Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T08:43:53.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Bubble rise in a Hele-Shaw cell: bridging the gap between viscous and inertial regimes

Published online by Cambridge University Press:  18 May 2022

Benjamin Monnet ,
Christopher Madec ,
Valérie Vidal Open the ORCID record for Valérie Vidal [Opens in a new window] ,
Sylvain Joubaud Open the ORCID record for Sylvain Joubaud [Opens in a new window]  and
J. John Soundar Jerome Open the ORCID record for J. John Soundar Jerome [Opens in a new window]
Benjamin Monnet
Affiliation:
ENSL, CNRS, Laboratoire de Physique, F-69342 Lyon, France
Christopher Madec
Affiliation:
ENSL, CNRS, Laboratoire de Physique, F-69342 Lyon, France
Valérie Vidal
Affiliation:
ENSL, CNRS, Laboratoire de Physique, F-69342 Lyon, France
Sylvain Joubaud*
Affiliation:
ENSL, CNRS, Laboratoire de Physique, F-69342 Lyon, France Institut Universitaire de France (IUF), 1 rue Descartes, 75005 Paris, France
J. John Soundar Jerome
Affiliation:
Univ Lyon, Univ Claude Bernard Lyon 1, CNRS, Ecole Centrale de Lyon, INSA Lyon, LMFA, UMR5509, 69622 Villeurbanne, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The rise of a single bubble confined between two vertical plates is investigated over a wide range of Reynolds numbers. In particular, we focus on the evolution of the bubble speed, aspect ratio and drag coefficient during the transition from the viscous to the inertial regime. For sufficiently large bubbles, a simple model based on power balance captures the transition for the bubble velocity and matches all the experimental data despite strong time variations of bubble aspect ratio at large Reynolds numbers. Surprisingly, bubbles in the viscous regime systematically exhibit an ellipse elongated along its direction of motion while bubbles in the inertia-dominated regime are always flattened perpendicularly to it.

JFM classification

Drops and Bubbles: Bubble dynamics Low-Reynolds-number flows: Hele-Shaw flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 942 , 10 July 2022 , R3
Check for updates
Copyright
© The Author(s), 2022. Published by 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

REFERENCES

Batchelor, G.K. 2000 An Introduction to Fluid Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Bush, J.W.M. & Eames, I. 1998 Fluid displacement by high Reynolds number bubble motion in a thin gap. Intl J. Multiphase Flow 24 (3), 411–430.CrossRefGoogle Scholar
Clift, R., Grace, J.R. & Weber, M.E. 1978 Bubbles, drops, and particles. Academic Press.Google Scholar
Collins, R. 1965 A simple model of the plane gas bubble in a finite liquid. J. Fluid Mech. 22 (4), 763–771.CrossRefGoogle Scholar
Danov, K., Lyutskanova-Zhekova, G. & Smoukov, S. 2021 Motion of long bubbles in gravity-and pressure-driven flow through cylindrical capillaries up to moderate capillary numbers. Phys. Fluids 33 (11), 113606.CrossRefGoogle Scholar
Davies, R.M. & Taylor, G.I. 1950 The mechanics of large bubbles rising through extended liquids and through liquids in tubes. Proc. R. Soc. Lond. A 200 (1062), 375–390.Google Scholar
Doi, M. 2011 Onsager's variational principle in soft matter. J. Phys.: Conden. Matter 23 (28), 284118.Google ScholarPubMed
Eck, W. & Siekmann, J. 1978 On bubble motion in a Hele-Shaw cell, a possibility to study two-phase flows under reduced gravity. Ing.-Arch. 47 (3), 153–168.CrossRefGoogle Scholar
Filella, A., Ern, P. & Roig, V. 2015 Oscillatory motion and wake of a bubble rising in a thin-gap cell. J. Fluid Mech. 778, 60–88.CrossRefGoogle Scholar
Gaillard, A., Keeler, J., Le Lay, G., Lemoult, G., Thompson, A., Hazel, A. & Juel, A. 2021 The life and fate of a bubble in a geometrically perturbed Hele-Shaw channel. J. Fluid Mech. 914, A34.CrossRefGoogle Scholar
Harper, J.F. 1972 The motion of bubbles and drops through liquids. Adv. Appl. Mech. 12, 59–129.CrossRefGoogle Scholar
Hashida, M., Hayashi, K. & Tomiyama, A. 2019 Rise velocities of single bubbles in a narrow channel between parallel flat plates. Intl J. Multiphase Flow 111, 285–293.CrossRefGoogle Scholar
Hashida, M., Hayashi, K. & Tomiyama, A. 2020 Effects of fine particles on terminal velocities of single bubbles in a narrow channel between parallel flat plates. Intl J. Multiphase Flow 127, 103270.CrossRefGoogle Scholar
Keiser, L., Jaafar, K., Bico, J. & Reyssat, E. 2018 Dynamics of non-wetting drops confined in a Hele-Shaw cell. J. Fluid Mech. 845, 245–262.CrossRefGoogle Scholar
Kelley, E. & Wu, M. 1997 Path instabilities of rising air bubbles in a Hele-Shaw cell. Phys. Rev. Lett. 79 (7), 1265.CrossRefGoogle Scholar
Madec, C., Collin, B., John Soundar Jerome, J. & Joubaud, S. 2020 Puzzling bubble rise speed increase in dense granular suspensions. Phys. Rev. Lett. 125 (7), 078004.CrossRefGoogle ScholarPubMed
Maxworthy, T. 1986 Bubble formation, motion and interaction in a Hele-Shaw cell. J. Fluid Mech. 173, 95–114.CrossRefGoogle Scholar
Maxworthy, T., Gnann, C., Kürten, M. & Durst, F. 1996 Experiments on the rise of air bubbles in clean viscous liquids. J. Fluid Mech. 321, 421–441.CrossRefGoogle Scholar
Park, C.-W. & Homsy, G.M. 1984 Two-phase displacement in hele shaw cells: theory. J. Fluid Mech. 139, 291–308.CrossRefGoogle Scholar
Pavlov, L., Cazin, S., Ern, P. & Roig, V. 2021 a Exploration by shake-the-box technique of the 3d perturbation induced by a bubble rising in a thin-gap cell. Exp. Fluids 62 (1), 22.CrossRefGoogle Scholar
Pavlov, L., D'Angelo, M.V., Cachile, M., Roig, V. & Ern, P. 2021 b Kinematics of a bubble freely rising in a thin-gap cell with additional in-plane confinement. Phys. Rev. Fluids 6 (9), 093605.CrossRefGoogle Scholar
Roig, V., Roudet, M., Risso, F. & Billet, A.-M. 2012 Dynamics of a high-Reynolds-number bubble rising within a thin gap. J. Fluid Mech. 707, 444–466.CrossRefGoogle Scholar
Tanveer, S. 1987 New solutions for steady bubbles in a Hele-Shaw cell. Phys. Fluids 30 (3), 651–658.CrossRefGoogle Scholar
Taylor, G. & Saffman, P.G. 1959 A note on the motion of bubbles in a Hele-Shaw cell and porous medium. Q. J. Mech. Appl. Maths 12 (3), 265–279.CrossRefGoogle Scholar
Toupoint, C., Joubaud, S. & Sutherland, B.R. 2021 Fall and break-up of viscous miscible drops in a Hele-Shaw cell. Phys. Rev. Fluids 6 (10), 103601.CrossRefGoogle Scholar
Tripathi, M.K., Sahu, K.C. & Govindarajan, R. 2015 Dynamics of an initially spherical bubble rising in quiescent liquid. Nat. Commun. 6 (1), 6268.CrossRefGoogle ScholarPubMed
Wang, X., Klaasen, B., Degrève, J., Blanpain, B. & Verhaeghe, F. 2014 Experimental and numerical study of buoyancy-driven single bubble dynamics in a vertical Hele-Shaw cell. Phys. Fluids 26 (12), 123303.CrossRefGoogle Scholar
Xu, X., Doi, M., Zhou, J. & Di, Y. 2020 Theoretical analysis for flattening of a rising bubble in a Hele-Shaw cell. Phys. Fluids 32 (9), 092102.CrossRefGoogle Scholar

Monnet et al. Supplementary Movie 1

Individual bubbles rising for two different Reynolds number (see figure 1(b))

Download Monnet et al. Supplementary Movie 1(Video)
Video 3.7 MB