Effect of Bubble/Droplet Morphology and Slippage on Attachment Induction Time in Deoiling Flotation Process

Authors

Computational Fluid Dynamics (CFD) Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran, Iran

Abstract

A modified model has been analytically developed to describe the induction time of an elliptic air bubble in contact with an elliptic hydrophobic oil droplet. The role of hydrophobicity was revealed in the slippage of liquid over the surfaces of bubble and droplet. In this condition, the analytical relationships for pressure distribution and consequently hydrodynamic resistance force through the water film have been reported. The obtaining results were compared with the previous models and different orientations of approaching bubble and droplet have been investigated. It was found that the induction time is very sensitive to the orientation of bubble and droplet in collision. On the other hand, the role of slippage can be shown by the decrease in pressure and hydrodynamic resistance force in liquid film and also in induction time, in comparison with the case of drainage of a film confined between two particles under no-slip boundary conditions on their surfaces.

Keywords


[1] Abid, S. and Chesters, A.K. (1993). “The drainage and rupture of partially mobile films between colliding drops at constant approach velocity.” Int. J. Multiphase Flow,Vol. 20, pp. 613-629.

[2] Moosai, R. and Dawe, R.A. (2002).“Oily wastewater cleanup by gas flotation.”West Indian J. Eng., Vol. 25, pp. 25-41.

[3] Moosai, R. and Dawe, R.A. (2003).“Gas attachment of oil droplets for gas flotation for oily wastewater cleanup.”Separation and Purification Technol.,Vol. 33, pp. 303-314.

[4] Gu, G., Sanders, R.S., Nandakumar, K., Xu, Z. and Masliyah, J.H. (2004).“A novel experimental technique to study single bubble-bitumen attachment in flotation.”Int. J. Mineral Processing, Vol. 74, pp.15-29.

[5] Nguyen, A.V., Schulze, H.J. and Ralston, J. (1997). “Elementary steps in particle-bubble attachment.” Int. J. Mineral Processing, Vol. 51, pp. 183-195.

[6] Taylor, G.I. and Michael, D.H. (1973).“On making holes in a sheet of fluid.”J. Fluid Mechanics, Vol. 58, pp. 625-639.

[7] Prokhorov, A.V. and Derjaguin, B.V. (1994).“On the generalized theory of bi-layer film rupture.”Progress in Surface Science, Vol. 45, pp. 29-39.

[8]Yoon, R. and Yordan, J.L. (1991).“Induction time measurements for the quartz-amine flotation system.”J. Colloid Interface Sci., Vol. 141, No. 2, pp.374-383.

[9] Ye, Y., Miller, J.D. and Khandrika, S.M. (1989). “Induction time measurements at a particle bed.”Int. J. Mineral Processing, Vol. 25, pp. 221-240.

[10] Hewitt, D., Fornasiero and Ralston, J. (1995).“Bubble-particle attachment.”J. Chemical Society, Faraday Transactions, Vol. 91, No. 13, pp. 1997-2001.

[11] Schulze H.J. (1984).“Physico-chemical elementary process in flotation.”Hydrometallurgy, Vol. 12, pp. 275.

[12] Li, D., Fitzpatrick, J.A. and Slattery, J.C. (1990).“Rate of collection of particles by flotation.”Ind. Eng. Chem. Res., Vol. 29, No. 6, pp. 955-967.

[13] Wang, W., Zhou, Z., Nandakumar, K., Masliyah J.H. and Xu Z. (2005). “An induction time model for attachment of an air bubble to a hydrophobic sphere in aqueous solutions.” Mineral Processing, Vol. 75, pp. 69-82.

[14] Eftekhardadkhah, M. and Hashemabadi, S.H. (2008). “Influence of bubble and droplet shape and size on flotation time.” Proc. of 12th Iranian Chemical Engineering Congress.

[15] Hodgison, T.D. and Woods, S.M. (1973).“The effect of applied force on drainage of the film between a liquid drop and horizontal surface.”AIChE J., Vol. 19, pp. 810-817.

[16] Burrill, K.A. and Woods, D.R. (1973). “Film shapes for deformable drops at liquid-liquid interfaces II, The mechanisms of film drainage.” J. Colloid Interface Sci., Vol. 42, No. 1, pp. 15-34.

[17] Malhotra, A.K. and Wasan, D.T., (1987).“Effect of film size on drainage of foam and emulsion films.”AIChE J., Vol. 33, No. 9, pp. 1533-1541.

[18] Joye, J.L., Miller, C.A. and Hirasaki, G.J. (1992). “Dimple formation and behavior during axisymmetric foam film drainage.”Langmuir 8, 3082.

[19] Tsekov, R. and Ruckenstein, E. (1994). “Dimple formation and its effect on the rate of drainage in thin liquid films.” Colloids Surfaces, Vol. 82, pp. 255-261.

[20] Loth, E. (2008).“Quasi steady shape and drag of deformable bubbles and drops.”Int. J. Multiphase Flow, Vol. 34, pp. 523-546.

[21] Grattoni C., Moosai R. and Dawe R.A. (2003).“Photographic observations showing spreading and non-spreading of oil on gas bubbles of relevance to gas flotation for oily wastewater cleanup.”Colloids Surfaces, Vol. 214, pp. 151-155.

[22] Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002).“Transport Phenomena.”2nd Edition, John Wiley & Sons Inc., New York.

[23] Vinogradova, O.I. (1995). “Drainage of a thin liquid film confined between hydrophobic surfaces.” Langmuir, Vol. 11, pp. 2213-2220.