表面纳米气泡表征及其强化微细颗粒浮选机理综述

马芳源; Patrick Zhang; 陶东平

doi:10.1007/s12613-022-2450-3

Volume 29 Issue 4

Apr. 2022

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文章导航 > 矿物冶金与材料学报（英文） > 2022 > 29(4): 727-738

Fangyuan Ma, Patrick Zhang, and Dongping Tao, Surface nanobubble characterization and its enhancement mechanisms for fine-particle flotation: A review, Int. J. Miner. Metall. Mater., 29(2022), No. 4, pp. 727-738. https://doi.org/10.1007/s12613-022-2450-3

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Fangyuan Ma, Patrick Zhang, and Dongping Tao, Surface nanobubble characterization and its enhancement mechanisms for fine-particle flotation: A review, Int. J. Miner. Metall. Mater., 29(2022), No. 4, pp. 727-738. https://doi.org/10.1007/s12613-022-2450-3

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特约综述

表面纳米气泡表征及其强化微细颗粒浮选机理综述

1)
山东理工大学资源与环境工程学院，淄博 255049，中国
2)
Florida Industrial and Phosphate Research Institute, Florida Polytechnic University, Florida 33830, USA

通讯作者:
陶东平 E-mail: dptao@qq.com

文章亮点

(1) 系统介绍了纳米气泡的产生方法、稳定理论及其适用性。

(2) 深入讨论了表面纳米气泡强化微细颗粒浮选的作用机理。

(3) 提出了现有研究的不足之处和未来研究的方向。

中文摘要

泡沫浮选常用于微细矿物颗粒分离，但其工艺效率会随着颗粒尺寸的减小而迅速降低，导致宝贵资源的大量浪费。微细颗粒的高效分离一直是矿物加工领域面临的主要挑战。近年来，在浮选过程中使用纳米气泡被认为是提高微细颗粒回收率的有效方法。与传统宏观气泡相比，纳米气泡具有独特的表面理化特性，它们对微细颗粒浮选行为的影响机理是当前研究的热点。本文重点讨论了表面纳米气泡的生成途径、稳定理论和独特性质，概述了其强化微细颗粒浮选性能的应用效果和作用机理，总结了近年来的主要研究成果和不足之处，提出了未来相关领域的研究方向和需求。文章可助读者全面深入地了解纳米气泡浮选的基本原理和最新动态，开发应用有效可行的微细颗粒浮选工艺和技术。

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Invited Review

Surface nanobubble characterization and its enhancement mechanisms for fine-particle flotation: A review

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Abstract

Abstract

Froth flotation is often used for fine-particle separation, but its process efficiency rapidly decreases with decreasing particle size. The efficient separation of ultrafine particles (UFPs) has been a major challenge in the mineral processing field for many years. In recent years, the use of surface nanobubbles in the flotation process has been recognized as an effective approach for enhancing the recovery of UFPs. Compared with traditional macrobubbles, nanobubbles possess unique surface and bulk characteristics, and their effects on the UFP flotation behavior have been a topic of intensive research. This review article is focused on the studies on various unique characteristics of nanobubbles and their mechanisms of enhancing the UFP flotation. The purpose of this article is to summarize the major achievements on the two topics and pinpoint future research needs for a better understanding of the fundamentals of surface nanobubble flotation and developing more feasible and efficient processes for fine and UFPs.
- surface nanobubbles;
- characterization;
- flotation;
- ultrafine particles;
- high-efficiency separation

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References

[1]	Q.Y. Sun, W.Z. Yin, D. Li, Y.F. Fu, J.W. Xue, and J. Yao, Improving the sulfidation−flotation of fine cuprite by hydrophobic flocculation pretreatment, Int. J. Miner. Metall. Mater., 25(2018), No. 11, p. 1256. doi: 10.1007/s12613-018-1678-4
[2]	H.Q. Hao, L.X. Li, P. Somasundaran, and Z.T. Yuan, Adsorption of pregelatinized starch for selective flocculation and flotation of fine siderite, Langmuir, 35(2019), No. 21, p. 6878. doi: 10.1021/acs.langmuir.9b00669
[3]	Z. Wang, N.Y. Liu, and D. Zou, Interface adsorption mechanism of the improved flotation of fine pyrite by hydrophobic flocculation, Sep. Purif. Technol., 275(2021), art. No. 119245. doi: 10.1016/j.seppur.2021.119245
[4]	A.R.S.d. Medeiros and C.A.M. Baltar, Importance of collector chain length in flotation of fine particles, Miner. Eng., 122(2018), p. 179. doi: 10.1016/j.mineng.2018.03.008
[5]	C. Yang, X.Y. Liu, W.H. Gao, Z.H. Zhang, H.Q. Wang, X.J. Lyu, J. Qiu, X.N. Zhu, and L. Li, Clean flotation of fine coal assisted by renewable collector prepared from waste oils, Energy Sources A, (2020). DOI: 10.1080/15567036.2020.1806406
[6]	X.N. Zhu, D.Z. Wang, Y. Ni, J.X. Wang, C.C. Nie, C. Yang, X.J. Lyu, J. Qiu, and L. Li, Cleaner approach to fine coal flotation by renewable collectors prepared by waste oil transesterification, J. Clean. Prod., 252(2020), art. No. 119822. doi: 10.1016/j.jclepro.2019.119822
[7]	A. Sobhy and D. Tao, High-efficiency nanobubble coal flotation, Int. J. Coal Prep. Util., 33(2013), No. 5, p. 242. doi: 10.1080/19392699.2013.810623
[8]	C.W. Li, M. Xu, Y.W. Xing, H.J. Zhang, and U.A. Peuker, Efficient separation of fine coal assisted by surface nanobubbles, Sep. Purif. Technol., 249(2020), art. No. 117163. doi: 10.1016/j.seppur.2020.117163
[9]	F.Y. Ma, D.P. Tao, Y.J. Tao, and S.Y. Liu, An innovative flake graphite upgrading process based on HPGR, stirred grinding mill, and nanobubble column flotation, Int. J. Min. Sci. Technol., 31(2021), No. 6, p. 1063. doi: 10.1016/j.ijmst.2021.06.005
[10]	D.P. Tao, Z.X. Wu, and A. Sobhy, Investigation of nanobubble enhanced reverse anionic flotation of hematite and associated mechanisms, Powder Technol., 379(2021), p. 12. doi: 10.1016/j.powtec.2020.10.040
[11]	A. Sobhy and D. Tao, Nanobubble column flotation of fine coal particles and associated fundamentals, Int. J. Miner. Process., 124(2013), p. 109. doi: 10.1016/j.minpro.2013.04.016
[12]	R. Ahmadi, D.A. Khodadadi, M. Abdollahy, and M. Fan, Nano-microbubble flotation of fine and ultrafine chalcopyrite particles, Int. J. Min. Sci. Technol., 24(2014), No. 4, p. 559-566. doi: 10.1016/j.ijmst.2014.05.021
[13]	W.G. Zhou, L.M. Ou, Q. Shi, Q.M. Feng and H. Chen, Different flotation performance of ultrafine scheelite under two hydrodynamic cavitation modes, Minerals, 8(2018), No. 7, p. 264. doi: 10.3390/min8070264
[14]	C.W. Li and H.J. Zhang, Surface nanobubbles and their roles in flotation of fine particles—A review, J. Ind. Eng. Chem., 106(2022), p. 37. doi: 10.1016/j.jiec.2021.11.009
[15]	J.G. Lee and R.W. Flumerfelt, A refined approach to bubble nucleation and polymer foaming process: Dissolved gas and cluster size effects, J. Colloid Interface Sci., 184(1996), No. 2, p. 335. doi: 10.1006/jcis.1996.0628
[16]	J.C. Eriksson and S. Ljunggren, On the mechanically unstable free energy minimum of a gas bubble which is submerged in water and adheres to a hydrophobic wall, Colloids Surf. A, 159(1999), No. 1, p. 159. doi: 10.1016/S0927-7757(99)00171-5
[17]	D.E. Yount and T.D. Kunkle, Gas nucleation in the vicinity of solid hydrophobic spheres, J. Appl. Phys., 46(1975), No. 10, p. 4484. doi: 10.1063/1.321381
[18]	X.Y. Zhang, Q.S. Wang, Z.X. Wu, and D.P. Tao, An experimental study on size distribution and zeta potential of bulk cavitation nanobubbles, Int. J. Miner. Metall. Mater., 27(2020), No. 2, p. 152. doi: 10.1007/s12613-019-1936-0
[19]	M.M. Fan, D. Tao, R. Honaker, and Z.F. Luo, Nanobubble generation and its application in froth flotation (part I): Nanobubble generation and its effects on properties of microbubble and millimeter scale bubble solutions, Min. Sci. Technol., 20(2010), No. 1, p. 1. doi: 10.1016/S1674-5264(09)60154-X
[20]	F.Y. Ma, D.P. Tao, and Y.J. Tao, Effects of nanobubbles in column flotation of Chinese sub-bituminous coal, Int. J. Coal Prep. Util., 2019. DOI: 10.1080/19392699.2019.1692340
[21]	R. Etchepare, H. Oliveira, M. Nicknig, A. Azevedo, and J. Rubio, Nanobubbles: Generation using a multiphase pump, properties and features in flotation, Miner. Eng., 112(2017), p. 19. doi: 10.1016/j.mineng.2017.06.020
[22]	H. Oliveira, A. Azevedo, and J. Rubio, Nanobubbles generation in a high-rate hydrodynamic cavitation tube, Miner. Eng., 116(2018), p. 32. doi: 10.1016/j.mineng.2017.10.020
[23]	A.F. Rosa and J. Rubio, On the role of nanobubbles in particle-bubble adhesion for the flotation of quartz and apatitic minerals, Miner. Eng., 127(2018), p. 178. doi: 10.1016/j.mineng.2018.08.020
[24]	C.W. Li, X. Li, M. Xu, and H.J. Zhang, Effect of ultrasonication on the flotation of fine graphite particles: Nanobubbles or not? Ultrason. Sonochem., 69(2020), art. No. 105243.
[25]	F.F. Zhang, L.J. Sun, H.C. Yang, X.H. Gui, H. Schönherr, M. Kappl, Y.J. Cao, and Y.W. Xing, Recent advances for understanding the role of nanobubbles in particles flotation, Adv. Colloid Interface Sci., 291(2021), art. No. 102403. doi: 10.1016/j.cis.2021.102403
[26]	N. Chen, Z.W. Wen, X.F. Li, Z.X. Ye, D.F. Ren, J.Q. Xu, Q.M. Chen, and S.Y. Ma, Controllable preparation and formation mechanism of monodispersed bulk nanobubbles in dilute ethanol-water solutions, Colloids Surf. A, 616(2021), art. No. 126372. doi: 10.1016/j.colsurfa.2021.126372
[27]	S.T. Lou, J.X. Gao, X.D. Xiao, X.J. Li, G.L. Li, Y. Zhang, M. Li, J.L. Sun, X.H. Li, and J. Hu, Studies of nanobubbles produced at liquid/solid interfaces, Mater. Charact., 48(2002), No. 2-3, p. 211. doi: 10.1016/S1044-5803(02)00241-3
[28]	R. Hao, Y.S. Fan, M.D. Howard, J.C. Vaughan, and B. Zhang, Imaging nanobubble nucleation and hydrogen spillover during electrocatalytic water splitting, PNAS, 115(2018), No. 23, p. 5878. doi: 10.1073/pnas.1800945115
[29]	M.M. Zhang, J.R.T. Seddon, and S.G, Lemay, Nanoparticle–nanobubble interactions: Charge inversion and re-entrant condensation of amidine latex nanoparticles driven by bulk nanobubbles, J. Colloid Interface Sci., 538(2019), p. 605. doi: 10.1016/j.jcis.2018.11.110
[30]	K. Kikuchi, S. Nagata, Y. Tanaka, Y. Saihara, and Z. Ogumi, Characteristics of hydrogen nanobubbles in solutions obtained with water electrolysis, J. Electroanal. Chem., 600(2007), No. 2, p. 303. doi: 10.1016/j.jelechem.2006.10.005
[31]	F.F. Zhang, Y.W. Xing, L.J. Sun, M. Liu, X.H. Gui, and Y.J. Cao, Characteristics of interfacial nanobubbles and their interaction with solid surfaces, Appl. Surf. Sci., 550(2021), art. No. 149258. doi: 10.1016/j.apsusc.2021.149258
[32]	S.J. Yang, S.M. Dammer, N. Bremond, H.J.W. Zandvliet, E.S. Kooij, and D. Lohse, Characterization of nanobubbles on hydrophobic surfaces in water, Langmuir, 23(2007), No. 13, p. 7072. doi: 10.1021/la070004i
[33]	L.M. Zhou, S. Wang, J. Qiu, L. Wang, X.Y. Wang, B. Li, L.J. Zhang, and J. Hu, Interfacial nanobubbles produced by long-time preserved cold water, Chin. Phys. B, 26(2017), No. 10, art. No. 106803. doi: 10.1088/1674-1056/26/10/106803
[34]	C.L. Xu, S.H. Peng, G.G. Qiao, V. Gutowski, D. Lohse, and X.H. Zhang, Nanobubble formation on a warmer substrate, Soft Matter, 10(2014), No. 39, p. 7857. doi: 10.1039/C4SM01025F
[35]	A. Azevedo, R. Etchepare, S. Calgaroto, and J. Rubio, Aqueous dispersions of nanobubbles: Generation, properties and features, Miner. Eng., 94(2016), p. 29. doi: 10.1016/j.mineng.2016.05.001
[36]	G. Ferraro, A.J. Jadhav, and M. Barigou, A Henry’s law method for generating bulk nanobubbles, Nanoscale, 12(2020), No. 29, p. 15869. doi: 10.1039/D0NR03332D
[37]	R. Etchepare, A. Azevedo, S. Calgaroto, and J. Rubio, Removal of ferric hydroxide by flotation with micro and nanobubbles, Sep. Purif. Technol., 184(2017), p. 347. doi: 10.1016/j.seppur.2017.05.014
[38]	N. Hain, S. Handschuh-Wang, D. Wesner, S.I. Druzhinin, and H. Schönherr, Multimodal microscopy-based identification of surface nanobubbles, J. Colloid Interface Sci., 547(2019), p. 162. doi: 10.1016/j.jcis.2019.03.084
[39]	H.S. Liao, C.W. Yang, H.C. Ko, E.T. Hwu, and I.S. Hwang, Imaging initial formation processes of nanobubbles at the graphite-water interface through high-speed atomic force microscopy, Appl. Surf. Sci., 434(2018), p. 913. doi: 10.1016/j.apsusc.2017.11.044
[40]	W. Guo, H. Shan, M. Guan, L.H. Gao, M.H. Liu, and Y.M. Dong, Investigation on nanobubbles on graphite substrate produced by the water-NaCl solution replacement, Surf. Sci., 606(2012), No. 17-18, p. 1462. doi: 10.1016/j.susc.2012.05.018
[41]	F.F. Zhang, Y.W. Xing, G.H. Chang, Z.L. Yang, Y.J. Cao, and X.H. Gui, Enhanced lignite flotation using interfacial nanobubbles based on temperature difference method, Fuel, 293(2021), art. No. 120313. doi: 10.1016/j.fuel.2021.120313
[42]	N. Ishida, T. Inoue, M. Miyahara, and K. Higashitani, Nano bubbles on a hydrophobic surface in water observed by tapping-mode atomic force microscopy, Langmuir, 16(2000), No. 16, p. 6377. doi: 10.1021/la000219r
[43]	L.M. Zhou, X.Y. Wang, S. Hyun-Joon, L.J. Zhang, and J. Hu, Surface nanobubbles produced by cold water investigated using scanning transmission X-ray microscopy, Microsc. Microanal., 24(2018), No. S2, p. 470. doi: 10.1017/S1431927618014587
[44]	C.L. Owens, E. Schach, T. Heinig, M. Rudolph, and G.R. Nash, Surface nanobubbles on the rare earth fluorcarbonate mineral synchysite, J. Colloid Interface Sci., 552(2019), p. 66. doi: 10.1016/j.jcis.2019.05.014
[45]	L.J. Zhang, Y. Zhang, X.H. Zhang, Z.X. Li, G.X. Shen, M. Ye, C.H. Fan, H.P. Fang, and J. Hu, Electrochemically controlled formation and growth of hydrogen nanobubbles, Langmuir, 22(2006), No. 19, p. 8109. doi: 10.1021/la060859f
[46]	Q.J. Chen, L. Luo, and H.S. White, Electrochemical generation of a hydrogen bubble at a recessed platinum nanopore electrode, Langmuir, 31(2015), No. 15, p. 4573. doi: 10.1021/acs.langmuir.5b00234
[47]	Q.J. Chen, L. Luo, H. Faraji, S.W. Feldberg, and H.S. White, Electrochemical measurements of single H₂ nanobubble nucleation and stability at Pt nanoelectrodes, J. Phys. Chem. Lett., 5(2014), No. 20, p. 3539. doi: 10.1021/jz501898r
[48]	X.H. Zhang, D.Y.C. Chan, D.Y. Wang, and N. Maeda, Stability of interfacial nanobubbles, Langmuir, 29(2013), No. 4, p. 1017. doi: 10.1021/la303837c
[49]	S. Calgaroto, K.Q. Wilberg, and J. Rubio, On the nanobubbles interfacial properties and future applications in flotation, Miner. Eng., 60(2014), p. 33. doi: 10.1016/j.mineng.2014.02.002
[50]	W. Xiao, X.X. Wang, L.M. Zhou, W.G. Zhou, J. Wang, W.Q. Qin, G.Z. Qiu, J. Hu, and L.J. Zhang, Influence of mixing and nanosolids on the formation of nanobubbles, J. Phys. Chem. B, 123(2019), No. 1, p. 317. doi: 10.1021/acs.jpcb.8b11385
[51]	W. Walczyk and H. Schönherr, Closer look at the effect of AFM imaging conditions on the apparent dimensions of surface nanobubbles, Langmuir, 29(2013), No. 2, p. 620. doi: 10.1021/la304193d
[52]	D.Y. Li, D.L. Jing, Y.L. Pan, W.J. Wang, and X.Z. Zhao, Coalescence and stability analysis of surface nanobubbles on the polystyrene/water interface, Langmuir, 30(2014), No. 21, p. 6079. doi: 10.1021/la501262a
[53]	J.R.T. Seddon, H.J.W. Zandvliet, and D. Lohse, Knudsen gas provides nanobubble stability, Phys. Rev. Lett., 107(2011), No. 11, art. No. 116101. doi: 10.1103/PhysRevLett.107.116101
[54]	G.X. Shen, X.H. Zhang, Y. Ming, L.J. Zhang, Y. Zhang, and J. Hu, Photocatalytic induction of nanobubbles on TiO₂ surfaces, J. Phys. Chem. C, 112(2008), No. 11, p. 4029. doi: 10.1021/jp711850d
[55]	X.Y. Wang, B.Y. Zhao, W.G. Ma, Y. Wang, X.Y. Gao, R.Z. Tai, X.F. Zhou, and L.J. Zhang, Interfacial nanobubbles on atomically flat substrates with different hydrophobicities, ChemPhysChem, 16(2015), No. 5, p. 1003. doi: 10.1002/cphc.201402854
[56]	L.J. Zhang, H.P. Fang, and J. Hu, Scientific mysteries of nanobubbles, Physics, 47(2018), No. 9, p. 574.
[57]	D.J. Johnson, S.A.A. Malek, B.A.M. Al-Rashdi, and N. Hilal, Atomic force microscopy of nanofiltration membranes: Effect of imaging mode and environment, J. Membr. Sci., 389(2012), p. 486. doi: 10.1016/j.memsci.2011.11.023
[58]	L.J. Zhang, X.H. Zhang, Y. Zhang, J. Hu, and H.P. Fang, The length scales for stable gas nanobubbles at liquid/solid surfaces, Soft Matter, 6(2010), No. 18, art. No. 4515. doi: 10.1039/c0sm00243g
[59]	H. Schönherr, N. Hain, W. Walczyk, D. Wesner, and S.I. Druzhinin, Surface nanobubbles studied by atomic force microscopy techniques: Facts, fiction, and open questions, Jpn. J. Appl. Phys., 55(2016), No. 8S1, art. No. 08NA01. doi: 10.7567/JJAP.55.08NA01
[60]	B.M. Borkent, S.d. Beer, F. Mugele, and D. Lohse, On the shape of surface nanobubbles, Langmuir, 26(2010), No. 1, p. 260. doi: 10.1021/la902121x
[61]	V.S.J. Craig, Very small bubbles at surfaces—The nanobubble puzzle, Soft Matter, 7(2011), No. 1, p. 40. doi: 10.1039/C0SM00558D
[62]	C.R. Mo, Research on the Generation Method and Properties of Nanobubble Based on Ultrasonic Cavitation [Dissertation], University of Chinese Academy of Sciences, Beijing, 2019, p. 3.
[63]	B. Song, W. Walczyk, and H. Schönherr, Contact angles of surface nanobubbles on mixed self-assembled monolayers with systematically varied macroscopic wettability by atomic force microscopy, Langmuir, 27(2011), No. 13, p. 8223. doi: 10.1021/la2014896
[64]	W.G. Zhou, C.N. Wu, H.Z. Lv, B.L. Zhao, K. Liu, and L.M. Ou, Nanobubbles heterogeneous nucleation induced by temperature rise and its influence on minerals flotation, Appl. Surf. Sci., 508(2020), art. No. 145282. doi: 10.1016/j.apsusc.2020.145282
[65]	S. Nazari, S.Z. Shafaei, B. Shahbazi, and S.C. Chelgani, Study relationships between flotation variables and recovery of coarse particles in the absence and presence of nanobubble, Colloids Surf. A, 559(2018), p. 284. doi: 10.1016/j.colsurfa.2018.09.066
[66]	D.P. Tao and A. Sobhy, Nanobubble effects on hydrodynamic interactions between particles and bubbles, Powder Technol., 346(2019), p. 385. doi: 10.1016/j.powtec.2019.02.024
[67]	J.W. Yang, J.M. Duan, D. Fornasiero, and J. Ralston, Very small bubble formation at the solid−water interface, J. Phys. Chem. B, 107(2003), No. 25, p. 6139. doi: 10.1021/jp0224113
[68]	S. Calgaroto, A. Azevedo, and J. Rubio, Flotation of quartz particles assisted by nanobubbles, Int. J. Miner. Process., 137(2015), p. 64. doi: 10.1016/j.minpro.2015.02.010
[69]	S.H. Ding, Y.W. Xing, X. Zheng, Y.F. Zhang, Y.J. Cao, and X.H. Gui, New insights into the role of surface nanobubbles in bubble-particle detachment, Langmuir, 36(2020), No. 16, p. 4339. doi: 10.1021/acs.langmuir.0c00359
[70]	K.W. Stöckelhuber, B. Radoev, A. Wenger, and H.J. Schulze, Rupture of wetting films caused by nanobubbles, Langmuir, 20(2004), No. 1, p. 164. doi: 10.1021/la0354887
[71]	M.A. Hampton and A.V. Nguyen, Systematically altering the hydrophobic nanobubble bridging capillary force from attractive to repulsive, J. Colloid Interface Sci., 333(2009), No. 2, p. 800. doi: 10.1016/j.jcis.2009.01.035
[72]	A.C. Simonsen, P.L. Hansen, and B. Klösgen, Nanobubbles give evidence of incomplete wetting at a hydrophobic interface, J. Colloid Interface Sci., 273(2004), No. 1, p. 291. doi: 10.1016/j.jcis.2003.12.035
[73]	Y. Lu, Drag reduction by nanobubble clusters as affected by surface wettability and flow velocity: Molecular dynamics simulation, Tribol. Int., 137(2019), p. 267. doi: 10.1016/j.triboint.2019.05.010
[74]	M.A. Hampton and A.V. Nguyen, Nanobubbles and the nanobubble bridging capillary force, Adv. Colloid Interface Sci., 154(2010), No. 1-2, p. 30. doi: 10.1016/j.cis.2010.01.006
[75]	K. Yasui, T. Tuziuti, N. Izu, and W. Kanematsu, Is surface tension reduced by nanobubbles (ultrafine bubbles) generated by cavitation, Ultrason. Sonochem., 52(2019), p. 13. doi: 10.1016/j.ultsonch.2018.11.020
[76]	Z.A. Zhou, Z.H. Xu, J. A. Finch, J. H. Masliyah, and R. S, Chow, On the role of cavitation in particle collection in flotation—A critical review II, Miner. Eng., 22(2009), No. 5, p. 419. doi: 10.1016/j.mineng.2008.12.010
[77]	J. Israelachvili, and R. Pashley, The hydrophobic interaction is long range, decaying exponentially with distance, Nature., 300(1982), No. 5890, p. 341. doi: 10.1038/300341a0
[78]	J.L. Parker, P.M. Claesson, and P. Attard, Bubbles, cavities, and the long-ranged attraction between hydrophobic surfaces, J. Phys. Chem., 98(1994), No. 34, p. 8468. doi: 10.1021/j100085a029
[79]	S. Ljunggren and J.C. Eriksson, The lifetime of a colloid-sized gas bubble in water and the cause of the hydrophobic attraction, Colloids Surf. A, 129-130(1997), p. 151. doi: 10.1016/S0927-7757(97)00033-2
[80]	W.G. Zhou, H. Chen, L.M. Ou, and Q. Shi, Aggregation of ultra-fine scheelite particles induced by hydrodynamic cavitation, Int. J. Miner. Process., 157(2016), p. 236. doi: 10.1016/j.minpro.2016.11.003
[81]	P. Knüpfer, L. Ditscherlein, and U.A. Peuker, Nanobubble enhanced agglomeration of hydrophobic powders, Colloids Surf. A, 530(2017), p. 117. doi: 10.1016/j.colsurfa.2017.07.056
[82]	Y.W. Xing, Y.F. Zhang, M. Liu, M.D. Xu, F.Y. Guo, H.S. Han, Z.Y. Gao, Y.J. Cao, and X.H. Gui, Improving the floatability of coal with varying surface roughness through hypobaric treatment, Powder Technol., 345(2019), p. 643. doi: 10.1016/j.powtec.2019.01.058
[83]	V. Chipakwe, A. Sand, and S.C. Chelgani, Nanobubble assisted flotation separation of complex Pb–Cu–Zn sulfide ore—Assessment of process readiness, Sep. Sci. Technol., 2021. DOI: 10.1080/01496395.2021.1981942
[84]	V. Chipakwe, R. Jolsterå, and S.C. Chelgani, Nanobubble-assisted flotation of apatite tailings: Insights on beneficiation options, ACS Omega, 6(2021), No. 21, p. 13888. doi: 10.1021/acsomega.1c01551
[85]	S. Nazari, S.Z. Shafaei, M. Gharabaghi, R. Ahmadi, B. Shahbazi, and M.M. Fan, Effects of nanobubble and hydrodynamic parameters on coarse quartz flotation, Int. J. Min. Sci. Technol., 29(2019), No. 2, p. 289. doi: 10.1016/j.ijmst.2018.08.011
[86]	P.S. Epstein and M.S. Plesset, On the stability of gas bubbles in liquid–gas solutions, J. Chem. Phys., 18(1950), No. 11, p. 1505. doi: 10.1063/1.1747520
[87]	P.E. Theodorakis and Z.Z. Che, Surface nanobubbles: Theory, simulation, and experiment. A review, Adv. Colloid Interface Sci., 272(2019), art. No. 101995. doi: 10.1016/j.cis.2019.101995
[88]	W.A. Ducker, Contact angle and stability of interfacial nanobubbles, Langmuir, 25(2009), No. 16, p. 8907. doi: 10.1021/la902011v
[89]	H. Peng, G.R. Birkett, and A.V. Nguyen, Progress on the surface nanobubble story: What is in the bubble? Why does it exist? Adv. Colloid Interface Sci., 222(2015), p. 573.
[90]	N.D. Petsev, M.S. Shell, and L.G. Leal, Dynamic equilibrium explanation for nanobubbles’ unusual temperature and saturation dependence, Phys. Rev. E, 88(2013), No. 1, art. No. 010402. doi: 10.1103/PhysRevE.88.010402
[91]	H. Peng, G.R. Birkett, and A.V. Nguyen, Origin of interfacial nanoscopic gaseous domains and formation of dense gas layer at hydrophobic solid–water interface, Langmuir, 29(2013), No. 49, p. 15266. doi: 10.1021/la403187p
[92]	Y.W. Liu, J.J. Wang, X.R. Zhang, and W.C. Wang, Contact line pinning and the relationship between nanobubbles and substrates, J. Chem. Phys., 140(2014), No. 5, art. No. 054705. doi: 10.1063/1.4863448
[93]	A. Brotchie and X.H. Zhang, Response of interfacial nanobubbles to ultrasound irradiation, Soft Matter, 7(2011), No. 1, p. 265. doi: 10.1039/C0SM00731E
[94]	Y. Takata, H. Matsubara, T. Matsuda, Y. Kikuchi, T. Takiue, B. Law, and M. Aratono, Study on line tension of air/hexadecane/aqueous surfactant system, Colloid Polym. Sci., 286(2008), No. 6-7, p. 647. doi: 10.1007/s00396-007-1806-6
[95]	N. Kameda and S. Nakabayashi, Size-induced sign inversion of line tension in nanobubbles at a solid/liquid interface, Chem. Phys. Lett., 461(2008), No. 1-3, p. 122. doi: 10.1016/j.cplett.2008.07.012
[96]	S.I. Koshoridze, Calculating line tension for a simple model of a surface nanobubble, Tech. Phys. Lett., 46(2020), No. 5, p. 416. doi: 10.1134/S1063785020050089
[97]	J.H. Weijs, J.H. Snoeijer, and D. Lohse, Formation of surface nanobubbles and the universality of their contact angles: A molecular dynamics approach, Phys. Rev. Lett., 108(2012), No. 10, p. 104501. doi: 10.1103/PhysRevLett.108.104501