailed results are given in Refs. [5] and [6L
To understand the laoccss and optimize the OlXa'ationconditions, knowledge of the charge distribution and the state of
agglomeration is needed.
2. Charge distribution
2.1. Experimental
The charge distribution of binary quartz/calcite mixtures
of three narrow fractions between 20 and 200 ~m have been
42
if. Schiinerret at./Powder Technology ,~6 (1996) 41~47
6
~
8
~i 4
< ), / 1i,.,(
)
5
9
5
Fig. I. Sketch of the tnbaelcctnc drum scparalor [51: (l) electrodes; 12.)
rotating polycarl~nate drums; ( 3 ) back aiectmdes; (a ~tJru.shes;( 5 ) product
chambers; (61 powder sample; (7) rotating brush; (8) air inlet; (9) air
uniter with a fill.
measured in two different devices. The first one. shown in
Fig. 2, comprises a vibration chamber as the tribocharging
unit, the usual free-fall separator and a particle collector with
ten sections [ 8]. The top and bottom of the vibration chamber
consist of metallic frits so that the inserted sample can be
conditioned with respect to the moisture content and the temperature of the air. An opening, covered with a screen at the
bottom, lets the particles flow into a 2 mm metallic capillary
robe leading to the separator. The unit is grounded. The acceleration of the linear oscillation can be adjusted up to 20g.
The particle collector is made of PTFE with ten small brass
boxes conntected to a very sensitive electrometer (Keithley
617). After the experiment, the charge and the particle mass
in each box are measured in order to calculate the charge
distribution. Two methods have been used, in which the fractions of both species are either equal in size (method A) or
different (method B). In the second case, the coarser fraction,
called here lhe partner fraction, is kept back by the screen
covering the opening, and the finer fraction, called the object
fraction, settles into the separator. This device can be used
down to a fineness of 4 0 - 8 0 / L m depending on the material.
More details can be found in Rcf, 18].
The 20125 ~ m fraction was investigated by measuring the
particle trajectories in a horizontal electrostatic field. Fig. 3
shows the arrangement. The particles are triboeharged in the
brush aerosol generator ~hown in Fig. l. The aerosol jet enters
a large cylinder with a diameter of 300 mm and a height of
300 ram, where the air flow is calmed. An opening of 0.9 mm
in the bottom allows the particles in the center to enter the
settling chamber with two electrodes. The trajectories are
recorded with a video camera. As long as Stokes" law can be
Fig. 2, Sketch of the electros'taticseparator for measuring particle charge
distribution [g]:l I ) vertical vibrating chamber for uibocharging; (2) electrQdcs; t3) particle collector with ten se..:ti,~r,zl; (4) capifla6cs for feeding
particles into the eluctrostaricfield; (~;) air inlet and outlet far conditioning
the sample: (6) box with sensors for temperature, humidity and volnmetde
flow.
applied, the charge density or can be calculated from a, the
angle with respect to thc vertical, and wr, thc settling velocity.
according to Eq. ( 1 ):
7
$
9
$
5
Fig. 3. Sketch of the sedimentation chamber aid ~plica| an'angemeat for
measuring particle charge dist~ibotioas [5 ]: ( I ) inlet for 11~ aerosol with
the charged particles; (2) chamber for calming the air flow; (3) air outlet;
(4) capillary far feeding particles into the ¢lecuoslalic field; (5) settling
chara~r; (6) ¢lcclct',,tes;(7) light source; (8) lenses; (9) apertures; it0)
vi¢~¢OCamors.
K. Schllnert ¢t a! / PowderTechnMogy 86 (1996)41.-47
~
[g~p~12(p~-pf) l'/~'[w~ r~ tan odE1
(i)
where ~ is the known viscosity, p~ the particle density, pt the
air density, E the field strength and g the gravitational acceleration.
The species cannot be distinguished; therefore a mixture
is inserted consisting of the object fraction 20/25 p,m and the
partner fraction 40150 #m so that the species are characterized by the settling velocity. At least 120 particle trajectories
were always evaluated in determining the charge distribution.
For general considerations, the charge density should be
normalized by a characteristic value o',. It seems reasonable
m evaluate o'~ with the general equation relating charge density to field strength and introducing the breakdown field
strength EB:
o'~=c~En;
eo=8.854X10-12AsV-im
t
(3)
This value corresponds to about 160 elementary charges
over 1 /.~m2 or to an average spacing of about 800 A in a
square arrangement. The ratio of the actual charge density to
o', is called the saturation grade ~.
The samples were washed in deionized water, dried for
about 10 h and cooled with dry air. The triobeharging unit
was always conditioned with a flow of air at the required
temperature and humidity before introducing the sample. The
mixture ratio was varied and is characterized by the surface
and mass ratios, which are related to each other by
SIIS:= (x21x~)(~lp~) (MtlMD
n
2
4
e
e
10
12
14
!6
18
20
Fig 4. Median~omraaongrade ~ndoscil1~g accclcraion.Quart I~I
200 pm, t= i0 min,tel. humidity2%. S~IS~ = I.
50 ~
....
J~
(2)
The only question is what value should be used for EB,
which depends on the particle size and shape. In principle Ea
increases as the particles become finer and decreases for nonspherical shapes. For the following, En is set equal to 3 X l 0~
V m - ~, which is approximately the value of the breakdown
field in dry air between plates [9]. It then follows that
OL:2.656× 10 -'~ A s m-"
45
(4)
where x is the particle size, p the density, S the surface, and
M the mass.
2,2, Results
The particle charges are expected tu depend on the two
species uf the sample, the mixture ratio, the particle size, the
moisture, the material of the tfibocharging unit, and the
mechanical action characterized by oscillating ~caleration,
oscillating time and brush speed. The essential findings are
discussed in the following section; more details are given in
Refs. [5] and [g]. The charge distributions are expressed
using either the distribution functions H(~) or the median
values ~so.
Quartz is always raainly negatively charged and calcite
mainly positively, according to the well-known Coehn's rule,
because the dielectric constants of quartz and calcite are
reported in the ranges 2.6--6.5 and 7,6-8.9, respectively.
o
I
2
3
4
o~,g
5
6
7
t ~ t , mm
8
9
10
Fig. 5. Median mtu.mdon grade and oscillating lime. Qtzanz 1601200 pro,
~¢¢elcr~iort 12g,tel. humidity 2%, 5 ~ 1 ~ - I.
The acceleration and time of oscillation influence the
saturation grade as shown in Figs. 4 and 5, with the quartz
fraction being 160/200 pro. For a constant oscillating time
of I0 min the median value rises from 26% at 38 to 48% at
12g. Higher accelerations cause much abrasion of the calcite,
and the saturation grade decreases. The charging occurs
within a few minutes, and further increases a~ small. Most
experiments, therefore, were done at 12g and with an oscillating dine of lO min.
The brush speed does not show any influence between 500
and 1500 rpm. The corresponding circumferential velocities
are 0.92 and 2.76 m s - I
The influence of the material was studied using a brush
aerosol generator with both the wall and the brush made of
steel or polyamide. Either a quartz or a calcite fraction was
fed; the results for both are shown in Fig. 6 in the form of
histograms. Both species are negatively charged, but since
palyamid¢ causes much higher charges than steel, steel was
used for all experiments. This result also indicates that the
charging could be optimized for a particular application by
selecting favoumble materials for the walls arid the brush.
A typical example of how the mixture ratio influences the
charge distribution is sh~.wn in Fig. 7 for the size fractiou
1601200/an vibrated together with the partner fraction 4001
500 pm according to method B. The mixtureswere composed
such that the surface ratio of the finer to the coarser fracdon
was 1:1 or 9: L At a ratio of 9: l the particles arc less charged
than at a ratio of t:l, because fewer panr~r particles are
available for contacting. The median satmation grade
increases from 36% to 44% for quartz and from 14% to 34%
for calci~e. A very small f."action is oppositely charged with
a 1ow charge density. The negative charges on calcite particles
could be caused by contact with the metallic walls, as can be
44
K. Schihzer~ et at, / Powder Technology g6 (I 996) 41-4 7
~'~151rttl'''h''l'''i(~Jar
tZ (-) I+) ....... i
,++
_
AI _P
~I+I,S,I,ITTTr,
+
~. . . . . .
e~,,i,,,
satarntloe,'/=
Fig. 6+Chargedistribution with different matefialsfor the brush andchamber
wall: left, steel; right, polyaraide,Qnarlznr calcitu 20[25 #m fractiontreated
separately, tel. humidity 2%.
i tlU~tZ 1-) t+l
"1
N
,+ ]+!.,.Pp'~,. 1..........
~ s 0calctie~ l I-YOI+1
~o 40 20 o 2u 40 ao
qutarlz (q (.)
I ....
I,HI~,,
sat~nl~. t~)
saMa~n,
Fig. 8. Charge distribution of separately treated quartz or calcite 160/'200
~m fraction, Accelerurion 12g. t - l0 rain, =eLhumidity 2%.
16 LI LJ=~h t= I,LLL~LL±~L
etmrJtz
(-) (+)
quartz ( l t+l
N
~s
,+ !!! ,re.m.+. ,~++~r.+.
~'~i~cn~clte i=11*1
no 40 20 o 20 4o 6o
utl~ntJarL,~+
sal~nllon,
Fig 7, Charge distribution of quartz/calcire mixture.~ofdifferentmiles::left,
3o+/Sr,m ~ 9; fight, So~/Srm. = 1. Object fraction 160/200 ,u.m,partner truelion 400/500/.tin, acceleration 12g, t - 10 rain, rot, humidity 2%,
seen in Fig. 8, which shows the charge distribution of a
separately vibrated quartz or calcite fraction. About 40% of
the calcite particles arc negatively charged, The positive
charges on quartz could be caused by local impurities on the
surface or by adhesion of abraded calcite dust to the quartz
surface. The increase in the oppositely charged fraction of
quartz with increased calcile content, decreased particle size
and at a high acceleration (over 12g) may be taken as an
indication that the second-memioned reason is the more
likely.
Fig. 9 demonstrates the influence of the atmospheric
humidity: the charges decrease and the fraction of oppositely
charged particles rises. At higher humidity, more water is
adsorbed onto the particle surface, causing an increase in the
surface conductivity. The triboeharging effect, therefore,
decreases. The increase in the oppositely charged fraction
could be explained by the difference between the electronic
properties of the surfaces of the two species decreasing as
more water molecules are adsorbed, TEen the materialdependent fluctuations of charges at the contact can be super-
].,o+,; ~'i;, i+J, ".....
0
60 4O 2O o ~o 40 60
saturation,1%)
jIITTT r P
60 40 20 O ao 40 60
saturM&~n,('/01
Fig, 9 Chargedistributionof quartz/calcite mixturnsat different hnraidities:
left, 2~.; right. [2%, Ot~iectfraction 160/200/zm. partner Imction 400/500
p.m, S,,t+/$r== I, acceleration 12g, ,' = I fl rain.
50
0e.27
Qt
4O
00.5
~
~'9#~':/"
°Ct'P-
==9
U~
Fig+I0. Median saturationgradeof(1) quartz and tit calcite for different
p~icle sizesand surfaceratios. Object fraction and partner fraction: 20/25
and 40/50; 8C,/lO0and 200/250; 160/20g.and 400/500. Acceleration 12g.
t= I0 rain, brash speed 1500 tpm. rel. humidity 2% The numbers on the
figure indicate the tmxtur¢ ratios iraterms or ( S,,h/Srm); the lines am interpoloriom of the gumvalues for ($,.j/Sr~ . ) = I,
K. SchOnert er aL / Powder Techm~logy 86 ( I 9~) 4 I--47
imposed by stochastic processes, It is known from dust
explosions that the particles of a uniform dust carry positive
and negative charges after being blown up.
In Fig. 10, the size influence is demonstrated by plotting
the median saturation grade over the particle size. At a constant mixture ratio, the ~so value decreases as the panicles
become smaller. Quartz is always charged more than calcite;
this difference increases with decreasing particle size. The
influence of the mixture ratio is demonstrated using the 20/
25 and 160/200 p,m fractions. It is remarkable that even the
very fine quartz particles can be charged highly if they are
imbedded in a feed containing mainly calcite, as is the ease
with the mixture ratio S,,~/S~a~0.27. An decrease in the
S,~/Sv,~, ratio shifts the ~distribution to higher q~'values.The
experiments have shown the following ~ma, and ff',n,nvalues
for the 20/25 pin quarlz particles:
s,,,/s,~
2
t
0.5
027
~m~ Io ~ , ~
t~12%
1-72%
6-70%
17-95%
3. State of agglomeration
In a highly bipolar charged particle system, agglomerates
are formed. Impressive simulations of this phenomenon have
recently been published [ I 0, l 1]. The agglomeration lowers
the performance of a tribe-electro.static separation because
the particles in a cluster cannot be charged sufficiently, and
agglomerates may not be broken down completely by the
Coulombic forces in the field; therefore the recovery and the
quality of the products become worse. The deglomeration of
an electrostatic agglomerate in an electric field can be understood by considering a two..partJcl¢ cluster and assuming a
uniform charge distribution on the particle surface. This ideal
approach does not take into account eilher any redistribution
of the charge due to the contact of the particles or pohrization
effects caused by the electric field. The Cgalombie adhesion
force F,~ between two nonconductive spheres of diameters x~
and x: and with surface charge densities o I and or2 is given
by
,5
45
10
50
for F2<F~
(9)
E>-EB~.~2/(I + ~ 2 for Fi <F2
(I0)
E>-EBq~/(I+~ ~"
The upper limits of these relations are E = EB and E= EB/
4, respectively, Therefore almost any two-particle agglomerate can be broken down, and also each multiparticle
agglomerate, if it stays long enough in the field to turn around
into the right position alter a particle has been drawn off.
For microfine particles the van der Waals attraction can
exceed the electrostatic adhesion. Some calculations for
spheres are possible with the Lif>hitz equation, and then the
ratio of bolh forces reads [ 12]
FJF~dw = [ 16¢r2ato'.,x,zal [so( 1 + ~ 1 /
[ ~,t~ff,( 1 + ~+ 2z~lx,)21
Fd/F~,~w=[167r'-crlo',.xlz2~l/|eofid(l+~]
(5)
For ~= I and o-~= a-2= a,
(6)
Fel/ Fvdw = 8"n'~o'-xlz~" ,"~fi05
and F2=,trx~a~g
(7)
Assuming the adhesion is caused only by the Coulombic
force, then the particles are separated if the minimum of F~
and F, exceeds Fa:
Min(F~,F,) ->Fa
(8)
Introducing the charge saturation grade ¢-- or/eoEn, it follows ilia[
(I I )
where 05is the Lifshitz-van der Waals constant and z is the
distance between the spheres; the other symbols have already
been introduced. For an ideal smooth surface, z is assumed
to be 4 A; however, z is estimated to increase up to 20 A for
~'ealparticles of 1-10/zm [ 12,13 ]. Toe term 2z~/-¢1 is always
small enough to be neglected, so it follows that
Fa = [ ¢~.xio-2x~/~] [ I~/( 1 + ~ I a ~=x2/xl
Fl~x~o'~E
5~
Fig I I Ratio of Coulornbic1o van dec WoolsaaracliOn,accofditlgt~
Eq. (l~).
Fa = [ ~ralcr~l ~] [x~x~l (xl + x~) 2]
The larger diameter should always be denoted xt, so ~:___1
by definition. The field acts on each particle with the Couturebic force
lqO
(I2)
(13)
Eq. (13) is plotted in Fig. 11 with o'=2.66× 10 -5 A s
m-'- (q,= 1) and fi~3--9× 10--'a N m (quartz/quastz contact). The electrostatic adhesion is equal to the van dcr Wools
force for 100 gm at z = 9 A and for 10 #m at z = 30 h,. Taking
into account the irregular particle sna~, it is to he ¢:~p~cted
that the Coulombic force can break down agglomerates of
particles larger than about l0 jzm, However, mierofine particles on very fine particles, e.g., a 3 p.m particle on a20 bun
particle, may h~,rdly be separate:. Therefore deglomeration
has to be performed before the aerosol enters the separator.
This was the reason for using the brush aerosol generator as
the tr/bocharging unit.
K.Sch#n¢,letal./ Po'~derTechnatogy86(1996)41~t7
46
3,1. Experhne.tal
3.2. Results
In order to determine the state of agglomeration after the
tribocharging unit, the aerosol jet was blown directly into the
la~er beam of the Halos 12 LA instrument to measure the in
situ particle size distribution. The result was compared with
the reference size distribution of the particular sample measured with the same instinmeni after careful dispersion by an
ultra.sound treatment in an aqueous NaIP:O7 solution. Six
RI0 sieve fractions (20/25/xm up to 63180 gin) and four
air-classifier fractions ( 1,4, 2/7, 4/12, 5/25 #m) of quartz
and calcite were used separately or as binary mixtures. The
grade of agglomeration was evaluated according to Koglin
[ 14] and Leschonski et al. [ 15], defined with the moments
of the distribution densities as follows:
"l'he state of agglomeration is expected to depend on the
particle size, mixture ratio, air velocity, brush speed and moisture content, which was kept constant at 2% because tribocharging demands dry air. The brush speed does not show
any influence between 500 and 900 rpm, which is the reasonable range for good separation performance.
Fig. 12 shows some examples with the air classifier fractions at a mixture ratio of 1:1 and an air velocity of 100 m
s- L The distributions after the aerosol generator are much
coarser than the reference; the corresponding agglomeration
grades/3 and (3') are: 0AS ( 0.11 ), 0,57 (0.15), 0.64 ( 0.33 ),
0.74 (0.42). The deglomeration can be enhanced by increasing the air velocity, as shown with the sieve fraction 25/32
/zm and the air classifier fraction 4/12 am in Figs. 13 and
14. The very line fraction needs a much higher air velocity,
but nevertheless a complete deglomeration can be achieved
at 200 m s - i In Fig. 15, the influence of the mixture ratio is
shown for example with the sieve fraction 25/32 ,am at the
low air velocity of 20 m s- ~. The maximum for ,& in the
range 0.4--0.6 wt.% quartz, corresponds to the maximum of
[3= 1 - ( M ~ o l M . , )
= i - (M ~.flM*-~3) (Koglin)
y= 1
(Sv/ST;)
-1-(M:.o/M~,)(M~/M*-.~.3)
y
=
(14)
(Leschonski)
(15)
1 - (M,_JM~Io) ( 1 - [3)
(16)
0.4
The asterisk indicates the reference distributi(m, and the
moments are delined as known:
0.3
(17)
Mko= !Xkqll(x) dx Mk.3= !;f*q3(x) dX
qo(x) represents the number frequency and q ~ ( x ) the mass
frequency of the particle assembiagc.
The program included a variation of the brush speed
(n = 500, 750,900 rpm corresponding in u ~ 0.92, 1.38> 1,65
m s-~), the air velocity in the inlet slot nozzle of 40×0.3
mm (t,t. = 18 to 200 m s- ~) and the mixture ratio (cm = fl.I0.9 wt,% quartz).
10@
9080-
-4112,~,~
I
0,4
0.0
la
24
28
2B
~0
air v~ogtty, m Z s
32
34
36
2 5 1 3 2 / t i n , b r u s h speed 9 0 0 t o m ,
1,e ~
/P .f
22
Fig. 13. A g g l o m e r a t i o n g r a d e a n d air wlt..xity. I:1 q u a r t z / c a l c i t e mixltlle
/T/Tf
7" L¢/
20
/
L •
,
,
,
,
,
,
,
,
i
,
i
,
i
,
0.8
I4 ~r~
P
40,
30
0.4-
O~OSOi
20I0-
ol
8
10
port;tie 5~ze, / ~
50
Fig, 12. P;u'(ide size dislributions o f quarlzfc;~lcile tnixt u~s aflerlribocharging (u~m~ol) and references. Mixtun¢ ratin l : l, o.irvelo~;ity l O0 In s- I, brush
speed 9 0 0 r p m .
20
40
60
$0 tO0 !20 140 180 180 200
el v r,~c~ity, ~ / $
Fig. 14. Aggloillcrati0B grade and air velocity. I:1 quarlz/calcile mixtur~
4/t2/~m, bnJL~h~p~ed 900 rpm.
K. 3chiinert et aL /Powder Technology 86 (1996) 41-47
OA
~
,
L
~
l
~
t
,
5. List of symbols
electric field strength
EB
breakdown field strength
F
Coulombic force acting on a particle
FA, F,~ electrostatic adhesion force
F~,aw van der Waals for,'e
g
gravitational acceleration
H(~b) charge distribution in terms of the saturation grade ~,
M
sample mass
Mk,~ moment of the size distribution
q(x) size d:.stribution frequency
S
particle surface
wf
particle settling velocity
x
particle size
z
eontart distance between two particles
E
0.3
~ o,2.
Q,t
O.O
47
O~,
fl.4
ft.6
per,~ent quartz
fl,S
1,O
Fig. IS, Agglomeration grade and mixlure z-alia, Quartz/calcite rnixluzes
:25132 p.m, brush speed 900 rpm
the tribocharging activity. More details are re~rted in Ref.
[51.
Greek letters
a
4. Conclusions
Binary mixtures of quartz and calcite fractions in the size
range 20-200 p.m can be charged highly with specially doraaped Iribocharging units. A vibration chamber oscillating ~t
12g performs well for particles coarser than about 100 #m,
but fails/or finer feed because of agglomeration effects. [n
this lower range, down to 1 pan, a brush aerosol generator
accomplishes effective trihocharging. For general considerations the dimensionless c barge saturation grade ~'is helpful.
This is defined as the ratio of tile actual charge density or to
the characteristic value or,, represe acing the maximum charge
density o',,~, However, the teal value of o',,,,~ for fine, iITegalarly shaped particles is unknown and cannot be evaluated,
and therefore this value is calculated using the bleakdown
field strength between two smooth plates.
The charge is distributed widely and depends on a variety
of parameters, dominated by the moisture and the mixture
ratio. The best results have been achieved with dry materials
and a composition such that both species have the same surface area. The particles are charged up to Offi60%; however,
a very small fraction is oppositely charged. At other mixture
ratios, the particles of the major species are less charged but
the median charge of the minor species increases depending
on the material (quartz is affected more than calcite).
Electrostatic agglomerates oo~sisting of only a few particles [urger than about 10 p,m can be broken up in the electrostatic field, if the field strength is high enough. The necessary
field strength depends on the charge density but is always
below the breakdown strength. In agglomerates of smaller
particles, van der Waals adhesion exceeds the electrostatic
adhesion. Such agglomerates have to be broken before entering the electrostatic field. This can be done by forcing the
aerosol through a narrow slit nozzle at a high velocity. In this
way, very fine feed, 4/12 p,m, could be deglomerated completely even after being charged highly.
angle of the trajectory of a charged pahicle in the
electric field
/3
agglomeration grade after Koglin
y
agglomeration grade after Leschonski
r/
air viscosity
particle size ratio
Ps, Pr density of the particle and tbe air, respectively
a
surface charge density
~b
saturarion grade, normalized charge density
~o
Lifshitz-van der Waals constant
Acknowledgements
The authors wish to thank the German Research Foundation (DFG) for the support of this research.
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