Hostname: page-component-6bf8c574d5-gr6zb Total loading time: 0 Render date: 2025-02-14T09:49:38.473Z Has data issue: false hasContentIssue false
  • English
  • Français

Near-wall rising behaviour of a deformable bubble at high Reynolds number

Published online by Cambridge University Press:  22 April 2015

Hyeonju Jeong  and
Hyungmin Park
Hyeonju Jeong
Affiliation:
Department of Mechanical & Aerospace Engineering, Seoul National University, Seoul 151-744, Korea
Hyungmin Park*
Affiliation:
Department of Mechanical & Aerospace Engineering, Seoul National University, Seoul 151-744, Korea Institute of Advanced Machines and Design, Seoul National University, Seoul 151-744, Korea
*
†Email address for correspondence: hminpark@snu.ac.kr
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamics of a large deformable bubble ($\mathit{Re}\sim \mathit{O}(10^{3})$) rising near a vertical wall in quiescent water is experimentally investigated. The reference (without the wall) rising path of the considered bubble is a two-dimensional zigzag. For a range of wall configurations (i.e. initial wall distance and boundary condition), using high-speed shadowgraphy, various rising behaviours such as periodic bouncing, sliding, migrating away, and non-periodic oscillation without collisions are measured and analysed. Unlike low-Reynolds- and Weber-number bubbles, the contribution of the surface deformation to the transport between the energy components becomes significant during the bubble’s rise. In particular, across the bubble–wall collision, the excess surface energy compensates the deficit of kinetic energy. This enables a large deformable bubble to maintain a relatively constant bouncing kinematics, despite the obvious wall-induced energy dissipation. The wall effect, predominantly appearing as energy loss, is found to decrease as the initial distance from the bubble centre to the wall increases. Compared to the regular (no-slip) wall, a hydrophobic surface enhances or reduces the wall effect depending on the wall distance, whereas a porous surface reduces the energy loss due to the wall, regardless of the initial distance from the wall. Furthermore, the bubble–wall collision behaviour is assessed in terms of a restitution coefficient and modified impact Stokes number (ratio of the inertia to viscous forces), which shows a good correlation, the trends of which agree well with the variations in the energy components. The dependence of near-wall bubble motion on the wall distance and boundary condition may suggest a way of predicting or controlling the near-wall gas void-fraction distribution in gas–liquid flow systems.

JFM classification

Drops and Bubbles: Bubble dynamics Drops and Bubbles: Drops and Bubbles Multiphase and Particle-laden Flows: Gas/liquid flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 771 , 25 May 2015 , pp. 564 - 594
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bachhuber, C. & Sanford, C. 1974 The rise of small bubbles in water. J. Appl. Phys. 45, 2567–2569.Google Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.Google Scholar
Barker, S. J. & Crow, S. C. 1977 The motion of two-dimensional vortex pairs in a ground effect. J. Fluid Mech. 82, 659–671.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bearman, P. W. & Zdravkovich, M. M. 1978 Flow around a circular cylinder near a plane boundary. J. Fluid Mech. 89, 33–47.Google Scholar
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207.Google Scholar
Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562, 35–72.Google Scholar
Bröder, D. & Sommerfeld, M. 2007 Planar shadow image velocimetry for the analysis of the hydrodynamics in bubbly flows. Meas. Sci. Technol. 18, 2513–2528.Google Scholar
Bruneau, C.-H. & Mortazavi, I. 2008 Numerical modeling and passive flow control using porous media. Comput. Fluids 37, 488–498.CrossRefGoogle Scholar
Cano-Lozano, J. C., Bohorquez, P. & Martínez-Bazán, C. 2013 Wake instability of a fixed axisymmetric bubble of realistic shape. Intl J. Multiphase Flow 51, 11–21.CrossRefGoogle Scholar
Cassie, A. B. D. & Baxter, S. 1944 Wettability of porous surfaces. Trans. Faraday Soc. 40, 546–551.Google Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops, and Particles. Academic.Google Scholar
Cuenot, B., Magnaudet, J. & Spennato, B. 1997 The effects of slightly soluble surfactants on the flow around a spherical bubble. J. Fluid Mech. 339, 25–53.Google Scholar
Duineveld, P. C.1994 Bouncing and coalescence of two bubbles in water. PhD thesis, University of Twente, The Netherlands.Google Scholar
Duineveld, P. C. 1995 The rise velocity and shape of bubbles in pure water at high Reynolds number. J. Fluid Mech. 292, 325–332.Google Scholar
Duineveld, P. C. 1998 Bouncing and coalescence of bubble pairs rising at high Reynolds number in pure water or aqueous surfactant solutions. In Fascination of Fluid Dynamics (ed. Biesheuvel, A. & van Heijst, G. F.), pp. 409–439. Kluwer Academic.Google Scholar
Ellingsen, K. & Risso, F. 2001 On the rise of an ellipsoidal bubble in water: oscillatory paths and liquid-induced velocity. J. Fluid Mech. 440, 235–268.Google Scholar
Ern, P., Risso, F., Fabre, D. & Magnaudet, J. 2012 Wake-induced oscillatory paths of bodies freely rising or falling in fluids. Annu. Rev. Fluid Mech. 44, 97–121.Google Scholar
Figueroa-Espinoza, B., Zenit, R. & Legendre, D. 2008 The effect of confinement on the motion of a single clean bubble. J. Fluid Mech. 616, 419–443.Google Scholar
Gangloff, J. J. Jr, Hwang, W. R. & Advani, S. G. 2014 Characterization of bubble mobility in channel flow with fibrous porous media walls. Intl J. Multiphase Flow 60, 76–86.Google Scholar
Gondret, P., Lance, M. & Petit, L. 2002 Bouncing motion of spherical particles in fluids. Phys. Fluids 14, 643–652.Google Scholar
Gore, R. A. & Crowe, C. T. 1989 Effect of particle size on modulating turbulent intensity. Intl J. Multiphase Flow 15, 279–285.Google Scholar
Hahn, S., Je, J. & Choi, H. 2002 Direct numerical simulation of turbulent channel flow with permeable walls. J. Fluid Mech. 450, 259–285.Google Scholar
Hallez, Y. & Legendre, D. 2011 Interaction between two spherical bubbles rising in a viscous liquid. J. Fluid Mech. 673, 406–431.Google Scholar
Hosokawa, S. & Tomiyama, A. 2013 Bubble-induced pseudo turbulence in laminar pipe flows. Intl J. Heat Fluid Flow 40, 97–105.Google Scholar
Huang, W.-X. & Sung, H. J. 2007 Vortex shedding from a circular cylinder near a moving wall. J. Fluids Struct. 23, 1064–1076.Google Scholar
Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle–wall collisions in a viscous fluid. J. Fluid Mech. 433, 329–346.Google Scholar
Krasowska, M. & Malysa, K. 2007 Kinetics of bubble collision and attachment to hydrophobic solids: I. Effects of surface roughness. Intl J. Miner. Process. 81, 205–216.Google Scholar
Krasowska, M., Zawala, J. & Malysa, K. 2009 Air at hydrophobic surfaces and kinetics of three phase contact formation. Adv. Colloid Interface Sci. 147–148, 155–169.Google Scholar
Krishna, R., Urseanu, M. I., van Baten, J. M. & Ellenberger, J. 1999 Wall effects on the rise of single gas bubbles in liquids. Intl Commun. Heat Mass Transfer 26, 781–790.Google Scholar
Lee, S. J.2012 Laminar flow around a sphere in groundeffect. Master’s thesis, Seoul National University, Korea.Google Scholar
Legendre, D., Daniel, C. & Guiraud, P. 2005 Experimental study of a drop bouncing on a wall in a liquid. Phys. Fluids 17, 097105.Google Scholar
Legendre, D., Magnaudet, J. & Mougin, G. 2003 Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid. J. Fluid Mech. 497, 133–166.Google Scholar
Leja, J. 1982 Surface Chemistry of Froth Floatation. Plenum.Google Scholar
Magnaudet, J. & Eames, I. 2000 The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32, 659–708.Google Scholar
Magnaudet, J. & Mougin, G. 2007 Wake instability of a fixed spheroidal bubble. J. Fluid Mech. 572, 311–337.Google Scholar
Malysa, K., Kraswska, M. & Krzan, M. 2005 Influence of surface active substances on bubble motion and collision with various interfaces. Adv. Colloid Interface Sci. 114–115, 205–225.Google Scholar
Manes, C., Poggi, D. & Ridolfi, L. 2011 Turbulent boundary layers over permeable walls: scaling and near-wall structure. J. Fluid Mech. 687, 141–170.Google Scholar
Martell, M. B., Perot, J. B. & Rothstein, J. P. 2009 Direct numerical simulations of turbulent flows over superhydrophobic surfaces. J. Fluid Mech. 620, 31–41.Google Scholar
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics. MacMillan.Google Scholar
Min, T. & Kim, J. 2004 Effects of hydrophobic surface on skin-friction drag. Phys. Fluids 16, L55–L58.Google Scholar
Moctezuma, M. F., Lima-Ochoterena, R. & Zenit, R. 2005 Velocity fluctuations resulting from the interaction of a bubble with a vertical wall. Phys. Fluids 17, 098106.Google Scholar
Mougin, G. & Magnaudet, J. 2002 Path instability of a rising bubble. Phys. Rev. Lett. 88, 014502.Google Scholar
Mougin, G. & Magnaudet, J. 2006 Wake-induced forces and torques on a zigzagging/spiralling bubble. J. Fluid Mech. 567, 185–194.Google Scholar
Nam, Y., Kim, H. & Shin, S. 2013 Energy and hydrodynamic analyses of coalescence-induced jumping droplets. Appl. Phys. Lett. 103, 161601.Google Scholar
Nguyen, A. V. & Schulze, H. J. 2004 Colloidal Science of Floatation. Marcel Dekker.Google Scholar
Nilsson, M. A., Daniello, R. J. & Rothstein, J. P. 2010 A novel and inexpensive technique for creating superhydrophobic surfaces using teflon and sandpaper. J. Phys. D 43, 045301.Google Scholar
Park, H., Parn, H. & Kim, J. 2013 A numerical study of the effects of superhydrophobic surface on skin-friction drag in turbulent channel flow. Phys. Fluids 25, 110815.Google Scholar
Park, H., Sun, G. & Kim, C. J. 2014 Superhydrophobic turbulent drag reduction as a function of surface grating parameters. J. Fluid Mech. 747, 722–734.Google Scholar
Peace, A. J. & Riley, N. 1983 A viscous vortex pair in ground effect. J. Fluid Mech. 129, 409–426.Google Scholar
Princen, H. M. 1969 The equilibrium shape of interfaces, drops and bubbles. Rigid and deformable particles at interfaces. In Surface and Colloid Science (ed. Matijevic, E. & Eirich, F. R.), vol. 2, pp. 1–84. Plenum.Google Scholar
Rensen, J., Luther, S. & Lohse, D. 2005 The effect of bubbles on developed turbulence. J. Fluid Mech. 538, 153–187.Google Scholar
Rothstein, J. P. 2010 Slip on superhydrophobic surfaces. Annu. Rev. Fluid Mech. 42, 89–109.Google Scholar
Saleh, S., Thovert, J. F. & Adler, P. M. 1993 Flow along porous media by particle image velocimetry. AIChE J. 39, 1765–1776.Google Scholar
Sanada, T., Sato, A., Shirota, M. & Watanabe, M. 2009 Motion and coalescence of a pair of bubbles rising side by side. Chem. Engng Sci. 64, 2659–2671.Google Scholar
Schulze, H. J., Stockelhuber, K. W. & Wenger, A. 2001 The influence of acting forces on the rupture mechanism of wetting films – nucleation or capillary waves. Colloids Surf. A 192, 61–72.Google Scholar
Sheludko, A. 1967 Thin liquid films. Adv. Colloid Interface Sci. 1, 391–464.Google Scholar
Stancik, E. J. & Fuller, G. G. 2004 Connect the drop: using solids as adhesives for liquids. Langmuir 20, 4805–4808.Google Scholar
Sugiyama, K. & Takemura, F. 2010 On the lateral migration of a slightly deformed bubble rising near a vertical plane wall. J. Fluid Mech. 662, 209–231.Google Scholar
Takagi, S. & Matsumoto, Y. 2010 Surfactant effects on bubble motion and bubbly flows. Annu. Rev. Fluid Mech. 43, 615–636.Google Scholar
Takemura, F. & Magnaudet, J. 2003 The transverse force on clean and contaminated bubbles rising near a vertical wall at moderate Reynolds number. J. Fluid Mech. 495, 235–253.Google Scholar
Takemura, F., Takagi, S., Magnaudet, J. & Matsumoto, Y. 2002 Drag and lift forces on a bubble rising near a vertical wall in a viscous liquid. J. Fluid Mech. 461, 277–300.Google Scholar
Tsutsui, T. 2008 Flow around a sphere in a plane turbulent boundary layer. J. Wind Engng Ind. Aerodyn. 96, 779–792.Google Scholar
Uno, S. & Kinter, R. C. 1956 Effect of wall proximity on the rate of rise of single air bubbles in a quiescent liquid. AIChE J. 2, 420–425.Google Scholar
de Vries, A. W. G.2001 Path and wake of a rising bubble. PhD thesis, University of Twente, The Netherlands.Google Scholar
Wasan, D. T. & Nikolov, A. D. 2003 Spreading of nanofluids on solids. Nature 423, 156–159.Google Scholar
Yang, B. & Prosperetti, A. 2007 Linear stability of the flow past a spheroidal bubble. J. Fluid Mech. 582, 53–78.Google Scholar
Zaruba, A., Lucasa, D., Prasser, H.-M. & Höhne, T. 2007 Bubble–wall interactions in a vertical gas–liquid flow: bouncing, sliding and bubble deformations. Chem. Engng Sci. 62, 1591–1605.Google Scholar
Zawala, J. & Dabros, T. 2013 Analysis of energy balance during collision of an air bubble with a solid wall. Phys. Fluids 25, 123101.Google Scholar
Zawala, J., Krasowska, M., Dabros, T. & Malysa, K. 2007 Influence of bubble kinetic energy on its bouncing during collisions with various interfaces. Can. J. Chem. Engng 85, 669–678.Google Scholar
Zenit, R. & Legendre, D. 2009 The coefficient of restitution for air bubbles colliding against solid walls in viscous liquids. Phys. Fluids 21, 083306.Google Scholar
Zenit, R. & Magnaudet, J. 2008 Path instability of rising spheroidal air bubbles: a shape-controlled process. Phys. Fluids 20, 061702.Google Scholar