Microflotation of fine particles in the presence of a bulk-insoluble surfactant

International Journal of Multiphase Flow

Volumn 26, Issue 6, 2000, Pages 891-920

  Ramirez, José A ^a   Davis, Robert H ^a   Zinchenko, Alexander Z ^a  

^a University of Colorado at Boulder   (United States)

Author keywords

Bubbles; Collisions; Flotation; Mobilities; Particles; Surfactants

Indexed keywords

ADSORPTION; BROWNIAN MOVEMENT; BUBBLES (IN FLUIDS); DIFFUSION IN LIQUIDS; GRAVITATIONAL EFFECTS; HYDRODYNAMICS; MULTIPHASE FLOW; PARTICLES (PARTICULATE MATTER); PHASE INTERFACES; SOLUBILITY; SURFACE ACTIVE AGENTS; VAN DER WAALS FORCES;

MARANGONI NUMBERS;

FLOTATION;

BUBBLE; COLLISION; FLOTATION; PARTICLE; SURFACTANT;

EID: 0034031189     PISSN: 03019322     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0301-9322(99)00074-9     Document Type: Article

References (33)

1. Agrawal S., Wasan D. The effect of interfacial viscosities on the motion of drops and bubbles. Chem. Eng. J. 18:1979;215-223.
2. Batchelor G.K. Sedimentation in a dilute polydisperse system of interacting spheres. Part I: general theory. J. Fluid Mech. 119:1982;379-408.
3. Blawzdziewicz, J., Wajnryb, E., Loewenberg, M., 1999. Hydrodynamic interactions and collision efficiencies of spherical drops covered with an incompressible surfactant film. J. Fluid Mech.395, 29-59.
4. Brunn P.O., Isemin D. Dimensionless heat-mass transfer coefficients for forced convection around a sphere: a good general low Reynolds number correlation. Int. J. Heat Mass Transfer. 27:1984;2339-2345.
5. Cristini V., Blawzdziewicz J., Loewenberg M. Near-contact motion of surfactant-covered spherical drops. J. Fluid Mech. 366:1998;259-287.
6. Cuenot B., Magnaudet J., Spennato B. The effects of slightly soluble surfactants on the flow around a spherical bubble. J. Fluid Mech. 339:1997;25-53.
7. Frumkin A., Levich V.G. O vliyanii poverkhnostno-aktivnikh veshestv na dvizhenie na granitse zhidkikh sred. Zhur. Fizic. Khimii. 21:1947;1183-1204.
8. Gaudin A.M. Flotation. 2nd ed :1957;McGraw-Hill, NY.
9. Griffith R. The effect of surfactants on the terminal velocity of drops and bubbles. Chem. Eng. Sci. 17:1962;1057-1070.
10. Happel J., Brenner H. Low Reynolds Number Hydrodynamics. 1986;Martinus Nijhoff Publishers, Boston, MA.
11. Harper J.F. The near stagnation region of a bubble rising steadily in a dilute surfactant solution. Q. J. Mech. Appl. Math. 41:1988;204-213.
12. Ho N.F., Higuchi W.I. Preferential aggregation and coalescence in netero dispersed system. J. Pharm. Sci. 57:1968;436-442.
13. Holbrook J.A., LeVan M.D. Retardation of droplet motion by surfactants. Part I: theoretical development asymptotic solutions. Chem. Eng. Commun. 20:1983;191-207.
14. Jeffery G.B. On a form of the solution of Laplace/s equation suitable for problems relating to two spheres. Proc. Roy. Soc. A87:1912;109-120.
15. Kawase Y., Ulbrecht J.J. The effect of surfactant on terminal velocity of and mass transfer from a fluid sphere in a non-Newtonian fluid. Can. J. Chem. Eng. 60:1982;87-93.
16. Lamb H. Hydrodynamics. 6th ed :1990;Dover, New York.
17. Lerner L., Harper J.F. Stokes flow past a pair of stagnant-cap bubbles. J. Fluid Mech. 232:1991;167-190.
18. Levich V. Physicochemical Hydrodynamics. 1962;Prentice-Hall, Englewood Cliffs, NJ.
19. Lochiel A.C. The influence of surfactants on mass transfer around spheres. Can. J. Chem. Eng. 43:1965;40-44.
20. Loewenberg M., Davis R.H. Flotation rates of fine spherical particles and droplets. Chem. Eng. Sci. 49:1994;3923-3941.
21. Ramirez, J.A., Davis, R.H., 1999. Mass transfer to a surfactant-covered bubble. AIChE J 45, 1355-1358.
22. Ramirez J.A., Zinchenko A., Loewenberg M.L., Davis R.H. The flotation rates of fine spherical particles under convective and Brownian motion. Chem. Eng. Sci. 54:1999;149-157.
23. Sadhal S., Johnson R. Stokes flow past bubbles and drops partially coated with thin films. J. Fluid Mech. 126:1983;237-250.
24. Saville D. The effect of interfacial tension gradients and droplet behaviour. Chem. Eng. J. 5:1973;251-259.
25. Schenkel J.H., Kitchener J.A. A test of the Derjaguin-Verwey-Overbeek theory with a colloidal suspension. Trans. Farad. Society. 56:1960;161-173.
26. Stimson M., Jefferey G.B. The motion of two spheres in a viscous fluid. Proc. Roy. Soc. A111:1926;110-116.
27. Wasserman M., Slattery J. Creeping flow past a fluid globule when a trace of surfactant is present. AIChE J. 15:1969;533-541.
28. Yang S.-M., Han S.P., Hong J.J. Capture of small particles on a bubble collection by Brownian diffusion and interception. J. Colloid Interf. Sci. 169:1995;125-134.
29. Zabel, T., 1984. Flotation in water treatment. In: Ives, K.J. (Ed.), The Scientific Basis of Flotation. NATO ASI Series, Series E: Applied Sciences - No. 75, 349. Martinus Nijhoff Publishers, The Hague, NL.
30. Zhang X., Davis R.H. The rate of collisions due to Brownian or gravitational motion of small drops. J. Fluid Mech. 230:1991;479-504.
31. Zinchenko A.Z. The slow asymmetric motion of two drops in a viscous medium. Prikl. Matem. Mekhan. 44:1980;30-37.
32. Zinchenko A.Z. Calculation of the effectiveness of gravitational coagulation of drops with allowance for internal circulation. Prikl. Matem. Mekhan. 46:(1):1982;58-65.
33. Zinchenko A.Z., Davis R.H. Gravity-induced coalescence of drops at arbitrary Péclet numbers. J. Fluid Mech. 280:1994;119-148.