Abstract
We present results of a theoretical study of the steady motion of a spherical gas bubble in a viscous fluid which contains a soluble surfactant. For the model studied we present, through extensive numerical silmulations, conclusive evidence of increased mobility at the bubble interface as the surfactant concentration increases. This is demonstrated for both Stokes and Navier-Stokes flows. In the latter case, wakes are found to form behind the bubble when surfactants are present and the Reynolds number is sufficiently high. These wakes increase in size with increasing Reynolds number giving rise to large regions of almost stagnant flow. We also show that for a given wake formation regime, the wake can be removed completely and the bubble fully remobilized to its clean value by increasing the bulk concentration of surfactant. This can lead to significant improvement of technologies relying on enhanced mass transfer from the liquid to the gas phase, for example.
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References
Levich, V.G. Physicochemical Hydrodynamics. Prentice Hall, Englewood Cliffs, NJ, 1962.
Edwards, D.A., Brenner, H. and Wasan, D.T. Interfacial Transport Processes and Rheology. Butterworth-Heinemann, Boston, MA, 1991.
Huang, W.S. and Kintner,R.C. Effects of Surfactants on Mass Transfer Inside Drops. AIChEJ., 15 (1969), pp. 735–744.
Beitel, A. and Heideger,W.J. Surfactant Effects on Mass Transfer from Drops Subject to Interfacial Instability. Chem. Engng. Sci.,, 26 (1971), pp. 711–717.
Kim, H. and Subramanian,R. Thermocapillary Migration of a Droplet with Insoluble Surfactant, II. General Case J. Colloid and Int. Sci., 130 (1989), pp. 112–125.
Nadim, A. and Borhan, A. The Effects of Surfactant on The Motion and Deformation of a Droplet in Thermocapillary Migration. PhysicoChemical Hydrodynamics, 11 (1989), pp. 753–764.
Chen, J. and Stebe, K. Surfactant-induced retardation of the thermocapillary migration of a droplet. J. Fluid Mech. 340 (1997), pp. 35–60.
Savic, P. Circulation and distortion of liquid drops falling through a viscous medium. Nat. Res. Counc. Can., Div. Mech. Eng. Rep. MT-22 (1953).
Griffith, R.M. The effect of surfactants on the terminal velocity of drops and bubbles. Chem. Engng. Sci. 17 (1962), pp. 1057–1070.
Harper, J. F. On bubbles with small immobile adsorbed films rising in liquids at Low Reynolds numbers J. Fluid Mech., 58 (1973), pp. 539–545.
Davis, R. E. and Acrivos, A. The influence of surfactants on the creeping motion of bubbles. Chem. Engng. Sci., 21 (1966), pp. 681–685.
Holbrook, J. A. and Levan, M. D. Retardation of Droplet Motion by Surfactant. Part I. Theoretical development and asymptotic solutions. Chem. Eng. Commun., 20 (1983), pp. 191–207.
He, Z., Maldarelli, C. and Dagan, Z. The size of stagnant caps of bulk soluble surfactant on the interfaces of translating fluid droplets. J. Colloid and Interface Sci., 146 (1991), pp. 442–451.
Kim, H and Subramanian, R. Thermocapillary Migration of a Droplet with Insoluble Surfactant, I. Surfacant Cap. J. Colloid and Int. Sci., 127 (1989), pp. 417–430.
Bel Fdhila, R. and Duineveld, P. C. The effect of surfactants on the rise of a spherical bubble at high Reynolds and Peclet numbers. Phys. Fluids, 8 (1996), pp. 310–321.
McLaughlin, J.B. Numerical simulation of bubble motion in water. J. Colloid Int. Sci., 184 (1997), pp. 614–625.
Deryagin, B.V., Dukhin, S.S. and Lisichenko, V.A. The kinetics of the attachment of mineral particles to bubbles during flotation. I. The electric field of a moving bubble Russ. J. Phys. Chem., 33 (1959), pp. 389–393.
Saville, D. The effects of interfacial tension on the motion of drops and bubbles. Chem. Eng. J., 5 (1973), pp. 251–259.
Harper, J. F. On spherical bubbles rising steadily in dilute surfactant solutions Q. J! Mech. Appl. Math., XXVII (1974), pp. 87–100.
Harper, J. F. Surface activity and bubble motion Appl. Sci. Res. 38 (1982), pp. 343–351.
Andrews, G.F., Fike, R. and Wong, S. Bubble hydrodynamics and mass transfer at high Reynolds number and surfactant concentration Chem. Engng. Sci., 43 (1988), pp. 1467–1477.
Levan, M. and Newman, J. The effect of surfactant on the terminal and interfacial velocities of a bubble or drop. AICHE J., 22 (1976), pp. 695–701.
Holbrook, J. A. & Levan, M. D. Retardation of Droplet Motion by Surfactant. Part II. Numerical solutions for exterior diffusion, surface diffusion, and adsorption kinetics. Chem. Eng. Commun., 20 (1983), pp. 273–290.
Wang, Y. Theoretical study of bubble motion in surfactant solutions. Ph.D. Thesis, New Jersey Institute of Technology, 1999.
Wang, Y., Papageorgiou, D.T. and Maldarelli, Increased mobility of a surfactant retarded bubble at high bulk concentrations, J. Fluid Mech.,390 (1999), pp. 251270.
Wang, Y., Papageorgiou, D.T. and Maldarelli, C. Using surfactants to control the formation and size of wakes behind moving bubbles at order one Reynolds numbers, In preparation (1999).
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Papageorgiou, D.T., Maldarelli, C., Wang, Y. (2000). Mobility Control of Surfactant-Retarded Bubbles at Small and Order One Reynolds Numbers. In: Chang, HC. (eds) IUTAM Symposium on Nonlinear Waves in Multi-Phase Flow. Fluid Mechanics and Its Applications, vol 57. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1996-4_16
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DOI: https://doi.org/10.1007/978-94-017-1996-4_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5517-0
Online ISBN: 978-94-017-1996-4
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