National University of Science and Technology “MISiS”, Moscow, Russia:

V. D. Samygin, Leading Expert of a Chair of Mineral Processing, e-mail: visamiguin@yandex.ru

Mass transfer of different ore fraction particles by pulp, air and foam flows into concentrate is described in a generalized equation of the first order kinetics flotation using a three-phase mass transfer coefficient K_mf instead of the rate constant. Three-phase coefficient K_mf is a product of a two-phase coefficient of mass transfer by pulp and air flows K_m and particle extraction from foam E_f. The two-phase mass transfer coefficient K_m differs from the flotation rate constant by presence of two new parameters: extraction by one bubble ε_b and a way to change the air flow structure. There are offered the selectivity criteria of two ore fraction separation, based on determining the optimum time at which the maximum difference in extracting and keeping the components in the separated ore fractions is reached. The selectivity, obtained by one bubble, can be improved in the air flow. Criteria for optimal residence time of individual bubbles and entire air flow (as well as the way of its distribution with height and chamber area) can be used to study the possibility of increasing the flotation machine use selectivity. A range shape and its position on Kmf axis are the set of criteria to evaluate the flotation machine use efficiency. Three-phase mass transfer coefficient K_mf depends on all the process factors, determining the material composition, reagent regime and machine parameter. Flotation machine, having the biggest K_mf value, will have a bigger flotation rate. It also has a range of minimum variance — the greater selectivity.
The studies were carried out with the support of Russian Science Foundation Grant (Project No. 14-17-00393).

1. Pogorelyy A. G. O flotatsionnoy kharakteristike promyshlennoy pulpy (About the flotation characteristics of industrial pulp). Izvestiya vuzov. Tsvetnaya metallurgiya = Universities' Proceedings. Nonferrous Metallurgy. 1961. No. 5. pp. 59–68.
2. Arbiter N., Harris C. C., Yap R. F. The air flow number in flotation machine scale-up. International Journal of Mineral Processing. 1976. Vol. 3, No. 3. pp. 257–280.
3. Schubert H. On some aspects of the hydrodynamics of flotation processes. Flotation of Sulphide Minerals. Netherlands : Elsevier, 1985. Vol. 6. pp. 337–355.
4. Forth M., Broussaud A., Monredon Th., Grebeneshnikov A. L., Kokorin A. M., Luchkov N. V., Smirnov A. O. Novoe pokolenie flotatsionnogo oborudovaniya kompanii Metso Minerals — osnova effektivnykh resheniy (New generation of flotation equipment of Metso Minerals — the basis of efficient decisions). Gornaya promyshlennost = Mining Industry. 2005. No. 5 (60). pp. 21–24.
5. Finch J. A., Dobby G. S. Column Flotation. Oxford : Pergamon, 1990. 180 p.
6. Gorain B. K., Napier-Munn T. J., Franzidis J.-P., Manlapig E. V. Studies on impeller type, impeller speed and air flowrate in an industrial scale flotation cell. Part 5: validation of k – Sb relationship and effect of froth depth. Minerals Engineering. 1998. Vol. 11, No. 7. pp. 615–626.
7. Heiskanen K. On the relationship between flotation rate and bubble surface area flux. Minerals Engineering. 2000. Vol. 13, No. 2. pp. 141–149.
8. Samygin V. D., Filippov L. O., Shekhirev D. V. Osnovy obogashcheniya rud (Basis of mineral processing). Moscow : Alteks, 2003.
9. Dai Z., Fornasiero D., Ralston J. Particle–bubble collision models — a review. Advances in Colloid and Interface Science. 2000. Vol. 85. pp. 231–256.
10. Yianatos J., Bucarey R., Larenas J., Henriquez F., Torres L. Collection zone kinetic model for industrial flotation columns. Minerals Engineering. 2005. Vol. 18. pp. 1373–1377.
11. Rubinshteyn, Yu. B., Filippov Yu. A. Kinetika flotatsii (Flotation kinetics). Moscow : Nedra, 1980. 367 p.
12. Saleh A. M. A study on the performance of second order models and two phase models in iron ore flotation. Physicochemical Problems of Mineral Processing. 2010. Vol. 44, No. 1. pp. 215–230.
13. Yianatos J. B., Bergh L. G., Diaz F., Rodríguez J. Mixing characteristics of industrial flotation equipment. Chemical Engineering Science. 2005. Vol. 60, No. 8/9. pp. 2273–2282.
14. Wierink G. A., Goniva C., Niceno B., Heiskanen K. Mechanistic modelling of particle-interface interaction in three-phase flows. Proceedings of 8th International Conference of CFD in the Oil & Gas, Metallurgical and Process Industries (CFD 2011), SINTEF/NTNU. Trondheim, Norway, 21–23 June 2011.
15. Samygin V. D., Grigorev P. V. Modeling hydrodynamic effect on flotation selectivity. Part I: Air bubble diameter and turbulent dissipation energy. Journal of Mining Science. 2015. Vol. 51, No. 1. pp. 157–163. DOI: http://link.springer.com/article/10.1134/S1062739115010214.
16. Abramov A. A., Din Ngok Dang, Ivanov V. A. O veroyatnostnoy kontseptsii protsessa flotatsii (About the probabilistic concept of the flotation process). Izvestiya vuzov. Gornyy zhurnal = News of the Higher Institutions. Mining Journal. 1978. No. 3. pp. 153–158.
17. Samygin V. D. Kinetika mineralizatsii puzyrkov vozdukha s uchetom otryva chastits i skorosti vsplyvaniya agregatov (Kinetics of the air bubble mineralization considering separation of particles and time of aggregate emerging). Izvestiya vuzov. Tsvetnaya metallurgiya = Universities' Proceedings. Nonferrous Metallurgy. 2016. No. 3. pp. 4–11.
18. Finch J. A. Bubbles and flotation. Johannesburg – Canada : McGill University, 2011.
19. Samiguin V., Lekhatinov Ch., Moshchanetskiy P. The Effective aerationhydrodynamic mode of multizone flotation cell. Proceeding of the XVI Balkan mineral processing congress. Serbia, Belgrad, 17–19 Juni 2015. Vol. 1. pp. 527–531.
20. Seaman D., Franzidis J., Manlapig E. Bubble load measurement in the pulp zone of industrial flotation machines — a new device for determining the froth recovery of attached particles. International Journal of Minerals Processing. 2004. Vol. 74, No. 1/2. pp. 1–13.
21. Moys M. H., Yianatos J. B., Larenas J. Measurement of particle loading on bubbles in the flotation process. Minerals Engineering Journal. 2010. Vol. 23. pp. 131–136.
22. Tikhonov O. N. Teoriya razdeleniya mineralov : uchebnik (Theory of mineral separation : tutorial). Moscow, Saint Petersburg, 2008. 832 p.
23. Duan J., Fornasiero D., Ralston J. Calculation of the flotation rate constant of chalcopyrite particles in an ore. International Journal of Mineral Processing. 2003. Vol. 72, No. 1/4. pp. 227–237.
24. Meyer C. J., Deglon D. A. Particle collision modeling — A review. Minerals Engineering. 2011. Vol. 24, No. 8. pp. 719–730.
25. Massinaei M., Kolahdoozan M., Noaparast M., Oliazadeh M., Yianatos J., Shamsadini R., Yarahmadi M. Hydrodynamic and metallurgical characteristics of industrial and pilot columns in rougher circuit. Minerals Engineering. 2009. Vol. 22, No. 1. pp. 96–99.
26. Schulze H. J. Dimensionless number and approximate calculation of the upper particle size of floatability in flotation machines. International Journal of Mineral Processing. 1982. Vol. 9. pp. 321–328.
27. Aslan A., Boz H. Effect of air distribution profile on selectivity at zinc cleaner circuit. Minerals Engineering. 2010. Vol. 23, No. 11–13. pp. 885–887.
28. Seaman D. R., Manlapig E. V., Franzidis J. P. Selective transport of attached particles across the pilp-froth interface. Minerals Engineering. 2006. Vol. 19. pp. 841–851.
29. Maksimov I. I. XXVII Mezhdunarodnyy kongress po obogashcheniyu poleznykh iskopaemykh (chast 1) (The XXVII International Mineral Processing Congress (Part 1)). Obogashchenie Rud = Mineral processing. 2015. No. 3. pp. 3–11. DOI: http://dx.doi.org/10.17580/or.2015.03.01
30. Yushina T. I., Petrov I. M., Belousova E. B. Flotation machines in Russia: State-of-the-art and prospects. Gornyi Zhurnal = Mining Journal. 2016. No. 3. pp. 61–67. DOI: http://dx.doi.org/10.17580/gzh.2016.03.13