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The interaction of a rising bubble and a particle in oscillating fluid

Published online by Cambridge University Press:  18 October 2016

D. V. Lyubimov ,
L. S. Klimenko ,
T. P. Lyubimova  and
L. O. Filippov
D. V. Lyubimov
Affiliation:
Perm State University, Perm 614990, Russia
L. S. Klimenko
Affiliation:
Institute of Continuous Media Mechanics UB RAS, Perm 614013, Russia
T. P. Lyubimova*
Affiliation:
Institute of Continuous Media Mechanics UB RAS, Perm 614013, Russia
L. O. Filippov
Affiliation:
Universite de Lorraine, Nancy 54000, France
*
†Email address for correspondence: [email protected]
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Abstract

This article considers the interaction of a rising bubble and a sedimenting fine particle in an incompressible viscous liquid under vibrations (ultrasound). The particle is subject to Stokes, Basset and buoyancy forces, and average force due to the inhomogeneity of the pulsating field. It is shown that the main contribution to the average force is made by interference of the external field and the field caused by the monopole mode of bubble oscillations. The interaction force is the attraction of the particle to the bubble. It is found that even weak vibrations lead to considerable increase of the effective cross-section of particle capture by the bubble. The evaluation of the efficiency of the flotation process exposed to an ultrasound action is discussed.

JFM classification

Drops and Bubbles: Bubble dynamics Multiphase and Particle-laden Flows: Particle/fluid flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 807 , 25 November 2016 , pp. 205 - 220
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Copyright
© 2016 Cambridge University Press 

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References

Aldrich, C. & Feng, D. 1999 Effect of particle size on flotation performance of complex sulphide ores. Miner. Engng 12, 701–707.CrossRefGoogle Scholar
Alexeev, V. N. 1983 K voprosy o radiocionnoi sile davleniya zvyka na sfery. Akust J. AS USSR 2, 129–136.Google Scholar
Alexeev, V. N. 1991 Sili, deistvyushie mezhdy puzirkom i chasticei v zvukovom pole. Akust J. 37, 597–606.Google Scholar
Bjerknes, C. A. 1915 Hydrodynamische Fernkrafte. Englemann, Leipzing.Google Scholar
Bjerknes, V. F. K. 1906 Field of Force. Columbia.Google Scholar
Danilov, S. D. & Mironov, M. A. 2000 Mean force on a small sphere in a sound field in a viscous fluid. J. Acoust. Soc. Am. 107, 143–153.Google Scholar
Diaz-Penafiel, P. & Dobby, G. S. 1994 Kinetic studies in flotation columns: bubble size effect. Miner. Engng 7, 465–478.Google Scholar
Diethelm, K., Ford, N. J., Freed, A. D. & Luchko, Y. 2005 Algorithms for the fractional calculus: a selection of numerical methods. Comput. Meth. Appl. Mech. Engng 194, 743–773.Google Scholar
Dobby, G. S. & Finch, J. A. 1987 Particle size dependence in flotation derived from a fundamental model of the capture process. Intl J. Miner. Process. 21, 241–260.Google Scholar
Doinikov, A. A. 2003 Acoustic radiation forces: classical theory and recent advances. Recent Res. Devel. Acoustics 1, 39–67.Google Scholar
Doinikov, A. A. 1994 Acoustic radiation pressure on a compressible sphere in a viscous fluid. J. Fluid Mech. 267, 1–21.Google Scholar
Doinikov, A. A. & Zavtrak, S. T. 1996 Interaction force between a bubble and a solid particle in a sound field. Ultrasonics 34, 807–815.Google Scholar
Elimelech, M., Gregory, J., Jia, X. & Williams, R. A. 1995 Particle Deposition and Aggregation. Measurement, Modelling and Simulation, p. 434. Butterworth-Heinemann, Woburn.Google Scholar
Embleton, T. F. W. 1954 Mean force on a sphere in a spherical sound field. i. (theoretical). J. Acoust. Soc. Am. 26, 40–45.Google Scholar
Faxen, H. 1922 Der Widerstand gegen die Bewegung einer starren Kugel in einer zähen Flüssigkeit, die zwischen zwei parallelen ebenen Wänden eingeschlossen ist. Ann. Phys. 373, 89–119.Google Scholar
Filippov, L. O., Matinin, A. S., Samiguin, V. D. & Filippova, I. V. 2013 Effect of ultrasound on flotation kinetics in the reactor–separator. J. Phys.: Conf. Ser. 416, 012016.Google Scholar
Flint, R. L. & Howarth, W. I. 1971 The collision efficiency of small particles with spherical air bubbles. Chem. Engng Sci. 26, 1155.CrossRefGoogle Scholar
Gaudin, A. M. 1957 Flotation, p. 573. McGraw-Hill.Google Scholar
Gogate, P. R., Tayal, R. K. & Pandit, A. B. 2006 Cavitation: a technology on the horizon. Curr. Sci. 91, 35–46.Google Scholar
Gorkov, L. P. 1962 On the forces acting on a small particle in an acoustical field in an ideal fluid. Sov. Phys. Dokl. 6, 773–775.Google Scholar
Hsieh, D. & Plesset, M. S. 1961 Theory of rectified diffusion of mass into gas bubbles. J. Acoust. Soc. Am. 33, 206–215.Google Scholar
King, L. V. 1934 On the acoustic radiation pressure on spheres. Proc. R. Soc. Lond. A 147, 212–240.Google Scholar
Klotsa, D., Swift, M. R., Bowley, R. M. & King, P. J. 2007 Interaction of spheres in oscillatory fluid flows. Phys. Rev. E 76, 056314.Google ScholarPubMed
Klotsa, D., Swift, M. R., Bowley, R. M. & King, P. J. 2009 Chain formation of spheres in oscillatory fluid flows. Phys. Rev. E 79, 021302.Google Scholar
Konig, W. 1891 Hydrodynamisch–akustische Untersuchungen. Ann. Phys. 278, 353–370.Google Scholar
Krasil’nikov, V. A. & Krylov, V. V. 1984 Vvedenie v Fizicheskuju Akustiku. M. Nauka.Google Scholar
Landau, L. D. & Lufshits, E. M. 1987 Fluid Mechanics – Course of Theoretical Physics. Butterworth-Heinemann.Google Scholar
Leighton, T. 2012 The Acoustic Bubble, p. 633. Academic.Google Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics, p. 573. Prentice Hall.Google Scholar
Lyubimov, D. V., Baydin, A. Y. & Lyubimova, T. P. 2013 Particle dynamics in a fluid under high frequency vibrations of linear polarization. Microgravity Sci. Technol. 25, 121–126.CrossRefGoogle Scholar
Lyubimov, D. V., Lyubimova, T. P. & Cherepanov, A. A. 2002 Behavior of a drop (bubble) in a non-uniform pulsating flow. Adv. Space Res. 29, 667–672.Google Scholar
Lyubimova, T., Lyubimov, D. & Shardin, M. 2011 Interaction of rigid cylinders in a low Reynolds number pulsational flow. Microgravity Sci. Technol. 23, 305–309.Google Scholar
Nguyen, A. V. 1999 Hydrodynamics of liquid flows around air bubbles in flotation: a review. Intl J. Miner. Process. 56, 165–205.Google Scholar
Nyborg, W. L. 1967 Radiation pressure on a small rigid sphere. J. Acoust. Soc. Am. 42, 947–952.Google Scholar
Ozkan, S. G. 2002 Beneficiation of magnesite slimes with ultrasonic treatment. Miner. Engng 15, 99–101.Google Scholar
Phan, C. M., Nguyen, A. V., Miller, J. D., Evans, G. M. & Jameson, J. G. 2003 Investigations of bubble–particle interactions. Intl J. Miner. Process. 72, 239–254.Google Scholar
Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamic and cavitation. Annu. Rev. Fluid Mech. 9, 145–185.Google Scholar
Settnes, M. & Bruus, H. 2012 Forces acting on a small particle in an acoustical field in a viscous fluid. Phys. Rev. E 85, 016327.Google Scholar
Wenze, K., Haixin, X. & Jun, H. 2008 Study of the effect of ultrasonic treatment on the surface composition and the flotation performance of high-sulfur coal. Fuel Process. Technol. 89, 1337–1344.Google Scholar
Yosioka, K. & Kawasima, Y. 1955 Acoustic radiation pressure on a compressible sphere. Acustica 5, 167–173.Google Scholar
Zaidi, S. A. H. 1997 Application of sonic energy to caustic cleaning of coals. Fuel Process. Technol. 53, 31–39.Google Scholar