Powder Technology 120 Ž2001. 187–193
www.elsevier.comrlocaterpowtec
Electrostatic dispersion of fine particles in the air
Jun Ren a,) , Shouci Lu b, Jian Shen a , Chunhong Yu a
a
Center of Research on Surface and Interface Chemical Engineering and Technology, College of Chemistry and Chemical Engineering,
Nanjing UniÕersity, Nanjing 210093, People’s Republic of China
b
Resources Engineering School, UniÕersity of Science and Technology Beijing, Beijing 100083, People’s Republic of China
Received 1 February 2000; received in revised form 1 December 2000; accepted 16 January 2001
Abstract
The paper studied the method of keeping fine particles from aggregating in the air by electrostatic dispersion. The effects of electrode
voltage, diameter, humidity and rest time, as well as van der Waals forces, electrostatic forces and liquid bridge forces between particles
on electrostatic dispersion of powder were discussed. It was shown that optimal electrostatic dispersion effect of calcium carbonate and
talcum particles can be achieved with corona voltage of 29 kV, particle size of 2–25 mm, and proper rest time of 48 h. Criteria for
electrostatic dispersion were put forward on the basis of experimental results. Theoretical calculation indicated that the criteria for
electrostatic dispersion were in good agreement with experimental results. q 2001 Elsevier Science B.V. All rights reserved.
Keywords: Fine particles; Electrostatic dispersion; Air; Interaction force
1. Introduction
The aggregation of fine particles in the air is a serious
problem, which makes troubles in particle technology and
related industry fields w1x. Drying or mechanical methods
are frequently employed to achieve particle dispersion.
Mechanical methods disperse particles using shear stress
or other fluid forces, but have little influence on surface
forces between the particles which may aggregate again
afterwards. In addition to that, mechanical dispersion can
result in fragmentation of large particles and produce
slime. Therefore, an essential way to disperse fine particles
is controlling the inter-particle forces, increasing the repulsive forces, and at the same time decreasing or eliminating
the attractive forces between particles w2,3x.
Masuda and Gotoh w4x reported that particle charging
induced by corona electrodes improves the efficiency of
fine particles feeder. In recent research, it was also been
tried to realize the dispersion of particles, by eliminating
attraction between particles. An idea of electrostatic dispersion was proposed earlier, but no further study was
reported w5x. Electrostatic dispersion is a process of having
particles charged with identical charge and dispersed by
coulomb repulsive force between particles.
In this paper, the possible way of electrostatic dispersion of fine particles in the air is described, the parameters
affecting particle electrostatic dispersion are analyzed, and
the mechanism of electrostatic dispersion in terms of the
physical and surface forces between particles is discussed.
2. Materials, experimental equipment and methods
2.1. Samples
Materials for experiment are natural hydrophilic calcium carbonate taken from Lingtao, China, and hydrophobic talcum from Haicheng, China. The samples were purified, ground, sieved, washed and dried in the air at low
temperature. Their main properties are listed in Table 1.
2.2. Experimental equipment
)
Corresponding author. Tel.: q86-25-3594933; fax: q86-25-3594933.
E-mail address: racjk@yahoo.com ŽJ. Ren..
RLW Žabbreviation of the author’s name. electrostatic
disperser was designed and assembled by the authors in
0032-5910r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 0 3 2 - 5 9 1 0 Ž 0 1 . 0 0 2 6 9 - 8
J. Ren et al.r Powder Technology 120 (2001) 187–193
188
Table 1
Properties of samples
Table 2
The optimised parameters of RLW disperser
Material
Purity
Ž%.
Density
Žg cmy3 .
Contact
angle Ž8.
Volume
diameter Žmm.
Item
Structure
parameter
Calcium carbonate
Talcum
98.57
91.17
2.76
2.61
5
56
2.20
1.58
Diameter of electrodes Žmm.
Number of disk electrodes
Number of needles
Distance between two electrodes Žmm.
Diameter of facing electrodes Žmm.
75
5
24
24
155
the laboratory. Its maximal load voltage is 30 kV. The
powders, charged sufficiently by the electrostatic disperser,
produces strong electrostatic repulsive force between particles which can overcome weaken aggregation of fine
powder and achieve dispersion state.
RLW electrostatic disperser is composed of power
feeder, voltage regulator, transformer, photoelectric reader,
charging device, etc. Its structural diagram is shown in Fig.
1. The charging device consists of discharging electrode
and facing electrode. Facing electrode is a metal cylinder.
Discharging electrode includes electrode shaft and disk
electrode. Electrode shaft is a circular metal column. Needles connected to metal disk serve as discharging end.
There are five disk electrodes, with 24 needles each, in
RLW electrostatic disperser. The structure parameters of
RLW electrostatic disperser are listed in Table 2.
2.3. Experimental methods
2.3.1. Electrostatic dispersion tests
The samples of fixed weight were dried at 1208C for 1
h before testing, and were then fed into RLW disperser
evenly to have the powder charged. The charged powder
was taken out of the disperser to evaluate its dispersion
effect, by measuring sliding friction conical angle of the
powder in an insulating container.
2.3.2. EÕaluation of dispersion effect
2.3.2.1. Measurement of sliding friction conical angle.
Sliding friction conical angle reflects frictional force caused
by press and shearing stress, acting at unit area inside
powder. When shearing stress attains to a certain value, the
particles will slip along the slope. The angle between the
Fig. 1. Frame diagram of RLW disperser structure.
slope and vertical direction is called sliding friction conical
angle.
The charged powder was put into the insulating container, where its compactness and height were kept constant for each test. Then, let the powder slip automatically,
and vibrate the base of the container at fixed intensity and
frequency. The vibrating friction surface of the powder
appeared; h, height of friction slope and c, horizontal
length of upper plane were measured then, and the sliding
friction conical angle a was calculated as follows:
a s arctg
byc
h
,
Ž 1.
where b is a constant. The measurement error was usually
within 2.5%.
2.3.2.2. Relationship between dispersion index and dispersion effect. The conical angle, caused by the change from
static state to moving state of powder, is related directly to
the flowability of the powder. This is an important parameter for practical processing operation, such as powder
storage, transportation and mixture, and must be taken into
account in studying mechanism and flowing properties of
powder w6,7x. This method of angle measurement is valid
for practical application due to its simplicity, convenience
and promptitude. The ratio of sliding friction conical angle, a , of powder electrostatically treated to sliding friction conical angle, a 0 , without treatment, is defined as
powder dispersion index f, that is:
a
fs
a0
Ž 2.
Since the a 0 of a certain powder has definite value, the
dispersion indexes f will increase with the increase of a ,
meaning a better flowability and dispersion properties of
the powder.
2.3.3. Microscopic obserÕation of dispersionr aggregation
state of powder
The dispersionraggregation state of powder was examined by Olympus BHZ-UMA microscope made in Germany, and pictures were taken with the device.
J. Ren et al.r Powder Technology 120 (2001) 187–193
189
3. Experimental results
3.1. The effects of electrode Õoltage on electrostatic dispersion
Electrode voltage is an essential factor that is adjustable
in the process of electrostatic dispersion. Its value influences directly the discharge current and the effects of the
electrostatic dispersion.
The effects of electrode voltage on discharge current
and electrostatic dispersion index are illustrated in Fig. 2.
The dispersion index of particles equals to 1 in natural
state. The discharge current increases and the dispersion
effect of particles is improved with the rise of electrode
voltage; there is a good correspondence between discharge
current and dispersion effect. When the corona voltage
increases to 29 kV, the dispersion index of calcium carbonate and talcum reach 1.43 and 1.42, increasing by 0.43
and 0.42, respectively. The dispersionraggregation state of
calcium carbonate and talcum powders before and after
electrostatic dispersion is illustrated in Fig. 3. The surface
of the original powder is rough, and large bumps can be
seen, while the surface is smooth and no bumps can be
observed after electrostatic dispersion. It can be concluded
that aggregated particles are separated by electrostatic
dispersion.
3.2. The influence of particle size
The influence of particle size on electrostatic dispersion
is illustrated in Fig. 4. The results show that good dispersion is observed when the particle size is larger than 25
mm, where electrostatic dispersion is not necessary. Particle aggregation becomes obvious when the particle size is
finer and electrostatic dispersion has the strongest effect on
Fig. 2. The effects of electrodes voltage on electrostatic dispersion:
1—calcium carbonate, 2—talcum, 3—corona current.
Fig. 3. Morphology of calcium carbonate and talcum particles before and
after electrostatic dispersion. 1—Original sample, 2—treated by electrostatic dispersion, a—calcium carbonate, b—talcum.
the particles with a size range from 2 to 25 mm. However,
the electrostatic dispersion effect is weakened markedly
for the particles smaller than 2 mm.
3.3. The effect of humidity on electrostatic dispersion
The humidity affects the electrostatic dispersion significantly. Fig. 5 illustrates the electrostatic dispersion effect
under different moisture content. It is obvious from the
figure that dispersion effect is much worse under higher
moisture, especially under higher electrode voltage. Fig. 6
Fig. 4. The influence of powder size of calcium carbonate on electrostatic
dispersion. Ž1. y45q37 mm, Ž2. y37q25 mm, Ž3. y25q10 mm, Ž4.
y10q2 mm, Ž5. y2 mm; a—original sample, b—treated by electrostatic dispersion.
190
J. Ren et al.r Powder Technology 120 (2001) 187–193
Fig. 5. The electrostatic dispersion behavior before and after water resorption: 1—before water resorption, 2—after water resortion; a—calcium carbonate,
b—talcum.
shows the dispersion index of calcium carbonate as a
function of the moisture content with and without electrostatic treatment. Figs. 5 and 6 mean that moisture content
should be strictly controlled, in order to achieve good
dispersion in the air. In that case, drying material is usually
very helpful.
3.4. The effect of rest time on dispersion of charged
particles
Tests are carried on at an air humidity of 70% in order
to study the effect of rest time. Fig. 7 shows that disper-
Fig. 6. The effect of water resortion amount on dispersion index of
calcium carbonate powder: 1—original sample, 2—treated by electrostatic dispersion.
sion index decreases progressively with the increase of rest
time. However, the speed of dispersion index decrease is
different with the change of rest time. Dispersion index
decreases slowly within the first 48 h, and then goes down
rapidly from 48 to 168 h, and the drop becomes gentle
again after 168 h. This results from the discharge of
charged particles according to physical principle.
3.5. Parameters optimisation
Under a charging voltage of 29 kV, the optimal parameters of electrostatic dispersion of calcium carbonate, tal-
Fig. 7. The effect of rest time on dispersion property: 1—calcium
carbonate, 2—talcum.
J. Ren et al.r Powder Technology 120 (2001) 187–193
191
Table 3
Optimised parameters of electrostatic dispersion and experimental results
Material
Experimental parameters
Calcium carbonate
Talcum
Calcium carbonateq Talcum
Experimental results
Voltage
ŽkV.
Humidity of
the air Ž%.
Ambient
temperature Ž8C.
a Before
dispersion Ž8.
a After
dispersion Ž8.
Dispersion
index, f
29
29
29
70
70
70
21
21
21
24.97
24.62
27.98
35.71
35.00
32.48
1.43
1.42
1.31
cum particles and the mixture of the two Ž1:1. were
studied and listed in Table 3.
electrostatic attractive force between particles in a natural
state can be represented as w2x:
Fg s 8.9 = 10y1 2 P d 2
Ž 6.
4. Discussion
4.1. Particle–particle interaction forces in the air
In general, fine particles in the air have great tendency
of aggregating due to the attractive surface force, such as
van der Waals force, liquid bridge force and attractive
force of surplus surface charges. After electrostatic dispersion, liquid bridge force and surplus charges on particle
surfaces are eliminated by electrostatic effect, except for
van der Waals force. At the same time, the particles carry
the same charge and the electrostatic force between particles is only the repulsive coulomb force.
4.1.1. Van der Waals force
In the air, van der Waals force between two particles
with same diameter can be represented as w8x:
FA s y
Ad
24 H 2
,
4.1.2. Liquid bridge force [1]
Another attractive force resulting in particle aggregation
is liquid bridge force, if the moisture content in powder is
high enough.
For particles with hydrophilic surface, liquid bridge
force at direct contact is:
Ž 4.
If u is defined as wetting contact angle of particles and
not equal to zero, liquid bridge force can be represented as:
FY s y2p R s P cos u
Fek s "
1
q1 q 2
Ž 5.
4.1.3. Electrostatic force
4.1.3.1. AttractiÕe force of surplus charges. In general,
surplus charges exist on the surface of particles, and the
Ž 7.
4p´ 0 r 2
where r s wŽ d 1 q d 2 . r2 x q H , q 1 s w3 ´ r r Ž ´ r q
2.xp´ 0 d i2 E0 . Put them into Eq. Ž7., then coulomb force Fek
can be written as:
Fek s 9p´ 0 E02
ž
´r
´r q 2
Ž 3.
where A is Hamaker constant of particles in vacuum, H is
the separation distance between two particles, d is the
diameter of particles.
FY s y Ž 1.4 ; 1.8 . p R s
4.1.3.2. Electrostatic repulsiÕe force. Electrostatic repulsive force arises between particles loaded with the same
charges. Provided the amount of charges on two spherical
particles equals to q1 and q2 , the distance between their
centers equals to r, the coulomb electrostatic force, Fek , of
two particles can be determined by w9x:
/ž
d1 d 2
d1 q d 2 q 2 H
2
/
Ž 8.
where ´ r is the dielectric constant of particles, H is the
distance between particles.
Coulomb forces, Fek , may be attractive or repulsive,
depending on the charge sign of two particles. For homogeneous charges, however, coulomb force, Fek , is always
repulsive and adjustable.
4.1.4. Total interaction force
In a natural state of powder, total interaction force
between two particles Ž FT . can be calculated by the addition of van der Waals force, attractive force of surplus
charges and liquid bridge force, that is:
FT s FA q FY q Fg
Ž 9.
After electrostatic dispersion, total interaction force between two charged particles Ž FT . can be calculated by the
addition of van der Waals force, electrostatic repulsive
force and liquid bridge force, that is:
FT s FA q FY q Fek
Ž 10 .
J. Ren et al.r Powder Technology 120 (2001) 187–193
192
Table 4
Critical radius of particles in electrostatic dispersion Žmm.
Particles
Calcium carbonate
Talcum
With liquid
bridge
No liquid
bridge
8.58
7.24
1.48
1.24
Introducing Eqs. Ž3., Ž7. and Ž14. into Eq. Ž13. yields:
36p´ 0
gs
ž
2
´r
/Ž
´r q 2
A11
12 H 2
Liquid bridge interaction can be left out of consideration in dry air, and the total force between two charged
particles will be expressed in the form:
FT s FA Fek
9p´ 0
gs
Fek G FA q FY
Ž 12 .
So the ratio of electrostatic repulsive force to the attractive forces, g, can serve as a criteria for electrostatic
dispersion:
gs
Fek
Ž 13 .
FA q FY
Particles will be electrostatically dispersed when g G 1.
From Eqs. Ž4. and Ž5., liquid bridge force can be
generally represented as follows:
FY s yhp R s
Ž 14 .
where h , a hydrophilic coefficient of particles, is correlated to the hydrophilicity of particles and equals to 2cos u .
2
E02
Ž 15 .
q hps
ž
2
´r
´r q 2
A11
12 H 2
Particles can be dispersed if the electrostatic repulsive
force is greater than the attractive forces, that is:
2 RqH .
It is accepted that the minimum distance between two
˚ Since H is so small
contacted particles is H s 4 A.
compared with radius of particles, that it can be neglected,
then Eq. Ž15. can be written as:
Ž 11 .
4.2. Criteria of electrostatic dispersion
R3
/
R
E02
Ž 16 .
q hps
g must be greater than 1 for a successful electrostatic
dispersion, and the critical radius of particles for electrostatic dispersion can be obtained then.
RG
ž
hps
A11
108p´ 0 H
2
q
9
/ž
1q
2
´r
2
/
1
Ž 17 .
E02
When liquid bridge force between two particles can be
neglected, the critical radius becomes:
RG
A11
108p´ 0 H
2
ž
1q
2
´r
2
/
1
Ž 18 .
E02
From Eqs. Ž17. and Ž18., the critical radius of particles
is related to the property of particles, the interfacial tension
of liquid in the liquid bridge and the intensity of charging
Table 5
Calculation results of interaction forces between particles Ž=10y8 N. and the criteria g for electrostatic dispersion
Radius
Žmm.
Calcium carbonate
FA
FY
Fek
FT
FAqY
gA
g AqY
Talcum
FA
FY
Fek
FT
FAqY
gA
g AqY
0.05
0.1
0.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
y0.16
y0.32
y1.62
y3.23
y6.46
y9.69
y12.96
y16.15
y19.23
y22.31
y25.84
y29.01
y32.30
y35.53
y38.76
y41.99
y45.22
y48.45
0.01
0.02
0.55
2.20
8.80
19.80
35.20
55.00
79.20
107.80
140.80
178.20
220.00
266.20
316.80
371.80
431.20
495.00
y0.93
y1.86
y8.87
y16.63
y28.86
y36.69
y40.16
y39.15
y33.63
y24.01
y9.84
8.73
31.70
59.07
90.84
127.01
167.58
212.50
y0.94
y1.88
y9.42
y18.83
y37.66
y56.49
y75.36
y94.15
y112.83
y131.81
y150.64
y169.47
y188.30
y207.13
y225.96
y244.79
y263.62
y282.50
0.06
0.06
0.34
0.68
1.36
2.04
2.72
3.41
4.10
4.83
5.45
6.14
6.81
7.49
8.17
8.85
9.54
10.22
0.01
0.01
0.06
0.12
0.22
0.35
0.47
0.58
0.70
0.82
0.93
1.05
1.17
1.29
1.40
1.52
1.64
1.75
y0.13
y0.26
y1.28
y2.56
y5.12
y7.68
y10.24
y12.80
y15.36
y17.92
y20.48
y23.04
y25.60
y28.16
y30.72
y33.28
y35.84
y38.40
y0.63
y1.25
y6.25
y12.50
y25.00
y37.50
y50.00
y62.50
y75.00
y87.50
y100.00
y112.50
y125.00
y137.50
y150.00
y166.50
y175.00
y187.50
0.0052
0.021
0.52
2.08
8.32
18.72
33.28
52.00
74.88
101.92
133.12
168.48
208.00
251.68
299.52
351.52
407.68
468.00
y0.76
y1.49
y7.01
y12.98
y21.80
y26.46
y26.96
y23.30
y15.48
y3.50
12.64
32.94
57.40
66.02
118.80
155.74
196.84
242.10
y0.76
y1.51
y7.53
y15.06
y30.12
y45.18
y60.24
y75.30
y90.36
y105.43
y120.48
y135.54
y150.60
y165.66
y180.72
y195.78
y210.48
y225.90
0.08
0.08
0.41
0.81
1.63
2.44
3.25
4.06
4.88
5.69
6.50
7.31
8.13
8.94
9.75
10.56
11.37
12.19
0.01
0.01
0.07
0.14
0.28
0.41
0.55
0.69
0.83
0.97
1.11
1.24
1.38
1.52
1.66
1.80
1.94
2.07
y0.78
y1.56
y7.80
y15.60
y31.20
y46.80
y62.40
y78.00
y93.60
y109.20
y124.80
y140.40
y156.00
y171.60
y187.20
y202.80
y218.40
y234.00
J. Ren et al.r Powder Technology 120 (2001) 187–193
field. When particle types and dispersion environment are
fixed, the critical radius of particles is inversely proportional to the square of the charging field intensity. So, the
critical radius of particles in electrostatic dispersion can be
reduced by increasing the charging field intensity.
4.3. Calculation and discussion
Electrostatic dispersion of dried calcium carbonate and
talcum particles is calculated using Eq. Ž12.. The original
data for calculation are: Hamaker constants w10,11x and
relative dielectric constants Ž ´ r . w12x of calcium carbonate
and talcum, 12.4 = 10y2 0 and 9.83 = 10y2 0 J, and 6.5 and
5.8, respectively; distance between two particles H s 4 =
10y1 0 m w13x; ´ 0 s 8.854 = 10y1 2 F; E0 s 2.57 = 10 7
Vrm; surface tension of water s s 0.071 Nrm w14x.
The relationship between critical radius of electrostatic
dispersion, criteria for electrostatic dispersion, and different interaction forces for calcium carbonate and talcum
particles are listed in Tables 4 and 5.
Corona charging can produce strong electrostatic repulsive force between particles. For particles with radius
larger than the critical radius, electrostatic repulsive force
is far stronger than the sum of van der Waals and liquid
bridge force. In such cases, the electrostatic repulsive force
dominates and the particles are dispersed. But the attractive forces may override, and particles are in aggregation
state when the particle size is smaller than the critical
radius. If the liquid bridge force between particles is
eliminated, the critical radius of particles in electrostatic
dispersion will be lowered significantly, as shown in Table
4. The critical radius of calcium carbonate and talcum are
reduced to 1.48 and 1.24 mm, respectively. Table 5 shows
that the calculated electrostatic dispersion criteria are in
good agreement with the experimental results.
5. Conclusion
Corona charging of particles can produce strong electrostatic repulsive force to resist the attractive forces between
particles. Electrostatic dispersion may be an effective way
to disperse fine particles, and the method is fit for the
powder of which good dispersion property is required,
while it is hard to achieve by common mechanical methods.
Nomenclature
A11
Hamaker constant ŽJ.
b,c
length Žm.
d
particle diameter Žm.
E0
intensity of electric field Žvrm.
f
FA
Fek
FY
FT
g
h
H
I
qi
R
V
a
r1
r2
´0
´r
s
u
193
dispersion index
van der Waals forces ŽN.
electrostatic forces ŽN.
liquid bridge forces ŽN.
total interaction forces ŽN.
criteria of electrostatic dispersion
height Žm.
inter-particle distance Žm.
electric current ŽA.
amount of powder charge ŽC.
particle radius Žm.
electric voltage ŽV.
sliding friction conical angle Ž8.
curvature radius of the circular meniscus Žm.
neck radius of the bridge Žm.
vacuum dielectric constant ŽF.
dielectric constant of powder
surface tension of liquid ŽNrm.
contact angle of powder with liquid Ž8.
Acknowledgements
This study was financed by the Nature Science Foundation of China.
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