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The lift force on a bubble in a sheared suspension in a slightly inclined channel

  • XIAOLONG YIN (a1) and DONALD L. KOCH (a1)


The lattice Boltzmann method was applied to simulate the free rise of monodisperse non-coalescing spherical bubbles in slightly inclined channels bound by solid walls. The Reynolds number based on the relative velocity between the bubbles and the fluid ranged from 4 to 16, the volume fraction from 5% to 10% and the inclination angle from 2° to 6°. The simulations revealed that the weak buoyancy component normal to the walls led to a layer of bubbles near the upper wall and a depleted layer near the bottom wall. These thin layers drove a nearly viscometric shear flow within the bulk of the channel that allowed an unambiguous determination of the lift force in a sheared homogeneous and freely evolving bubble suspension. The lift force coefficients calculated from our simulations were always higher than those for isolated spherical bubbles, suggesting that the lift force is enhanced by hydrodynamic interactions among the bubbles. Experimental measurements of the velocity gradient in 10% volume fraction bubble suspensions in glycerine–water–electrolyte mixtures in slightly inclined channels yielded lift coefficients in excess of those predicted for isolated bubbles and confirmed the qualitative predictions of the simulations.



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Auton, T. R. 1987 The lift force on a spherical body in a rotational flow. J. Fluid Mech. 197, 241257.
Biesheuval, A. & Spoelstra, S. 1989 The added mass coefficient of a dispersion of spherical gas bubbles in liquid. Intl J. Multiphase Flow 15, 911924.
Bulthuis, H. F., Prosperetti, A. & Sangani, A. S. 1995 ‘Particle stress’ in disperse two-phase potential flow. J. Fluid Mech. 294, 116.
Bunner, B. & Tryggvason, G. 2003 Effect of bubble deformation on the properties of bubbly flows. J. Fluid Mech. 495, 77118.
Chen, A. U., Notz, P. K. & Basaran, O. A. 2002 Computational and experimental analysis of pinch-off and scaling. Phys. Rev. Lett. 88, 174501.
d'Humières, D., Ginzburg, I., Krafczyk, M., Lallemand, P. & Luo, L.-S. 2002 Multiple-relaxation-time lattice Boltzmann models in three dimensions. Phils. Trans. R. Soc. A 360, 437451.
Kang, S.-Y., Sangani, A. S., Tsao, H.-K. & Koch, D. L. 1997 Rheology of dense bubble suspensions. Phys. Fluids 9 (6), 15401561.
Kim, S. & Karrila, S. J. 2005 Microhydrodynamics: Principles and Selected Applications. Dover.
Ladd, A. J. C. 1994 a Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285309.
Ladd, A. J. C. 1994 b Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J. Fluid Mech. 271, 311339.
Ladd, A. J. C. & Verberg, R. 2001 Lattice-Boltzmann simulations of particle–fluid suspensions. J. Stat. Phys. 104, 11911251.
Legendre, D. & Magnaudet, J. 1997 A note on the lift force on a bubble or a drop in a low-{R}eynolds-number shear flow. Phys. Fluids 9, 35723574.
Legendre, D. & Magnaudet, J. 1998 Lift force on a bubble in a viscous linear shear flow. J. Fluid Mech. 368, 81126.
Lessard, R. R. & Zieminski, S. A. 1971 Bubble coalescence and gas transfer in electrolitic aqueous solutions. Ind. Engng Chem. Fundam. 10, 260269.
Lighthill, M. J. 1956 Drift. J. Fluid Mech. 1, 3153.
Magnaudet, J. & Eames, I. 2000 The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32, 659708.
Maxworthy, T., Gnann, C., Kürten, M. & Durst, F. 1996 Experiments on the rise of air bubbles in clean viscous liquids. J. Fluid Mech. 321, 421441.
McLaughlin, J. B. 1991 Inertial migration of a small sphere in linear shear flows. J. Fluid Mech. 224, 261274.
Nguyen, N.-Q. & Ladd, A. J. C. 2002 Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. Phys. Rev. E 66, 046708.
Rensen, J., Bosman, D., Magnaudet, J., Ohl, C.-D., Prosperetti, A., Tögel, R., Versluis, M. & Lohse, D. 2001 Spiraling bubbles: how acoustic and hydrodynamic forces compete. Phys. Rev. Lett. 86, 48194822.
Saffman, P. G. 1965 The lift force on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385400.
Sangani, A. S. & Acrivos, A. 1983 Creeping flow through cubic arrays of spherical bubbles. Intl J. Multiphase Flow 9, 181185.
Sangani, A. S. & Didwania, A. K. 1993 Dispersed-phase stress tensor of bubbly liquids at large Reynolds numbers. J. Fluid Mech. 248, 2754.
Sangani, A. S. & Mo, G. 1994 Inclusion of lubrication forces in dynamical simulations. Phys. Fluids 6, 16531662.
Sankaranarayanan, K. & Sundaresan, S. 2002 Lift force in bubbly suspensions. Chem. Engng Sci. 57, 35213542.
Spelt, P. D. M. & Sangani, A. S. 1998 Properties and averaged equations for flows of bubbly liquids. Appl. Sci. Res. 58, 337386.
Sridhar, G. & Katz, J. 1995 Drag and lift forces on microscopic bubbles entrained by a vortex. Phys. Fluids 7, 389399.
Taylor, G. I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A 138, 4148.
Tomiyama, A., Tamai, H., Zun, I. & Hosokawa, S. 2002 Transverse migration of single bubbles in simple shear flows. Chem. Engng Sci. 57, 18491858.
Tsao, H.-K. & Koch, D. L. 1994 Collisions of slightly deformable, high Reynolds number bubbles with short-range repulsive forces. Phys. Fluids 6, 25912605.
Van Nierop, E. A., Luther, S., Bluemink, J. J., Magnaudet, J., Prosperetti, A. & Lohse, D. 2007 Drag and lift forces on bubbles in a rotating flow. J. Fluid Mech. 571, 439454.
Weissenborn, P. K. & Pugh, R. J. 1996 Surface tension of aqueous solutions of electrolytes: Relationship with ion hydration, oxygen solubility, and bubble coalescence. J. Colloid Interface Sci. 14, 550563.
Wells, J. C. 1996 A geometrical interpretation of force on a translating body in rotational flow. Phys. Fluids 8, 442450.
van Wijngaarden, L. 1976 Hydrodynamic interactions between bubbles in liquid. J. Fluid Mech. 77, 2744.
Yin, X. 2007 Structure-property relations in bubble and solid particle suspensions with moderate Reynolds numbers. PhD thesis. Cornell University, Ithaca, NY, USA.
Yin, X., Koch, D. L. & Verberg, R. 2006 Lattice-Boltzmann method for simulating spherical bubbles with no-tangential stress boundary conditions. Phys. Rev. E 73, 026301.
Zenit, R., Koch, D. L. & Sangani, A. S. 2001 Measurements of the average properties of a suspension of bubbles rising in a vertical channel. J. Fluid Mech. 429, 307342.
Zenit, R., Koch, D. L. & Sangani, A. S. 2003 Impedance probe to measure local gas volume fraction and bubble velocity in a bubbly liquid. Rev. Sci. Instrum. 74, 28172827.
Zenit, R., Tsang, Y. H., Koch, D. L. & Sangani, A. S. 2004 Shear flow of a suspension of bubbles rising in an inclined channel. J. Fluid Mech. 515, 261292.
Zhang, D. Z. & Prosperetti, A. 1994 Averaged equations for inviscid disperse two-phase flow. J. Fluid Mech. 267, 185219.
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