Analytical solution of equation relating maximum size of floating particle and its hydrophobicity;Analityczne rozwiązanie równania wiążącego maksymalny rozmiar flotującego ziarna i jego hydrofobowość

Physicochemical Problems of Mineral Processing

Volumn 46, Issue , 2011, Pages 13-20

  Watanabe, Masahiro ^a   Kowalczuk, Przemyslaw B ^b   Drzymala, Jan ^b  

^a Wrocław University of Technology ^*  (Japan)

^b WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Contact angle; Cubic equation; Flotation; Flotometry; Particle size

Indexed keywords

EID: 78649436927     PISSN: 16431049     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. Bewersdorff, J., 2006. Galois Theory for Beginners: A Historical Perspective. American Mathematical Society, Providence, Chap.2.
2. Birkhoff, G., Mac Lane, S., 1965. A Survey of Modern Algebra, third ed. Macmillan, New York, pp.90-91.
3. Chau, T.T., 2009. A review of techniques for measurement of contact angles and their applicability on mineral surfaces. Miner. Eng. 22, 213-219.
4. Cox, D.A., 2004. Galois Theory, John Wiley & Sons, Hoboken, Chap.1.
5. Dickson, L.E., 1914. Elementary Theory of Equations, John Wiley & Sons, New York, Chap.3.
6. Drzymala, J., 1994. Characterization of materials by Hallimond tube flotation. Part 2: maximum size of floating particles and contact angle. Int. J. Miner. Process. 42, 153-167; Erratum, Int. J. Miner. Process. 43, 135.
7. Drzymala, J., Lekki, J., 1989. Flotometry - another way of characterizing flotation. J. Colloid Interface Sci. 130, 205-210.
8. Gontijo, C. de F., Fornasiero, D., Ralston, J., 2007. The limits of fine and coarse particle flotation. Can. J. Chem. Eng. 85, 739-747.
9. Hannig, R.N., Rutter, P.R., 1989. A simple method of determining contact angles on particles and their relevance to flotation. Int. J. Miner. Process. 27, 133-146.
10. King, R.B., 1996. Beyond the Quartic Equation, Birkhäuser, Boston, Chap.5.
11. Koch, R., Noworyta, A., 1992. Mechanical processing in chemical engineering, WNT Warszawa (in Polish).
12. Konovalov, S.A., Tikhonov, O.N., 1982. Flotometric analysis using the variation principle in the regularisation method. Izv. VUZ. Tsvetnaya Metallurgiya 25, No.1, 100-104 (in Russian); English summary, Sov. Non-ferr. Met. Res. 10, 65.
13. Mitrofanov, S.I., Yatsenko, N.N., Kurochkina, A.V., 1970. Determining the critical inertial forces causing mineral particles to detach from air bubbles. Tsvetnye Metally 43, No.8, 87-89 (in Russian); English translation, Sov. J. Non-ferr. Met. 11, No.8, 85-87.
14. Morris, R.M., Matthesius, G.A., 1988. Froth flotation of coal fines: The influence of turbulence on cell performance. J. S. Afr. Inst. Min. Metall. 88, 385-391.
15. Nguyen, A.V, 2003. New method and equations for determining attachment tenacity and particle size limit in flotation. Int. J. Miner. Process. 68, 167-182.
16. Nguyen, A.V., Schulze, H.J., 2004. Colloidal Science of Flotation (Surfactant Science Series, vol. 118), Marcel Dekker, New York, Part 5: Stability of bubble-particle aggregates, Chap.23-24.
17. Rotman, J.J., 2000. A First Course in Abstract Algebra, second ed., Prentice Hall, Upper Saddle River, Chap.4.
18. Rotman, J.J., 2007. Journey into Mathematics: An Introduction to Proofs, Dover Publications, Mineola, Chap.4.
19. Scheludko, A., Toshev, B.V., Bojadjiev, D.T., 1976. Attachment of particles to a liquid surface (capillary theory of flotation). J. Chem. Soc. Faraday Trans. I 72, 2815-2828.
20. Schulze, H.J, 1993. Flotation as a heterocoagulation process: possibilities of calculating the probability of flotation. In: Coagulation and Flocculation. Theory and Applications, B. Dobias (Ed.) Marcel Dekker, New York, pp.321-353.
21. Tignol, J.-P., 1988. Galois' Theory of Algebraic Equations, Longman Scientific & Technical, Harlow, Chap.6.
22. Uspensky, J.V., 1948. Theory of Equations, McGraw-Hill, New York, Chap.5.