Literature overview of basic characteristics and flotation laws of flocs

Abstract

Flocculation flotation is the most efficient method for recovering fine-grained minerals, and its essence lies in flotation and recovery of flocs. Fundamental physical characteristics of flocs are mainly determined by their apparent particle size and structure (density and morphology). Substantial researches have been conducted regarding the effect of floc characteristics on particle settling and water treatment. However, the influence of floc characteristics on flotation has not been widely studied. Based on the floc formation and flocculation flotation, this study reviews the fundamental physical characteristics of flocs from the perspectives of floc particle size and structure, summarizing the interaction between floc particle size and structure. Moreover, it thoroughly discusses the effect of floc particle size and structure on floc floatability, further revealing the influence of floc characteristics on bubble collision and adhesion and elucidating the mechanisms of interaction between flocs and bubbles. Thus, it is observed that floc particle size is not the only factor influencing flocculation flotation. Within the appropriate apparent particle size range, flocs with a compact structure exhibit higher efficiency in bubble collision and adhesion during flotation, thereby resulting in enhanced flotation performance. This study aims to provide a reference for flocculation flotation, targeting the development of more efficient and refined flocculation flotation processes in the future.

Keywords

flocs / basic characteristics / particle size and structure / flotation laws / bubbles

References

[1] Duzyol S, Ozkan A. Correlation of flocculation and agglomeration of dolomite with its wettability. Sep. Sci. Technol., 2011, 46(5): 876,

[2] M. Hyrycz, M. Ochowiak, A. Krupińska, S. Włodarczak, and M. Matuszak, A review of flocculants as an efficient method for increasing the efficiency of municipal sludge dewatering: Mechanisms, performances, influencing factors and perspectives, Sci. Total Environ., 820(2022), art. No. 153328.

[3] Cheng WP, Chen PH, Yu RF, Chang JN. Assessing coagulant dosage in full-scale drinking water treatment plants using nephelometry. Environ. Eng. Sci., 2012, 29(3): 212,

[4] B. Huang, X.H. Li, W. Zhang, C. Fu, Y. Wang, and S.Q. Fu, Study on demulsification-flocculation mechanism of oil-water emulsion in produced water from alkali/surfactant/polymer flooding, Polymers, 11(2019), No. 3, art. No. 395.

[5] L.P. Ye, A.J. Manning, and T.J. Hsu, Oil-mineral flocculation and settling velocity in saline water, Water Res., 173(2020), art. No. 115569.

[6] Yin WZ, Tang Y. Interactive effect of minerals on complex ore flotation: A brief review. Int. J. Miner. Metall. Mater., 2020, 27(5): 571,

[7] Jiang ZP, Guan YT. Flocculation morphology: Effect of particulate shape and coagulant species on flocculation. Water Sci. Technol., 2006, 53(7): 9,

[8] M.S. Zhan, M.H. You, L.L. Liu, et al., Numerical simulation of mechanical flocculation in water treatment, J. Environ. Chem. Eng., 9(2021), No. 4, art. No. 105536.

[9] Samaras K, Zouboulis A, Karapantsios T, Kostoglou M. A CFD-based simulation study of a large scale flocculation tank for potable water treatment. Chem. Eng. J., 2010, 162(1): 208,

[10] Liu YM, Ma J, Lian LL, et al.. Flocculation performance of alginate grafted polysilicate aluminum calcium in drinking water treatment. Process Saf. Environ. Prot., 2021, 155: 287,

[11] J. Ma, R.N. Wang, X.Y. Wang, et al., Drinking water treatment by stepwise flocculation using polysilicate aluminum magnesium and cationic polyacrylamide, J. Environ. Chem. Eng., 7(2019), No. 3, art. No. 103049.

[12] C.D. Wang, M.T. Jin, S. Yue, et al., Computational fluid dynamics analysis of Trichosporon fermentans flocculation in refined soybean oil wastewater and flocculation rate prediction method, Sci. Total Environ., 835(2022), art. No. 155415.

[13] Ma JY, Fu K, Jiang LY, et al.. Flocculation performance of cationic polyacrylamide with high cationic degree in humic acid synthetic water treatment and effect of Kaolin particles. Sep. Purif. Technol., 2017, 181: 201,

[14] F. Sun, F.Y. Wang, H.L. Jiang, et al., Analysis on the flocculation characteristics of algal organic matters, J. Environ. Manage., 302(2022), art. No. 114094.

[15] Suresh A, Grygolowicz-Pawlak E, Pathak S, et al.. Understanding and optimization of the flocculation process in biological wastewater treatment processes: A review. Chemosphere, 2018, 210: 401,

[16] Oliveira C, Rubio J. A short overview of the formation of aerated flocs and their applications in solid/liquid separation by flotation. Miner. Eng., 2012, 39: 124,

[17] Wei H, Gao BQ, Ren J, Li AM, Yang H. Coagulation/flocculation in dewatering of sludge: A review. Water Res., 2018, 143: 608,

[18] Yin WZ, Yang XS, Zhou DP, Li YJ, Lü ZF. Shear hydrophobic flocculation and flotation of ultrafine Anshan hematite using sodium oleate. Trans. Nonferrous Met. Soc. China, 2011, 21(3): 652,

[19] Song SX, Zhang XW, Yang BQ, Lopez-Mendoza A. Flotation of molybdenite fines as hydrophobic agglomerates. Sep. Purif. Technol., 2012, 98: 451,

[20] Huang XT, Xiao W, Zhao HB, et al.. Hydrophobic flocculation flotation of rutile fines in presence of styryl phosphonic acid. Trans. Nonferrous Met. Soc. China, 2018, 28(7): 1424,

[21] S.L. Li, X.M. Ma, J.C. Wang, Y.W. Xing, X.H. Gui, and Y.J. Cao, Effect of polyethylene oxide on flotation of molybdenite fines, Miner. Eng., 146(2020), art. No. 106146.

[22] M.Y. Li, Y.H. Xiang, T.J. Chen, X.P. Gao, and Q. Liu, Separation of ultra-fine hematite and quartz particles using asynchronous flocculation flotation, Miner. Eng., 164(2021), art. No. 106817.

[23] G.Z. Chen, C.P. Li, Z.E. Ruan, R. Bürger, and H.Z. Hou, Research on floc structure and physical properties based on pipeline flocculation, J. Water Process Eng., 53(2023), art. No. 103627.

[24] M.X. Wang, L. Feng, X.Y. You, and H.L. Zheng, Effect of fine structure of chitosan-based flocculants on the flocculation of bentonite and humic acid: Evaluation and modeling, Chemosphere, 264(2021), art. No. 128525.

[25] Chen W, Feng QM, Zhang GF, Li LF, Jin SZ. Effect of energy input on flocculation process and flotation performance of fine scheelite using sodium oleate. Miner. Eng., 2017, 112: 27,

[26] W.H. Leiva, E. Piceros, P. Robles, and R.I. Jeldres, Impact of hydrodynamic conditions on the structure of clay-based tailings aggregates flocculated in freshwater and seawater, Miner. Eng., 176(2022), art. No. 107313.

[27] L.P. Chang, Y.J. Cao, W.J. Peng, et al., Enhancing the ion flotation removal of Cu(II) via regulating the oxidation degree of nano collector-graphene oxide, J. Cleaner Prod., 295(2021), art. No. 126397.

[28] X.M. Chen, J.L. Zhang, H.Z. Jiao, et al., Mechanism of rake frame shear drainage during gravity dewatering of ultrafine unclassified tailings for paste preparation, Minerals, 12(2022), No. 2, art. No. 240.

[29] Dwari RK, Mishra BK. Evaluation of flocculation characteristics of kaolinite dispersion system using guar gum: A green flocculant. Int. J. Min. Sci. Technol., 2019, 29(5): 745,

[30] Liang GJ, Nguyen AV, Chen WM, Nguyen TAH, Biggs S. Interaction forces between goethite and polymeric flocculants and their effect on the flocculation of fine goethite particles. Chem. Eng. J., 2018, 334: 1034,

[31] Zhang YZ, Zhang GG. Simulation study on flocculation morphology of cohesive sediment. J. Sediment Res., 2021, 46(3): 16

[32] Zheng D, Song WD, Tan YY, Cao S, Yang ZL, Sun LJ. Fractal and microscopic quantitative characterization of unclassified tailings flocs. Int. J. Miner. Metall. Mater., 2021, 28(9): 1429,

[33] X. Guo and J.L. Wang, Modeling of the fractal-like adsorption systems based on the diffusion limited aggregation model, J. Mol. Liq., 324(2021), art. No. 114692.

[34] J.J. Yu, H. Xu, X.F. Yang, H.Y. Sun, Z.Y. Jin, and D.S. Wang, Floc formation and growth during coagulation removing humic acid: Effect of stirring condition, Sep. Purif. Technol., 302(2022), art. No. 122084.

[35] Wu CH, Wang Y, Gao BY, Zhao YX, Yue QY. Coagulation performance and floc characteristics of aluminum sulfate using sodium alginate as coagulant aid for synthetic dying wastewater treatment. Sep. Purif. Technol., 2012, 95: 180,

[36] C. Wang, C.B. Sun, and Q. Liu, Formation, breakage, and re-growth of quartz flocs generated by non-ionic high molecular weight polyacrylamide, Miner. Eng., 177(0200), art. No. 106546.

[37] X.L. Liu, H.L. Yin, J. Zhao, Z.Q. Guo, Z. Liu, and Y.Z. Sang, Investigation of molecular weight effect on lignin flocculation induced by poly(diallyldimethylammonium chloride) (PDADMAC) through population balance modeling, Sep. Purif. Technol, 254(2021), art. No. 117569.

[38] W.J. Zhang, W. Sun, Y.H. Hu, J. Cao, and Z.Y. Gao, Selective flotation of pyrite from galena using chitosan with different molecular weights, Minerals, 9(2019), No. 9, art. No. 549.

[39] Yin ZG, Khoso SA, Sun W, et al.. Flocculation of flotation tailings in presence of silicate gel and polymer. J. Cent. South Univ., 2018, 25(8): 1928,

[40] H.L. Yu, H.L. Zhang, Z.N. Sun, et al., Effect of polyaluminium silicate sulphate with different alkyl chain lengths on oily sewage in oil fields, Chem. Eng. J., 450(2022), art. No. 138125.

[41] L.J. Wang, F.F. Min, J. Chen, T. Wang, and Z. Zhou, Study of flocculation performance and mechanism of ultrafine montmorillonite particles with NPAM, Physicochem. Probl. Miner. Process., 58(2022), No. 3, art. No. 147790.

[42] Zhang W, Sun CB, Kou J, et al.. The influence of polyethyleneimine dosages and molecular weight on sedimentation and rheology behavior of copper tailings. J. Dispers. Sci. Technol., 2020, 41(9): 1390,

[43] X. Feng, J.J. Wan, J.C. Deng, et al., Study on the regulation of sludge dewatering by hydrophobically associating cationic polyacrylamide coupled with framework materials, J. Water Process Eng., 45(2022), art. No. 102502.

[44] Fan YP, Ma XM, Dong XS, Feng ZY, Dong YD. Characterisation of floc size, effective density and sedimentation under various flocculation mechanisms. Water Sci. Technol., 2020, 82(7): 1261,

[45] Feng X, Deng JC, Wan JJ, He JQ, Huang ZJ, Yan AQ. Preparation of a hydrophobically associated cationic polyacrylamide and its regulation of the sludge dewatering performance. Water Sci. Technol., 2020, 82(7): 1350,

[46] D. Liu and Y.J. Peng, Foaming and aggregation behaviours of polyethylene oxide and polyacrylamide in inhibiting mechanical entrainment of kaolinite in flotation using saline water, J. Mol. Liq., 359(2022), art. No. 119299.

[47] Lawrence TJ, Carr SJ, Wheatland JAT, Manning AJ, Spencer KL. Quantifying the 3D structure and function of porosity and pore space in natural sediment flocs. J. Soils Sediments, 2022, 22(12): 3176,

[48] Z.Y. Sun, Y.J. Li, X. Ming, B.M. Chen, and Z.J. Li, Enhancing anti-washout behavior of cement paste by polyacrylamide gelation: From floc properties to mechanism, Cem. Concr. Compos., 136(2023), art. No. 104887.

[49] Wang ZB, Nan J, Ji XY, Yang YM. Effect of the micro-flocculation stage on the flocculation/sedimentation process: The role of shear rate. Sci. Total Environ., 2018, 633: 1183,

[50] Li YF, Xu L, Shi T, Yu WZ. The influence of various additives on coagulation process at different dosing point: From a perspective of structure properties. J. Environ. Sci., 2021, 101: 168,

[51] Nasser MS. Characterization of floc size and effective floc density of industrial papermaking suspensions. Sep. Purif. Technol., 2014, 122: 495,

[52] Vahedi A, Gorczyca B. Application of fractal dimensions to study the structure of flocs formed in lime softening process. Water Res., 2011, 45(2): 545,

[53] MacIver MR, Alizadeh H, Kuppusamy VK, Hamza H, Pawlik M. The macro-structure of quartz flocs. Powder Technol., 2022, 395: 255,

[54] Zhang YQ, Gao WJ, Fatehi P. Structure and settling performance of aluminum oxide and poly(acrylic acid) flocs in suspension systems. Sep. Purif. Technol., 2019, 215: 115,

[55] H. Bagherzadeh, Z. Mansourpour, and B. Dabir, Numerical analysis of asphaltene particles evolution and flocs morphology using DEM-CFD approach, J. Pe. Sci. Eng., 199(2021), art. No. 108309.

[56] Kazzaz AE, Feizi ZH, Kong FG, Fatehi P. Interaction of poly(acrylic acid) and aluminum oxide particles in suspension: Particle size effect. Colloids Surf. A, 2018, 556: 218,

[57] X.T. Wang, B.Y. Cui, Q. Zhao, et al., Particle flocculation in a stirred tank: A microscopic test by coupled CFD-DEM approach, J. Environ. Chem. Eng., 10(2022), No.1, art. No. 107005.

[58] Sun R, Xiao H, Sun HL. Investigating the settling dynamics of cohesive silt particles with particle-resolving simulations. Adv. Water Resour., 2018, 111: 406,

[59] A. Gonzalez-Torres, M. Pivokonsky, and R.K. Henderson, The impact of cell morphology and algal organic matter on algal floc properties, Water Res., 163(2019), art. No. 114887.

[60] Cui Y, Ravnik J, Steinmann P, Hriberšek M. Settling characteristics of nonspherical porous sludge flocs with non-homogeneous mass distribution. Water Res., 2019, 158: 159,

[61] X.L. Li, Selective flocculation performance of amphiphilic quaternary ammonium salt in Kaolin and bentonite suspensions, Colloids Surf. A, 636(2022), art. No. 128140.

[62] C.T. Chen, T. Zhang, L. Lv, Y.X. Chen, W.X. Tang, and S.W. Tang, Destroying the structure of extracellular polymeric substance to improve the dewatering performance of waste activated sludge by ionic liquid, Water Res., 199(2021), art. No. 117161.

[63] Y.K. Zong, X. Jin, Y. Li, et al., Assessing the performance of coral reef-like floc towards the removal of low molecular weight organic contaminant, Sci. Total Environ., 811(2022), art. No. 152413.

[64] D. Shi, J.B. Zhang, H.Q. Li, et al., Insight into the mechanism of gasification fine slag enhanced flotation with selective dispersion flocculation, Fuel, 336(2023), art. No. 127134.

[65] R.J. Xu, W.J. Zou, T. Wang, J. Huang, Z.J. Zhang, and C.Y. Xu, Adsorption and interaction mechanisms of Chi-g-P(AM-DMDAAC) assisted settling of kaolinite in a two-step flocculation process, Sci. Total Environ., 816(2022), art. No. 151576.

[66] Wang BY, Chen ZL, Zhu J, Shen JM, Han Y. Pilot-scale fluoride-containing wastewater treatment by the ballasted flocculation process. Water Sci. Technol., 2013, 68(1): 134,

[67] Zhao BQ, Wang DS, Li T, Chow CWK, Huang C. Influence of floc structure on coagulation–microfiltration performance: Effect of Al speciation characteristics of PACls. Sep. Purif. Technol., 2010, 72(1): 22,

[68] Liu A, Fan MQ, Fan PP. Interaction mechanism of miscible DDA-Kerosene and fine quartz and its effect on the reverse flotation of magnetic separation concentrate. Miner. Eng., 2014, 65: 41,

[69] Y. Liu, X. Zhang, W.M. Jiang, M.R. Wu, and Z.H. Li, Comprehensive review of floc growth and structure using electro-coagulation: Characterization, measurement, and influencing factors, Chem. Eng. J., 417(2021), art. No. 129310.

[70] X.J. Chai, S.Y. Lin, J.H. Zhai, J.H. Kang, P. Chen, and R.Q. Liu, A new combined collector for flotation separation of ilmenite from titanaugite in acidic pulp, Sep. Purif. Technol., 278(2021), art. No. 119647.

[71] Z.Y. Tong, L. Liu, Z.T. Yuan, J.T. Liu, J.W. Lu, and L.X. Li, The effect of comminution on surface roughness and wettability of graphite particles and their relation with flotation, Miner. Eng., 169(2021), art. No. 106959.

[72] Wu HY, Wang WJ, Huang YF, et al.. Comprehensive evaluation on a prospective precipitation-flotation process for metal-ions removal from wastewater simulants. J. Hazard. Mater., 2019, 371: 592,

[73] Ma FY, Zhang P, Tao DP. Surface nanobubble characterization and its enhancement mechanisms for fine-particle flotation: A review. Int. J. Miner. Metall. Mater., 2022, 29(4): 727,

[74] Ni C, Zhang QS, Jin MG, et al.. Effect of high-speed shear flocculation on the flotation kinetics of ultrafine microcrystalline graphite. Powder Technol., 2022, 396: 345,

[75] Guérin L, Frances C, Liné A, Coufort-Saudejaud C. Fractal dimensions and morphological characteristics of aggregates formed in different physico-chemical and mechanical flocculation environments. Colloids Surf. A, 2019, 560: 213,

[76] Younker JM, Walsh ME. Effect of adsorbent addition on floc formation and clarification. Water Res., 2016, 98: 1,

[77] 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.

[78] Jin X, Wang W, Wang S, et al.. Application of a hybrid gravity-driven membrane filtration and dissolved ozone flotation (MDOF) process for wastewater reclamation and membrane fouling mitigation. J. Environ. Sci., 2019, 81: 17,

[79] Y.L. Wang, W.T. Sun, L.M. Ding, et al., A study on the feasibility and mechanism of enhanced co-coagulation dissolved air flotation with chitosan-modified microbubbles, J. Water Process. Eng., 40(2021), art. No. 101847.

[80] Oliveira C, Rodrigues RT, Rubio J. A new technique for characterizing aerated flocs in a flocculation-microbubble flotation system. Int. J. Miner. Process., 2010, 96(1–4): 36,

[81] Wang YL, Ma HY, Wang XB, et al.. Study on the operation performance and floc adhesion mechanism of dissolved air flotation equipment. Environ. Sci. Pollut. Res. Int., 2022, 29(36): 54219,

[82] Liu H, Ding WD, Zhang KF. High air flotation efficiency of multiphase flow pump with the addition of dodecyl dimethyl benzyl ammonium chloride (DDBAC). Water Supply, 2020, 20(6): 2156,

[83] I. Demir-Yilmaz, M.S. Ftouhi, S. Balayssac, P. Guiraud, C. Coudret, and C. Formosa-Dague, Bubble functionalization in flotation process improve microalgae harvesting, Chem. Eng. J., 452(2023), art. No. 139349.

[84] Qi J, Lan HC, Liu HJ, Liu RP, Miao SY, Qu JH. Simultaneous surface-adsorbed organic matter desorption and cell integrity maintenance by moderate prechlorination to enhance Microcystis aeruginosa removal in KMnO₄-Fe(II) process. Water Res., 2016, 105: 551,

[85] W.Z. Yin, Y. Xie, J. Yao, N.B. Song, K.Q. Chen, and X.M. Yin, Study on the effect of flocculation morphology on the floatability of talc flocs and the adhesion mechanism with air bubbles, Miner. Eng., 203(2023), art. No. 108317.

[86] Liu B, Qu FS, Chen W, et al.. Microcystis aeruginosa-laden water treatment using enhanced coagulation by persulfate/Fe(II), ozone and permanganate: Comparison of the simultaneous and successive oxidant dosing strategy. Water Res., 2017, 125: 72,

[87] Liu XL, Yin HL, Zhao J, Guo ZQ, Liu Z, Sang YZ. Understanding the coagulation mechanism and floc properties induced by Fe(VI) and FeCl₃: Population balance modeling. Water Sci. Technol., 2021, 83(10): 2377,

[88] H.Y. Zhang, C. Li, L.L. Li, et al., Uncovering the optimal structural characteristics of flocs for microalgae flotation using Python-OpenCV, J. Cleaner Prod., 385(2023), art. No. 135748.

[89] H.Y. Wu, Y.F. Huang, B.B. Liu, et al., An efficient separation for metal-ions from wastewater by ion precipitate flotation: Probing formation and growth evolution of metal-reagent flocs, Chemosphere, 263(2021), art. No. 128363.

[90] B. Yang, Z.L. Zhu, W.Z. Yin, et al., Selective adsorption of an eco-friendly and efficient depressant PBTCA onto dolomite for effective flotation of fluorapatite from dolomite, Chem. Eng. J., 400(2020), art. No. 125780.

[91] G.H. Han, S. Chen, S.P. Su, Y.F. Huang, B.B. Liu, and H. Sun, A review and perspective on micro and nanobubbles: What They Are and Why They Matter, Miner. Eng., 189(2022), art. No. 107906.

[92] Y. Wang, X. Jin, S.J. Yang, et al. Interactions between flocs and bubbles in the separation zone of dissolved air flotation system, Sci. Total Environ., 761(2021), art. No. 143222.

[93] A. Wang, M.M. Hoque, G. Evans and S. Mitra, Determining collision efficiency in multi-bubble-particle systems in presence of turbulence, Miner. Eng., 189(2022), art. No. 107889.

[94] Y.R. Chen, H.R. Zheng, V.N.T. Truong, G.Y. Xie, and Q.X. Liu, Selective aggregation by ultrasonic standing waves through gas nuclei on the particle surface, Ultrason. Sonochem., 63(2020), art. No. 104924.

[95] Li ZL, Rao F, Corona-Arroyo MA, Bedolla-Jacuinde A, Song SX. Comminution effect on surface roughness and flotation behavior of malachite particles. Miner. Eng., 2019, 132: 1,

[96] Q.M. Zhuo, W.L. Liu, H.X. Xu, X.P. Sun, H. Zhang, and W. Liu, The effect of collision angle on the collision and adhesion behavior of coal particles and bubbles, Processes, 6(2018), No. 11, art. No. 218.

[97] Li CW, Gao ZY. Effect of grinding media on the surface property and flotation behavior of scheelite particles. Powder Technol., 2017, 322: 386,

[98] Xia WC. Role of particle shape in the floatability of mineral particle: An overview of recent advances. Powder Technol., 2017, 317: 104,

[99] W.J. Wang, Y.F. Huang, J.P. Zuo, et al., A feasible strategy for separating oxyanions-loaded microfine Fe-MOF adsorbents from solution by bubble flotation, Chem. Eng. J., 454(2023), art. No. 140299.

[100] Xia WC, Ma GX, Bu XN, Peng YL. Effect of particle shape on bubble-particle attachment angle and flotation behavior of glass beads and fragments. Powder Technol., 2018, 338: 168,

[101] Zhao J, Fu XH, Song GY, Liu JT, Zhang LL. Effect of floccule morphological characteristics on the collision and attachment between floccule and bubble. J. China Coal Soc., 2017, 42(3): 738

[102] Liang L, Tian F, Wang LG, Xie GY. Effect of polyaluminum chloride on coal flotation performance with different reagent addition regimes. Powder Technol., 2019, 349: 84,

[103] Z.H. Xue, L.P. Dong, H.P. Li, et al., Study on the mechanism of flotation of coal gasification fine slag reinforced with naphthenic acids, Fuel, 324(2022), art. No. 124557.

[104] Hassanzadeh A, Firouzi M, Albijanic B, Celik MS. A review on determination of particle-bubble encounter using analytical, experimental and numerical methods. Miner. Eng., 2018, 122: 296,

[105] Firouzi M, Nguyen AV, Hashemabadi SH. The effect of microhydrodynamics on bubble-particle collision interaction. Miner. Eng., 2011, 24(9): 973,

[106] Nguyen PT, Nguyen AV. Validation of the generalised Sutherland equation for bubble-particle encounter efficiency in flotation: Effect of particle density. Miner. Eng., 2009, 22(2): 176,

[107] J. Je, D. Lee, J. Kwon, and H. Cho, Simulation of bubble-particle collision process and estimation of collision probability using a coupled smoothed particle hydrodynamics-discrete element method model, Miner. Eng., 176(2022), art. No. 107309.

[108] Ma GX, Xia WC, Xie GY. Effect of particle shape on the flotation kinetics of fine coking coal. J. Cleaner Prod., 2018, 195: 470,

[109] Wen BF, Xia WC. Effect of particle shape on coal flotation. Energy Sources Part A, 2017, 39(13): 1390,

[110] Vaziri Hassas B, Caliskan H, Guven O, Karakas F, Cinar M, Celik MS. Effect of roughness and shape factor on flotation characteristics of glass beads. Colloids Surf. A, 2016, 492: 88,

[111] Zhuo QM, Liu WL, Xu HX, Zhang H, Sun XP. Experimental investigation of the attachment performance between coal particle and bubble. ACS Omega, 2021, 6(12): 7979,