Abstract
The specific property of nanobubbles with spontaneous spreading over the solid hydrophobic particle substrate adhered to them, which is caused by a high capillary gas pressure in nanobubbles (P c > 106 N/m2), is considered. The computational principle of bubble spreading curves is considered and parameter X characterizing the intensity is introduced. Dependence X(a) (a is the bubble base diameter) is presented by a bimodal curve, which confirms that the nanobubble spreading is energetically provided by two sequentially acting independent sources. The first source is conditioned by the reduction (approximately by 11%) of the nanobubble curvilinear surface area at the initial spreading stage, and the second source is conditioned by the work of gas expansion caused by the drop of P c when the bubble is spreading. Parameter X is characterized by a considerably larger slope of dependence X(a) at the first spreading stage compared to the second one. It now turned out that the revealed property, which determines the efficiency of industrial flotation processes in past, finds prospects for application again after its recognition. Since it manifests itself in a limited range of bubble sizes, it is proposed to attribute it to the proper or natural fractal by analogy with the Brownian motion, which manifests itself in a definite range of particle sizes. The influence of the surface activity of flotation reagents on the shape of bubble spreading curves is shown.
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Melik-Gaikazyan, V.I., Emel’yanova, N.P., and Yushina, T.I., Influence of capillary pressure in bubbles on their attachment to particles during froth flotation: Part one, Russ. J. Non-Ferrous Met., 2013, vol. 54, no. 1, pp. 119–127.
Melik-Gaikazyan, V.I., Emel’yanova, N.P., and Yushina, T.I., Influence of capillary pressure in bubbles on their attachment to particles during froth flotation: Part two, Russ. J. Non-Ferrous Met., 2013, vol. 54, no. 4, pp. 281–286.
Melik-Gaikazyan, V.I., Emel’yanova, N.P., and Dolzhenkov, D.V., Influence of capillary pressure in bubbles on their attachment to particles during froth flotation: Part three, Russ. J. Non-Ferrous Met., 2014, vol. 55, no. 4, pp. 309–317.
Melik-Gaikazyan, V.I., Emel’yanova, N.P., Kozlov, P.S., Yushina, T.I., and Lipnaya, E.N., Investigation of froth flotation and selection of reagents on the basis of the mechanism of their effect: Report 1. Substantiation of the selected methods for investigation of the process, Russ. J. Non-Ferrous Met., 2009, vol. 50, no. 2, pp. 69–80.
Hoover, T.J., Concentrating Ores by Flotation, London: Mining Mag., 1916, 3rd ed.
Sutherland, K.L. and Wark, J.W., Principles of Flotation, Melbourne: Australian Inst. Mining Met., 1955.
Edser, E., The concentration of minerals by flotation // fourth report on colloid chemistry and its general and industrial applications, London: Majesty’s Stationery Office, 1922.
Bashforth, F. and Adams, J.C., An Attempt to Test the Theories of Capillary Action by Comparing the Theoretical and Measured Forms of Drops of Fluids, Cambridge: Cambridge Univ., 1883.
Bogdanov, O.S., Gol’man, A.M., Kakovskii, I.A., Klassen, V.I., and Solozhenkin, P.M., and Chanturija, V.A., Fiziko-khimicheskie osnovy teorii flotatsii: uchebnoe posobie (Physicochemical Foundations of the Flotation Theory: Textbook), Moscow, Gornaya Kniga, 2013.
Melik-Gaikazyan, V.I., Emel’yanova, N.P., and Yushina, T.I., Metody resheniya zadach teorii i praktiki flotatsii (Methods of the Solving Problems of Flotation Theory and Practice), Moscow: Gornaya Kniga, 2013.
Rakovskii, A.V., Kurs fizicheskoi khimii (Course of physical chemistry), Moscow: Gostekhizdat, 1939.
Papaleksi, N.D., Andreev, N.N., Rzhevskii, S.N., and Gorelik, G.S., Kurs fiziki (Course of Physics), Moscow–Leningrad: OGIZ, 1948, vol. 1.
Nanoabubbles exist, and are more stable than previously thought, http://www.physorg.com/news94728858.html, Cited April 28, 2015.
Lenindzher, A.L., Osnovy biokhimii (Fundamentals of Fiochemistry) Moscow: Mir, 1985.
Mandel’brot, B., Fraktal’naya geometriya prirody (Fractal Geometry of Nature), Moscow-Izhevsk: Inst. Comp. Sci., 2002.
Pockels, A.T., Surface tension, Nature, 1891, vol. 43, no. 1115, pp. 437–439.
Devaux, H.E., Oil films on water and on mercury, Annual Rep. Smithson. Inst., 1913, pp. 261–273.
Langmuir, I., The constitution and fundamental properties of solids and liquids. II. Liquids, J. Am. Chem. Soc., 1917, vol. XXXIX, no. 9, pp. 1848–1906.
George, L. and Gaines JR., The history of Langmuir–Blodgett films, Thin Solid Films, 1983, vol. 99, nos. 1/2/3, pp. 9–13.
Adam, N.K., Physical Chemistry of Surfaces, New York: Dover, 1968.
Melik-Gaikazyan, V.I., Abramov, A.A., Rubinshtein, Yu.B., Avdohin, V.M., and Solozhenkin, P.M., Metody issledovaniya flotatsionnogo protsessa (Research Methods of Flotation), Moscow: Nedra, 1990.
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Original Russian Text © V.I. Melik-Gaikazyan, V.S. Titov, N.P. Emel’yanova, D.V. Dolzhenkov, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii, Tsvetnaya Metallurgiya, 2016, No. 4, pp. 4–12.
Part I is published in [1], Part II is published in [2], and Part III is published in [3].
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Melik-Gaikazyan, V.I., Titov, V.S., Emel’yanova, N.P. et al. The influence of the capillary pressure in nanobubbles on their attachment to particles during froth flotation: Part IV. Spreading nanobubbles as natural fractals. Russ. J. Non-ferrous Metals 57, 521–528 (2016). https://doi.org/10.3103/S1067821216060110
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DOI: https://doi.org/10.3103/S1067821216060110