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工业过程中粉体颗粒不可避免地会相互摩擦碰撞而荷电. 荷电颗粒的存在可能会危害正常的工业生产过程, 也可能对工业过程起促进作用. 因此, 荷电粉体颗粒及其特性受到了广泛的关注, 但目前对粉体颗粒的荷电机理依然缺乏透彻的了解, 尤其是在气固两相流动中的粉体颗粒荷电现象. 事实上, 工业中存在的粉体颗粒的运动都受到流体的影响, 是典型的气固两相流系统, 流体对粉体颗粒的作用使粉体颗粒接触的荷电现象变得更为复杂, 因此从两相流动的观点来研究粉体颗粒荷电的物理本质就显得越来越重要. 本文介绍了工业过程中的几种不同类型的粉体颗粒荷电行为, 回顾了颗粒的荷电机理与描述颗粒荷电的数学模型. 对于工业过程中颗粒的荷电现象及颗粒在多相流体中的动力学行为, 介绍了研究颗粒受流体影响时荷电特性的数值模拟方法. 本文旨在对粉体颗粒的荷电机理、应用以及研究方法进行梳理与探讨, 为正确认识工业过程中粉体颗粒的荷电现象并加以控制利用提供理论借鉴.Particles in industrial flows can be charged under an action of external electric field, while in the absence of external electric field, tribo-electrostatic charges are almost unavoidable in gas-solid two-phase flows due to the consecutive particle contacts. The particle charging may be beneficial, or detrimental. In the past decade considerable progress has been made in understanding the physics of particles charging. However, the particle charging mechanism, especially in the gas-solid phase flow, is still poorly understood. The purpose of this review is to present a clear understanding of the particle charging and movement of charged particle in two-phase flow, by summarizing the charging mechanisms, physical models of particle charging, and methods of charging/charged particle entrained fluid flow simulations. In this review, charged particles in industry, which would be beneficial (triboelectrostatic separation, electrostatic precipitator) or detrimental (electrification in gas-solid fluidized bed and manufacturing plant) are discussed separately. The particle charging through collisions could be attributed to electron transfer, ion transfer, material transfer, and/or aqueous ion shift on particle surfaces. For conductive particle contacts, the difference in work function is often used to explain the charge transfer. For insulation particle contacts, the charging tendency can be explained by the ion transfer and material transfer. In addition, aqueous ion shift transfer would be an important charge transfer mechanism considering water content in environmental conditions and the influences of temperature and humidity. The charges on particle through collision can be quantitatively predicted by using the particle charging model. According to the differently induced ways of charge transfer, the charging models are related to the external electric field, asymmetry contact, and/or aqueous ion shift on particle surfaces. In fact, the motions of particles in industry are influenced by fluid flow. The effect of fluid on particle dynamics makes the particle charging more complicated. Thus it is more reasonable to study the particle charging from the viewpoint of the gas-solid two-phase flow. The method combining particle charging model with computational fluid dynamics and discrete element method is applicable to the studying of the particle charging/charged processes in gas-solid two phase flow in which the charge behaviors are significantly influenced by the fluid mechanics behavior. By this method, the influence factors of particle charging, such as gas-particle interaction, contact force, contact area, and various velocities, are described systematically. This review presents a clear understanding of the particle charging and provides theoretical references on controlling and utilizing the charging/charged particles in industrial technology.
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Keywords:
- particle charging /
- charging mechanism /
- charging model /
- numerical methodology
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[2] Liu S H 2004 Electrostatic Discharge and Hazard Prevention (Beijing: Beijing University of Post and Telecommunications Press) p45 (in Chinese) [刘尚合 2004 静电放电及危害防护 (北京: 北京邮电大学出版社) 第45页]
[3] Sun K P 2000 Physics 29 364 (in Chinese) [孙可平 2000 物理 29 364]
[4] Enayati M, Chang M W, Bragman F, Edirisinghe M, Stride E 2011 Colloid Surf. A: Physicochem. Eng. Asp. 382 154
[5] Schein L B 2007 Science 316 1572
[6] Lacks D J, Sankaran R M 2011 J. Phys. D: Appl. Phys. 44 453001
[7] Liu X H, He W, Yang F, Wang H Y, Liao R J, Xiao H G 2012 Chin. Phys. B 21 075201
[8] Wu G Q, Li J, Xu Z M 2013 Waste Manage. 33 585
[9] Wu G Q 2013 Master Thesis (Shanghai: Shanghai Jiaotong University) (in Chinese) [吴贵青 2013 硕士学位论文 (上海: 上海交通大学)]
[10] Wang H F 2010 Ph. D. Dissertation (Xuzhou: China University of Mining & Technology) (in Chinese) [王海锋 2010 博士学位论文 (徐州: 中国矿业大学)]
[11] Manouchehri H R, Rao K H, Forssberg K S E 2000 Miner. Metall. Proc. 17 139
[12] Benabboun A, Tilmatine A, Brahami Y, Bendimerad S E, Miloudi M, Medles K 2014 Separ. Sci. Technol. 49 464
[13] Engers D A, Fricke M N, Newman A W, Morris K R 2007 J. Electrostat. 65 571
[14] Zhang J P, Du Y Y, Dai Y X, Pan W G 2011 Environmental Engineering 29 78 (in Chinese) [张建平, 杜玉颖, 戴咏夏, 潘卫国 2011 环境工程 29 78]
[15] Wang W 2013 Master Thesis (Hangzhou: Zhejiang University of Technology) (in Chinese) [王威 2013 硕士学位论文 杭州: 浙江工业大学]
[16] Jiang X D, Xu H, Wang X 2014 Chin. Phys. B 23 125201
[17] Adamiak K 2013 J. Electrostat. 71 673
[18] Long Z W,Yao Q 2012 Powder Technol. 215-216 26
[19] Long Z W, Yao Q 2010 J. Aerosol. Sci. 41 702
[20] Nouri H, Zouzou N, Moreau E, Dascalescu L, Zebboudj Y 2012 J. Electrostat. 70 20
[21] Rokkam R G, Sowinski A, Fox R O, Mehrani P, Muhle M E 2013 Chem. Eng. Sci. 92 146
[22] Wang F 2008 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [王芳 2008 博士学位论文 (杭州: 浙江大学)]
[23] Peng X 2013 Qilu Petrochemical Technology 41 140 (in Chinese) [彭啸 2013 齐鲁石油化工 41 140]
[24] Zhu Z C, Sun J Y, Huang Z L, Wang J D, Yang Y R 2013 Journal of Chemical Industry and Engineering (China) 64 490 (in Chinese) [朱子川, 孙婧元, 黄正梁, 王靖岱, 阳永荣 2013 化工学报 64 490]
[25] Moughrabiah W O, Grace J R, Bi X T 2012 Chem. Eng. Sci. 75 198
[26] Chen A H, Bi H T, Grace J R, van Willigen F K, van Ommen J R 2006 Aiche J. 52 174
[27] Chen A, Bi H T, Grace J R 2007 Powder Technol. 177 113
[28] Yu D Z 1988 Fire Science and Technology 21 3 (in Chinese) [俞大忠 1988 消防科学与技术 21 3]
[29] Zou X B, Mao Z G, Wang X X, Jiang W H 2013 Chin. Phys. B 22 045206
[30] Williams M W 2012 AIP Advances 2 010701
[31] Matsusaka S, Maruyama H, Matsuyama T, Ghadiri M 2010 Chem. Eng. Sci. 65 5781
[32] McCarty L S, Whitesides G M 2008 Angew. Chem. Int. Edit. 47 2188
[33] Lowell J, Truscott W S 1986 J. Phys. D: Appl. Phys. 19 1281
[34] Liu C, Bard A J 2008 Nat. Mater. 7 505
[35] Liu C, Bard A J 2009 Chem. Phys. Lett. 480 145
[36] Liu C, Bard A J 2009 J. Am. Chem. Soc. 131 6397
[37] Harper R W 1998 Contact and Frictional Electrification (Morgan Hill: Laplacian Press)
[38] Kornfeld M I 1976 J. Phys. D: Appl. Phys. 9 1183
[39] Apodaca M M, Wesson P J, Bishop K J M, Ratner M A, Grzybowski B A 2010 Angew. Chem. Int. Edit. 49 946
[40] Baytekin H T, Patashinski A Z, Branicki M, Baytekin B, Soh S, Grzybowski B A 2011 Science 333 308
[41] Baytekin H T, Baytekin B, Incorvati J T, Grzybowski B A 2012 Angewandte Chemie 124 4927
[42] Piperno S, Cohen H, Bendikov T, Lahav M, Lubomirsky I 2011 Angew. Chem. Int. Edit. 50 5654
[43] Ducati T R D, Simoões L S H, Galembeck F 2010 Langmuir. 26 13763
[44] Hogue M D, Mucciolo E R, Calle C I, Buhler C R 2005 J. Electrostat. 63 179
[45] Friedle S, Thomas S W 2010 Angew. Chem. Int. Edit. 49 7968
[46] Freier G D 1960 J. Geophys. Res. 65 3504
[47] Stow C D 1969 Rep. Prog. Phys. 32 1
[48] Farrell W M 2004 J. Geophys. Res. 109 E03004
[49] Williams E, Nathou N, Hicks E, Pontikis C, Russell B, Miller M, Bartholomew M J 2009 Atmos. Res. 91 292
[50] Inculet I I, Peter Castle G S, Aartsen G 2006 Chem. Eng. Sci. 61 2249
[51] Mehrani P, Bi H T, Grace J R 2005 J. Electrostat. 63 165
[52] Sowinski A, Miller L, Mehrani P 2010 Chem. Eng. Sci. 65 2771
[53] Pahtz T, Herrmann H J, Shinbrot T 2010 Nat. Phys. 6 364
[54] Lacks D J, Levandovsky A 2007 J. Electrostat. 65 107
[55] Kok J F, Lacks D J 2009 Phys. Rev. E 79 051304
[56] Zheng X J, Zhang R, Huang H J 2014 Sci. Rep. 4 4399
[57] Hu W, Xie L, Zheng X 2012 The European Physical Journal E: Soft Matter 35 1
[58] Kok J F, Renno N O 2008 Phys. Rev. Lett. 100 014501
[59] Gu Z L, Wei W, Su J W, Yu C W 2013 Sci. Rep. 3 1377
[60] Wei W, Lu L Y, Gu Z L 2012 Acta Phys. Sin. 61 158301 (in Chinese) [危卫, 鲁录义, 顾兆林 2012 物理学报 61 158301]
[61] Lu L Y, Gu Z L, Luo X L, Lei K B 2008 Acta Phys. Sin. 57 6939 (in Chinese) [鲁录义, 顾兆林, 罗昔联, 雷康斌 2008 物理学报 57 6939]
[62] Zhu H P, Zhou Z Y, Yang R Y, Yu A B 2007 Chem. Eng. Sci. 62 3378
[63] Zhu H P, Zhou Z Y, Yang R Y, Yu A B 2008 Chem. Eng. Sci. 63 5728
[64] Markatos N C 1986 Appl. Math. Model. 10 190
[65] Gui N 2010 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [桂南 2010 博士学位论文 (杭州: 浙江大学)]
[66] Gu Z, Jiao J, Zhang Y, Su J 2012 Int. J. Numer. Meth. Fl. 69 1457
[67] Gu Z, Jiao J, Su J 2011 Bound-lay. Meteorol. 139 439
[68] Fujihiro H 2003 Theor. Comp. Fluid Dyn. 16 387
[69] Spalart P R, Deck S, Shur M L, Squires K D 2006 Theor. Comp. Fluid Dyn. 20 181
[70] Shura M L, Spalartb P R, Streletsa M K, Travina A K 2008 Int. J. Heat Fluid Fl. 29 1638
[71] Gu Z L, Jiao J Y, Zhang Y W, Su J W 2011 Europhys. Lett. 94 34003
[72] Falkovich G 2011 Fluid Mechanics: A Short Course for Physicists (Cambridge: Cambridge University Press)
[73] Gu Z L 2010 Eolian Dust: Near Surface Layer Turbulence and Gas-Solid Flow (Beijing: Science Press) p273 (in Chinese) [顾兆林 2010 风扬粉尘: 近地层湍流与气固两相流 (北京: 科学出版社) 第273页]
[74] Lu L Y, Gu Z L, Lei K B 2009 Europhys. Lett. 87 44004
[75] Matsusaka S, Masuda H 2003 Adv. Powder Technol. 14 143
[76] Liu Z L, Bi X T T, Grace J R 2010 J. Electrostat. 68 321
[77] Iuga A, Calin L, Neamtu V, Mihalcioiu A, Dascalescu L 2005 J. Electrostat. 63 937
[78] Mehrani P, Bi H T, Grace J R 2005 J. Electrostat. 63 165
[79] Schmid H J, Vogel L 2003 Powder Technol. 135 118
[80] Lim E W C, Zhang Y, Wang C H 2006 Chem. Eng. Sci. 61 7889
[81] Jalalinejad F, Bi X T T, Grace J R 2012 Int. J. Multiphas. Flow 44 15
[82] Lim E W C, Yao J, Zhao Y L 2012 Aiche J. 58 1040
[83] Bo T L, Zhang H, Zhu W, Zheng X J 2013 J. Geophys. Res. 118 4494
[84] Nwose E N, Pei C, Wu C Y 2012 Particuology 10 229
[85] Cheng Y P, Lau D Y J, Guan G Q, Fushimi C, Tsutsumi A, Wang C H 2012 Ind. Eng. Chem. Res. 51 14258
[86] Laurentie J C, Traore P, Dascalescu L 2013 J. Electrostat. 71 951
[87] Matsusaka S, Ghadiri M, Masuda H 2000 J. Phys. D: Appl. Phys. 33 2311
[88] Pei C L, Wu C Y, England D, Byard S, Berchtold H, Adams M 2013 Powder Technol. 248 34
[89] Zheng X, Huang N, Zhou Y 2003 J. Geophys. Res. 108 4322
[90] Castle G S P, Schein L B 1995 J. Electrostat. 36 165
[91] Girardi M 2010 J. Electrostat. 68 409
[92] Ireland P M 2010 Powder Technol. 198 199
[93] Pham R, Virnelson R C, Sankaran R M, Lacks D J 2011 J. Electrostat. 69 456
[94] Sow M, Lacks D J, Sankaran R M 2013 J. Electrostat. 71 396
[95] Shinbrot T, Komatsu T S, Zhao Q 2008 Europhys. Lett. 83 24004
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[1] Zhou B M, Liu S H, Fan B C 2004 Physics 33 759 (in Chinese) [周本谋, 刘尚合, 范宝春 2004 物理 33 759]
[2] Liu S H 2004 Electrostatic Discharge and Hazard Prevention (Beijing: Beijing University of Post and Telecommunications Press) p45 (in Chinese) [刘尚合 2004 静电放电及危害防护 (北京: 北京邮电大学出版社) 第45页]
[3] Sun K P 2000 Physics 29 364 (in Chinese) [孙可平 2000 物理 29 364]
[4] Enayati M, Chang M W, Bragman F, Edirisinghe M, Stride E 2011 Colloid Surf. A: Physicochem. Eng. Asp. 382 154
[5] Schein L B 2007 Science 316 1572
[6] Lacks D J, Sankaran R M 2011 J. Phys. D: Appl. Phys. 44 453001
[7] Liu X H, He W, Yang F, Wang H Y, Liao R J, Xiao H G 2012 Chin. Phys. B 21 075201
[8] Wu G Q, Li J, Xu Z M 2013 Waste Manage. 33 585
[9] Wu G Q 2013 Master Thesis (Shanghai: Shanghai Jiaotong University) (in Chinese) [吴贵青 2013 硕士学位论文 (上海: 上海交通大学)]
[10] Wang H F 2010 Ph. D. Dissertation (Xuzhou: China University of Mining & Technology) (in Chinese) [王海锋 2010 博士学位论文 (徐州: 中国矿业大学)]
[11] Manouchehri H R, Rao K H, Forssberg K S E 2000 Miner. Metall. Proc. 17 139
[12] Benabboun A, Tilmatine A, Brahami Y, Bendimerad S E, Miloudi M, Medles K 2014 Separ. Sci. Technol. 49 464
[13] Engers D A, Fricke M N, Newman A W, Morris K R 2007 J. Electrostat. 65 571
[14] Zhang J P, Du Y Y, Dai Y X, Pan W G 2011 Environmental Engineering 29 78 (in Chinese) [张建平, 杜玉颖, 戴咏夏, 潘卫国 2011 环境工程 29 78]
[15] Wang W 2013 Master Thesis (Hangzhou: Zhejiang University of Technology) (in Chinese) [王威 2013 硕士学位论文 杭州: 浙江工业大学]
[16] Jiang X D, Xu H, Wang X 2014 Chin. Phys. B 23 125201
[17] Adamiak K 2013 J. Electrostat. 71 673
[18] Long Z W,Yao Q 2012 Powder Technol. 215-216 26
[19] Long Z W, Yao Q 2010 J. Aerosol. Sci. 41 702
[20] Nouri H, Zouzou N, Moreau E, Dascalescu L, Zebboudj Y 2012 J. Electrostat. 70 20
[21] Rokkam R G, Sowinski A, Fox R O, Mehrani P, Muhle M E 2013 Chem. Eng. Sci. 92 146
[22] Wang F 2008 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [王芳 2008 博士学位论文 (杭州: 浙江大学)]
[23] Peng X 2013 Qilu Petrochemical Technology 41 140 (in Chinese) [彭啸 2013 齐鲁石油化工 41 140]
[24] Zhu Z C, Sun J Y, Huang Z L, Wang J D, Yang Y R 2013 Journal of Chemical Industry and Engineering (China) 64 490 (in Chinese) [朱子川, 孙婧元, 黄正梁, 王靖岱, 阳永荣 2013 化工学报 64 490]
[25] Moughrabiah W O, Grace J R, Bi X T 2012 Chem. Eng. Sci. 75 198
[26] Chen A H, Bi H T, Grace J R, van Willigen F K, van Ommen J R 2006 Aiche J. 52 174
[27] Chen A, Bi H T, Grace J R 2007 Powder Technol. 177 113
[28] Yu D Z 1988 Fire Science and Technology 21 3 (in Chinese) [俞大忠 1988 消防科学与技术 21 3]
[29] Zou X B, Mao Z G, Wang X X, Jiang W H 2013 Chin. Phys. B 22 045206
[30] Williams M W 2012 AIP Advances 2 010701
[31] Matsusaka S, Maruyama H, Matsuyama T, Ghadiri M 2010 Chem. Eng. Sci. 65 5781
[32] McCarty L S, Whitesides G M 2008 Angew. Chem. Int. Edit. 47 2188
[33] Lowell J, Truscott W S 1986 J. Phys. D: Appl. Phys. 19 1281
[34] Liu C, Bard A J 2008 Nat. Mater. 7 505
[35] Liu C, Bard A J 2009 Chem. Phys. Lett. 480 145
[36] Liu C, Bard A J 2009 J. Am. Chem. Soc. 131 6397
[37] Harper R W 1998 Contact and Frictional Electrification (Morgan Hill: Laplacian Press)
[38] Kornfeld M I 1976 J. Phys. D: Appl. Phys. 9 1183
[39] Apodaca M M, Wesson P J, Bishop K J M, Ratner M A, Grzybowski B A 2010 Angew. Chem. Int. Edit. 49 946
[40] Baytekin H T, Patashinski A Z, Branicki M, Baytekin B, Soh S, Grzybowski B A 2011 Science 333 308
[41] Baytekin H T, Baytekin B, Incorvati J T, Grzybowski B A 2012 Angewandte Chemie 124 4927
[42] Piperno S, Cohen H, Bendikov T, Lahav M, Lubomirsky I 2011 Angew. Chem. Int. Edit. 50 5654
[43] Ducati T R D, Simoões L S H, Galembeck F 2010 Langmuir. 26 13763
[44] Hogue M D, Mucciolo E R, Calle C I, Buhler C R 2005 J. Electrostat. 63 179
[45] Friedle S, Thomas S W 2010 Angew. Chem. Int. Edit. 49 7968
[46] Freier G D 1960 J. Geophys. Res. 65 3504
[47] Stow C D 1969 Rep. Prog. Phys. 32 1
[48] Farrell W M 2004 J. Geophys. Res. 109 E03004
[49] Williams E, Nathou N, Hicks E, Pontikis C, Russell B, Miller M, Bartholomew M J 2009 Atmos. Res. 91 292
[50] Inculet I I, Peter Castle G S, Aartsen G 2006 Chem. Eng. Sci. 61 2249
[51] Mehrani P, Bi H T, Grace J R 2005 J. Electrostat. 63 165
[52] Sowinski A, Miller L, Mehrani P 2010 Chem. Eng. Sci. 65 2771
[53] Pahtz T, Herrmann H J, Shinbrot T 2010 Nat. Phys. 6 364
[54] Lacks D J, Levandovsky A 2007 J. Electrostat. 65 107
[55] Kok J F, Lacks D J 2009 Phys. Rev. E 79 051304
[56] Zheng X J, Zhang R, Huang H J 2014 Sci. Rep. 4 4399
[57] Hu W, Xie L, Zheng X 2012 The European Physical Journal E: Soft Matter 35 1
[58] Kok J F, Renno N O 2008 Phys. Rev. Lett. 100 014501
[59] Gu Z L, Wei W, Su J W, Yu C W 2013 Sci. Rep. 3 1377
[60] Wei W, Lu L Y, Gu Z L 2012 Acta Phys. Sin. 61 158301 (in Chinese) [危卫, 鲁录义, 顾兆林 2012 物理学报 61 158301]
[61] Lu L Y, Gu Z L, Luo X L, Lei K B 2008 Acta Phys. Sin. 57 6939 (in Chinese) [鲁录义, 顾兆林, 罗昔联, 雷康斌 2008 物理学报 57 6939]
[62] Zhu H P, Zhou Z Y, Yang R Y, Yu A B 2007 Chem. Eng. Sci. 62 3378
[63] Zhu H P, Zhou Z Y, Yang R Y, Yu A B 2008 Chem. Eng. Sci. 63 5728
[64] Markatos N C 1986 Appl. Math. Model. 10 190
[65] Gui N 2010 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [桂南 2010 博士学位论文 (杭州: 浙江大学)]
[66] Gu Z, Jiao J, Zhang Y, Su J 2012 Int. J. Numer. Meth. Fl. 69 1457
[67] Gu Z, Jiao J, Su J 2011 Bound-lay. Meteorol. 139 439
[68] Fujihiro H 2003 Theor. Comp. Fluid Dyn. 16 387
[69] Spalart P R, Deck S, Shur M L, Squires K D 2006 Theor. Comp. Fluid Dyn. 20 181
[70] Shura M L, Spalartb P R, Streletsa M K, Travina A K 2008 Int. J. Heat Fluid Fl. 29 1638
[71] Gu Z L, Jiao J Y, Zhang Y W, Su J W 2011 Europhys. Lett. 94 34003
[72] Falkovich G 2011 Fluid Mechanics: A Short Course for Physicists (Cambridge: Cambridge University Press)
[73] Gu Z L 2010 Eolian Dust: Near Surface Layer Turbulence and Gas-Solid Flow (Beijing: Science Press) p273 (in Chinese) [顾兆林 2010 风扬粉尘: 近地层湍流与气固两相流 (北京: 科学出版社) 第273页]
[74] Lu L Y, Gu Z L, Lei K B 2009 Europhys. Lett. 87 44004
[75] Matsusaka S, Masuda H 2003 Adv. Powder Technol. 14 143
[76] Liu Z L, Bi X T T, Grace J R 2010 J. Electrostat. 68 321
[77] Iuga A, Calin L, Neamtu V, Mihalcioiu A, Dascalescu L 2005 J. Electrostat. 63 937
[78] Mehrani P, Bi H T, Grace J R 2005 J. Electrostat. 63 165
[79] Schmid H J, Vogel L 2003 Powder Technol. 135 118
[80] Lim E W C, Zhang Y, Wang C H 2006 Chem. Eng. Sci. 61 7889
[81] Jalalinejad F, Bi X T T, Grace J R 2012 Int. J. Multiphas. Flow 44 15
[82] Lim E W C, Yao J, Zhao Y L 2012 Aiche J. 58 1040
[83] Bo T L, Zhang H, Zhu W, Zheng X J 2013 J. Geophys. Res. 118 4494
[84] Nwose E N, Pei C, Wu C Y 2012 Particuology 10 229
[85] Cheng Y P, Lau D Y J, Guan G Q, Fushimi C, Tsutsumi A, Wang C H 2012 Ind. Eng. Chem. Res. 51 14258
[86] Laurentie J C, Traore P, Dascalescu L 2013 J. Electrostat. 71 951
[87] Matsusaka S, Ghadiri M, Masuda H 2000 J. Phys. D: Appl. Phys. 33 2311
[88] Pei C L, Wu C Y, England D, Byard S, Berchtold H, Adams M 2013 Powder Technol. 248 34
[89] Zheng X, Huang N, Zhou Y 2003 J. Geophys. Res. 108 4322
[90] Castle G S P, Schein L B 1995 J. Electrostat. 36 165
[91] Girardi M 2010 J. Electrostat. 68 409
[92] Ireland P M 2010 Powder Technol. 198 199
[93] Pham R, Virnelson R C, Sankaran R M, Lacks D J 2011 J. Electrostat. 69 456
[94] Sow M, Lacks D J, Sankaran R M 2013 J. Electrostat. 71 396
[95] Shinbrot T, Komatsu T S, Zhao Q 2008 Europhys. Lett. 83 24004
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