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Electrostatic dispersion of fine particles in the air
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: [email protected] 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.
References w1x S.C. Lu, Processing Technology of Powder, Light Industry Press, Beijing, 1998, pp. 43–49 Žin Chinese.. w2x H. Yamamoto, S. Shioji, J. Soc. Powder Technol., Jpn. 27 Ž1990. 159–163 Žin Japanese.. w3x H. Yamamoto, T. Mastuyama, J. Soc. Powder Technol., Jpn. 28 Ž1991. 188–193 Žin Japanese.. w4x H. Masuda, K. Gotoh, J. Soc. Powder Technol., Jpn. 30 Ž1993. 703–708 Žin Japanese.. w5x J. Ren, Dispersion behavior and new dispersion methods of microparticles in liquid phase and the air, Doctoral Dissertation, University of Science and Technology Beijing, p. 4, 1999 Žin Chinese.. w6x F. Zeng, Y.P. Hu, Particuology of Mineral Processing, Chinese Mining Univ. Press, Beijing, 1995, p. 180 Žin Chinese.. w7x K. Kawakika, M. Koishi, S. Taneya, Yejin Jiancai Huagong Shipin, Powder Engineering, Wuhan, Wuhan Industry Univ. Press, Wuhan, 1991, p. 74 Žin Chinese.. w8x H.C. Hamaker, Phvsica 4 Ž1937. 1058–1072. w9x Q.M. Sun, Static Electr. 3 Ž1993. 19–21 Žin Japanese.. w10x J.N. Israelachvili, Intermolecular and Surface Forces, Academic Press, London, 1985, p. 295. w11x Y.H. Hu, Mine Metall. Eng. 14 Ž1994. 23 Žin Chinese.. w12x Institute of Mine and Metallurgy Changsha, Electrical Selection of Mine, Metallurgy Industry Press, Baijing, 1982, p. 65 Žin Chinese.. w13x Y. Endo, Y. Kousaka, J. Soc. Powder Technol., Jpn. 33 Ž1996. 30–36 Žin Japanese.. w14x N.L. Cheng, S.W. Hu, Solvent Manual, Chemical Industry Press, Beijing, 1986, p. 378 Žin Chinese..
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: [email protected] 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.
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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.
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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 .
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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
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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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