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Mineralization kinetics of air bubbles allowing for the particle detachment and time of buoying of aggregates

  • Mineral Processing of Nonferrous Metals
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Abstract

The joint consideration of subprocesses of particle capture and detachment, and buoying of aggregates in the periodic nonfrothing flotation conditions shows that the mineral load formed on a separate part for its buoying time (τm). This load is a part of the equilibrium mineral load, which can be attained under the infinite mineralization time. It is proposed to characterize the composition and attainment rate of the mineral load by two dimensionless parameters, which depend on intensities of subprocesses. The sort parameter of particles (B) has been uniquely determined by the ratio of the detachment intensity to the capture intensity, while the dimensionless time (D) is determined by the ratio of the particle capture and detachment rate to the buoying velocity of the air bubble. The mineralization kinetic equation by many bubbles is derived in the exponential form similarly to the first-order Beloglazov equation. Intensities of capture and detachment subprocesses in the mineralization rate constant (K m) determine the magnitude of recovery by a separate bubble (εbm) for time τm, while the air consumption determines the summary recovery ε.

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References

  1. Zheng, X., Johnson, N.W., and Franzidis, J.P., Modelling of entrainment in industrial flotation cells: water recovery and degree of entrainment, Miner. Eng., 2006, vol. 19, no. 11, pp. 1191–1203.

    Article  Google Scholar 

  2. Yianatos, J., Contreras, F., Diaz, F., and Villanueva, A., Direct measurement of entrainment in large flotation cells, Powder Technol., 2009, vol. 189, no. 1, pp. 42–47.

    Article  Google Scholar 

  3. Dobby, G.S. and Finch, J.A., Particle size dependence in flotation derived from a fundamental model of the capture process, Int. J. Miner. Process., 1987, vol. 21, pp. 241–253.

    Article  Google Scholar 

  4. Dai, Z., Fornasiero, D., and Ralston, J., Particle-bubble collision models: A review, Adv. Colloid Interface Sci., 2000, vol. 85, pp. 231–256.

    Article  Google Scholar 

  5. Yianatos, J., Bucarey, R., Larenas, J., Henriquez, F., and Torres, L., Collection zone kinetic model for industrial flotation columns, Miner. Eng., 2005, vol. 18, pp. 1373–1377.

    Article  Google Scholar 

  6. Duan, J., Fornasiero, D., and Ralston, J., Calculation of the flotation rate constant of chalcopyrite particles in an ore, Int. J. Miner. Process., 2003, vol. 72, pp. 227–237.

    Article  Google Scholar 

  7. Samygin, V.D., Filippov, L.O., and Shekhirev, D.V., Osnovy obogashcheniya rud Foundations of the Ore Concentration), Moscow: Al’teks, 2003.

    Google Scholar 

  8. Bogdanov, O.S., Maximov, I.I., Podnek, A.K., and Yanis, N.A., Teoriya i tekhnologia flotatsii rud (Theory and Technology of Ore Flotation), Moscow: Nedra, 1990.

    Google Scholar 

  9. Tikhonov, O.N., Teoriya razdeleniya mineralov. Uchebnik (Separation Theory of Minerals. Textbook), St. Petersburg: St. Petersburg Gornyi Univ., 2008.

    Google Scholar 

  10. Mika, T. and Fuerstenau, D., Microscopy model of flotation process, in: VIII Mezhdunarodnyi congress po obogashcheniyu poleznykh iskopaemykh (VIII Int. Mineral Processing Congr.), vol. 2, Leningrad, 1969, pp. 246–269.

    Google Scholar 

  11. Rubinshtein, J.B., Effect of particle and bubble size on flotation kinetics, in Frothing in Flotation, London, New York: Gordon and Breath, 1998, vol. 2, pp. 51–80.

    Google Scholar 

  12. Saleh, A.M., A study on the performance of second order models and two phase models in iron ore flotation, Physicochem. Probl. Miner. Process., 2010, vol. 44, pp. 215–230.

    Google Scholar 

  13. Shekhirev D.V., Filipov L.O., Samygin V.D. Mathematical modelling of the process of separation of the raw materials in the column flotation, in: Proc. XVIII Intern. Mineral Processing Congr., Sydney: Aus. IMM, pp. 1357–1362.

  14. Abramov, A.A., Din’ Ngok Dang, and Ivanov, B.A., The probabilistic concept of the flotation process, Izv. Vyssh. Uchebn. Zaved., Gornyi Zh., 1978, no. 3, pp. 153–158.

    Google Scholar 

  15. Koh, P.T.L. and Schwarz, M.P., CFD modelling of bubble-particle collision rates and efficiencies in mineral flotation cells, Miner. Eng., 2003, vol. 16, pp. 1055–1059.

    Article  Google Scholar 

  16. Koh, P.T.L. and Schwarz, M.P., CFD model of a selfaerating flotation cell, Int. J. Miner. Process., 2007, vol. 85, no. 3, pp. 16–24.

    Article  Google Scholar 

  17. Koh, P.T.L. and Schwarz, M.P., Modelling attachment rates of multi-sized bubbles with particles in a flotation cell, Miner. Eng., 2008, vol. 21, pp. 989–993.

    Article  Google Scholar 

  18. Koh, P.T.L. and Smith, L.K., The effect of stirring speed and induction time on flotation, Miner. Eng., 2011, vol. 24, no. 5, pp. 442–448.

    Article  Google Scholar 

  19. Huang, Z., Legendre, D., and Guiraud, P., Effect of interface contamination on particle-bubble collision, Chem. Eng. Sci., 2012, vol. 68, no. 1, pp. 1–18.

    Article  Google Scholar 

  20. Bocharov, V.A., Ignatkina, V.A., and Alekseichuk, D.A., Influence of mineral compositions and their modification on the selection flowchart and collectors of selective flotation of ores of nonferrous metals, Russ. J. Non-Ferrous Met., 2012, vol. 53, pp. 279–288.

    Article  Google Scholar 

  21. Samygin, V.D. and Grigoryev, P.V., Modeling of the influence of the hydrodynamic factors on the flotation process. Pt. 1. Influence of the bubble diameter and turbulent energy dissipation, Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., 2015, no. 1, pp. 1–8.

    Google Scholar 

  22. Arbiter, N., Flotation rate and flotation efficiency, Miner. Eng., 1951, vol. 190, no. 3, pp. 791–796.

    Google Scholar 

  23. Yianatos, J., Bucarey, R., Larenas, J., Henriquez, F., and Torres, L., Collection zone kinetic model for industrial flotation columns, Miner. Eng., 2005, vol. 18, pp. 1373–1377.

    Article  Google Scholar 

  24. Barskii, L.A. and Kozin, V.Z., Sistemnyi analiz v obogashchenii poleznykh iskopaemykh (System Analysis in Concentration of Minerals), Moscow: Nedra, 1978.

    Google Scholar 

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Correspondence to V. D. Samygin.

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Original Russian Text © V.D. Samygin, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii, Tsvetnaya Metallurgiya, 2016, No. 3, pp. 4–11.

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Samygin, V.D. Mineralization kinetics of air bubbles allowing for the particle detachment and time of buoying of aggregates. Russ. J. Non-ferrous Metals 57, 389–394 (2016). https://doi.org/10.3103/S1067821216050199

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  • DOI: https://doi.org/10.3103/S1067821216050199

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