EFFECT OF CAPILLARY PRESSURE IN NANOBUBBLES ON THEIR ADHERENCE TO PARTICLES DURING FROTH FLOATATION. PART 6. INFORMATIVITY OF BUBBLE SPREADING CURVES

Spreading curves (SCs) are calculated for bubble diameters (de) 1 mm and 1 μm on substrates with different wettability: from maximumhydrophobicity (Г) to maximum-hydrophilicity (Ф) as well as incompletely wettable (Нх) ones, where x = 0,8; 0,6; 0,4 and 0,2 is the fraction of an ionized collector monolayer under the bubble. The calculations were based on the results of a numerical solution of the Laplace equation in the form of 12-figure tables such as Bashforth and Adams tables. They demonstrate firstly that the SCs obtained are identical to those calculated for bubbles with de = 20 and 10 nm, and thus SC shapes are unchanged in the 105 range, i.e. virtually for all flotation bubbles, and secondly that SC shapes and their mutual arrangement depend on substrate wettability. Spreading curves clearly illustrate the advantages of substrate Г adhesion to the bubble in comparison with substrate Ф, and for Нх an advantage of the substrate with a larger fraction of x. It is quantitatively shown that even with small spreading of nanobubbles adhered to the particle, their adherence force increases billion times so that large bubbles can fix on their increased perimeters and lead the particle to flotation. If, however, the adhesion of large bubbles to nanobubbles occurs before spreading of the latter, they will come off together, and the particle will not float. This mechanism was used for particle flotation in the processes of the Bessel brothers, Potter-Delpra and two processes of F. Elmor in the late 19th and early 20th centuries. The prospect of increasing the productivity and cost-efficiency of modern froth flotation by activating particle flotation not only with nanobubbles but also with larger bubbles is considered.

spreading curves, Laplace equation, solid surface wettability, nanobubbles, maximum-hydrophobicity substrate, maximumhydrophilicity substrate, incompletely wettable substrate

1. Melik-Gaikazyan V.I., Emel’yanova N.P., Yushina T.I. Vliyanie kapillyarnogo davleniya v puzyr’karkh na ikh prilipanie k chastitsam pri pennoi flotatsii. Chast’ 1 [Influence effect of capillary pressure in bubbles upon their adhesion to particles at froth flotation. Pt. 1]. Izvestiya vuzov. Tsvetnaya metallurgiya. 2013. No. 1. P. 3—12. URL: http://dx.doi.org/10.17073/0021-3438-2013-1-3-12.

2. Melik-Gaikazyan V.I., Emel’yanova N.P., Yushina T.I. Vliyanie kapillyarnogo davleniya v puzyr’kakh na ikh prilipanie k chastitsam pri pennoi flotatsii. Chast’ 2 [Influence effect of capillary pressure in bubbles upon their adhesion to particles at froth flotation. Pt. 2]. Izvestiya vuzov. Tsvetnaya metallurgiya. 2013. No. 3. P. 7—12. URL: http://dx.doi.org/10.17073/0021-3438-2013-3-7-12.

3. Melik-Gaikazyan V.I., Emel’yanova N.P., Dolzhenkov D.V. Vliyanie kapillyarnogo davleniya v nanopuzyr’karkh na ikh prilipanie k chastitsam pri pennoi flotatsii. Chast’ 3 [Influence effect of capillary pressure in nanobubbles upon their adhesion to particles at froth flotation. Pt. 3]. Izvestiya. vuzov. Tsvetnaya metallurgiya. 2014. No. 3. P. 3— 10. URL: http://dx.doi.org/10.17073/0021-3438-2014-3-3-10.

4. Melik-Gaikazyan V.I., Titov V.S., Emel’yanova N.P., Dolzhenkov D.V. Vliyanie kapillyarnogo davleniya v nanopuzyr’karkh na ikh prilipanie k chastitsam pri pennoi flotatsii. Chast’ 4. Rastekayushchiesya nanopuzyr’ki — prirodnye fraktaly [Influence effect of capillary pressure in nanobubbles upon their adhesion to particles at froth flotation. Pt. 4. Spreading nanobubbles — natural fractals]. Izvestiya vuzov. Tsvetnaya metallurgiya. 2016. No. 4. P. 4—12. URL: http://dx.doi.org/10.17073/0021-3438-2016-4-4-12.

5. Melik-Gaikazyan V.I., Titov V.S., Emel’yanova N.P., Dolzhenkov D.V. Vliyanie kapillyarnogo davleniya v nanopuzyr’karkh na ikh prilipanie k chastitsam pri pennoi flotatsii. Chast’ 5. Krivye rastekaniya nanopuzyr’kov na poverkhnosti s razlichnoi smachivaemost’yu [The effect of capillary pressure in nanobubbes on their adhesion to particles during froth flotation. Pt. 5. Curves of nanobubble spreading upon a surface with various wettability]. Izvestiya vuzov. Tsvetnaya metallurgiya. 2017. No. 3. P. 11—22. URL: http://dx.doi.org/10.17073/0021-3438-2017-3-11-22.

6. Bashforth F., Adams J.C. An attempt to test the theories of capillary action: by comparing the theoretical and measured forms of drops of fluid. Cambridge: University Press, 1883.

7. Frumkin A.N. Fiziko-khimicheskie osnovy teorii flotatsii [Physico-chemical principles of the flotation theory]. Uspekhi khimii. 1933. Vol. 2. No. 1. P. 1—15.

8. Gegel’ G.V.F. Nauka logiki. Chast’ 1. Ob’’ektivnaya logika. Kniga 1. Uchenie o bytii [The science of logic. Pt. 1. Objective logic. Book 1. The doctrine of being]. Moscow: Profkom slushatelei Instituta Krasnoi professury, 1929. URL: https://royallib.com/read/gegel_georg_vilgelm_fridrih/uchenie_o_bitii.html#0 (accessed: 30.09.2017).

9. Guggengeim E.A. Sovremennaya termodinamika, izlozhennaya po metodu U. Gibbsa [Modern thermodynamics by the methods of W. Gibbs]. Moscow, Leningrad: Goschimizdat, 1941.

10. Guggenheim E.A. Modern thermodynamics by the methods of Willard Gibbs. London: Methuen & Co. Ltd., 1933.

11. Prigozhin I., Kondepudi D. Sovremennaya termodinamika [Modern thermodynamics]. Moscow: Mir, 2002. URL: http://mexalib.com/view/48445.

12. Kondepudi D., Prigogine I. Modern thermodynamics: from heat engines to dissipative structures. N.Y.: John Wiley & Sons, 2014.

13. Kabanov B., Frumkin A. Velichina puzyr’kov gaza, vydelyayushchikhsya pri elektrolize [The value of gas bubbles released during electrolysis]. Zhurnal fizicheskoi khimii. 1933. Vol. 4. No. 5. P. 538—548.

14. Kabanow В., Frumkin A. Nachtrag zu der Arbeit: «Über die Grösse elektrolytisch entwickelter Gasblasen». Z. Phys. Chem. A. 1933. Bd. 166. No. 3/4. S. 316—317; 1933. Bd. 164. No. 1/2. S. 121—133.

15. Hoover T.J. Concentrating ores by flotation. 3-rd ed. London: The Mining Magazine, 1916.

16. Sazerlend K.L., Uork I.V. Printsipy flotatsii [Principles of flotation]. Moscow: Metallurgizdat, 1958.

17. Edser E. The concentration of minerals by flotation. In; Forth report of colloid chemistry and its general and industrial applications. London: Majesty’s Stationery Office, 1922. P. 263—326.

18. Melik-Gaikazyan V.I., Emel’yanova N.P. Konkuriruyushchie predstavleniya v rabotakh po pennoi flotatsii i perspektivy ikh primeneniya dlya podbora reagentov [Competing views in works on flotation and prospects of their application for the selection of reagents]. Izvestiya vuzov. Tsvetnaya metallurgiya. 2007. No. 4. P. 4—21.

19. Frumkin A.N., Gorodetskaya A.V., Kabanov B.N., Nekrasov N.I. Elektrokapillyarnye yavleniya i smachivaemost’ metallov elektrolitami [Electrocapillary phenomena and wettability of metals with electrolytes]. Zhurnal fizicheskoi khimii. 1932. Vol. 3. No. 5—6. P. 351—367.

20. Langmuir I. The constitution and fundamental properties of solids and liquids. II. Liquids. J. Am. Chem. Soc. 1917. Vol. 39. No. 9. P. 1848—1906.

21. Langmuir I. The mechanism of the surface phenomena of flotation. Trans. Faraday Soc. 1920. Vol. 25. No. 6. P. 62—74.

22. Blodgett K.B. Films built by depositing successive monomolecular layers on a solid surface. J. Am. Chem. Soc. 1935. Vol. 57. No. 6. P. 1007—1022.

23. Adam N.K. The physics and chemistry of surfaces. London: Oxford University Press, 1941.