Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-26T17:38:53.091Z Has data issue: false hasContentIssue false
  • English
  • Français

Surface bubble coalescence

Published online by Cambridge University Press:  25 March 2021

Daniel B. Shaw Open the ORCID record for Daniel B. Shaw [Opens in a new window]  and
Luc Deike Open the ORCID record for Luc Deike [Opens in a new window]
Daniel B. Shaw
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
Luc Deike*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA High Meadows Environmental Institute, Princeton University, Princeton, NJ08544, USA
*
†Email address for correspondence: ldeike@princeton.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We present an experimental study of bubble coalescence at an air–water interface and characterize the evolution of both the underwater neck and the surface bridge. We explore a wide range of Bond number, $Bo$, which compares gravity and capillary forces and is a dimensionless measure of the free surface's effect on bubble geometry. The nearly spherical $Bo\ll 1$ bubbles exhibit the same inertial–capillary growth of the classic underwater dynamics, with limited upper surface displacement. For $Bo>1$, the bubbles are non-spherical – residing predominantly above the free surface – and, while an inertial–capillary scaling for the underwater neck growth is still observed, the controlling length scale is defined by the curvature of the bubbles near their contact region. With it, an inertial–capillary scaling collapses the neck contours across all Bond numbers to a universal shape. Finally, we characterize the upper surface with a simple oscillatory model which balances capillary forces and the inertia of liquid trapped at the centre of the liquid-film surface.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Bubble dynamics Waves/Free-surface Flows: Capillary waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A105
Check for updates
Copyright
© The Author(s), 2021. 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

Aarts, D.G.A.L., Lekkerkerker, H.N.W., Guo, H., Wegdam, G.H. & Bonn, D. 2005 Hydrodynamics of droplet coalescence. Phys. Rev. Lett. 95, 164503.CrossRefGoogle ScholarPubMed
Berny, A., Deike, L., Séon, T. & Popinet, S. 2020 Role of all jet drops in mass transfer from bursting bubbles. Phys. Rev. Fluids 5, 033605.CrossRefGoogle Scholar
Berry, J.D. & Dagastine, R.R. 2017 Mapping coalescence of micron-sized drops and bubbles. J. Colloid Interface Sci. 487, 513–522.CrossRefGoogle ScholarPubMed
Brasz, C.F., Bartlett, C.T., Walls, P.L.L., Flynn, E.G., Yu, Y.E. & Bird, J.C. 2018 Minimum size for the top jet drop from a bursting bubble. Phys. Rev. Fluids 7 (3), 1–17.Google Scholar
Chesters, A.K. 1991 The modelling of coalescence processes in fluid-liquid dispersions: a review of current understanding. Chem. Engng Res. Des. 69 (4), 259–270.Google Scholar
Clift, R., Grace, J. & Weber, M. 1978 Bubbles, Drops, and Particles. Dover.Google Scholar
Cochran, R.E., Ryder, O.S., Grassian, V.H. & Prather, K.A. 2017 Sea spray aerosol: the chemical link between the oceans, atmosphere, and climate. Acc. Chem. Res. 50 (3), 599–604.CrossRefGoogle ScholarPubMed
Coutris, N. 1993 Balance equations for fluid lines, sheets, filaments and membranes. Intl J. Multiphase Flow 19 (4), 611–637.CrossRefGoogle Scholar
Craig, V.S.J., Ninham, B.W. & Pashley, R.M. 1993 Effect of electrolytes on bubble coalescence. Nature 364, 317–319.CrossRefGoogle Scholar
Dalbe, M.J., Cosic, D., Berhanu, M. & Kudrolli, A. 2011 Aggregation of frictional particles due to capillary attraction. Phy. Rev. E 83 (5), 1–10.CrossRefGoogle ScholarPubMed
Deike, L., Ghabache, E., Liger-Belair, G., Das, A.K., Zaleski, S., Popinet, S. & Séon, T. 2018 Dynamics of jets produced by bursting bubbles. Phys. Rev. Fluids 3 (1), 1–20.CrossRefGoogle Scholar
Deike, L. & Melville, W.K. 2018 Gas transfer by breaking waves. Geophys. Res. Lett. 45 (19), 10482–10492.CrossRefGoogle Scholar
Drenckhan, W., Dollet, B., Hutzler, S. & Elias, F. 2008 Soap films under large-amplitude oscillations. Phil. Mag. Let. 88 (9-10), 669–677.CrossRefGoogle Scholar
Eddi, A., Winkels, K.G. & Snoeijer, J.H. 2013 Influence of droplet geometry on the coalescence of low viscosity drops. Phys. Rev. Lett. 111 (14), 1–5.CrossRefGoogle ScholarPubMed
Eggers, J., Lister, J.R. & Stone, H.A. 1999 Coalescence of liquid drops. J. Fluid Mech. 401, 293–310.CrossRefGoogle Scholar
Grinfeld, P. 2012 Small oscillations of a soap bubble. Stud. Appl. Maths 128 (1), 30–39.CrossRefGoogle Scholar
Kornek, U., Müller, F., Harth, K., Hahn, A., Ganesan, S., Tobiska, L. & Stannarius, R. 2010 Oscillations of soap bubbles. New J. Phys. 12, 073031.CrossRefGoogle Scholar
Lai, C.Y., Eggers, J. & Deike, L. 2018 Bubble bursting: universal cavity and jet profiles. Phys. Rev. Lett. 121 (14), 144501.CrossRefGoogle ScholarPubMed
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Langevin, D. 2015 Bubble coalescence in pure liquids and in surfactant solutions. Curr. Opin. Colloid Interface Sci. 20 (2), 92–97.CrossRefGoogle Scholar
de Leeuw, G., Andreas, E.L., Anguelova, M.D., Fairall, C.W., Lewis, E.R., O'Dowd, C., Schulz, M. & Schwartz, S.E. 2011 Production flux of sea spray aerosol. Rev. Geophys. 49, 1–39.CrossRefGoogle Scholar
Lhuissier, H. & Villermaux, E. 2012 Bursting bubble aerosols. J. Fluid Mech. 696, 5–44.CrossRefGoogle Scholar
Miller, D.N. 1983 Interfacial area, bubble coalescence and mass transfer in bubble column reactors. AIChE J. 29 (2), 312–319.CrossRefGoogle Scholar
Moreno Soto, Á., Maddalena, T., Fraters, A., Van Der Meer, D. & Lohse, D. 2018 Coalescence of diffusively growing gas bubbles. J. Fluid Mech. 846, 143–165.CrossRefGoogle Scholar
Néel, B. & Deike, L. 2021 Collective bursting of free surface bubbles, and the role of surface contamination. J. Fluid Mech. (submitted).Google Scholar
Nicolson, M.M. 1948 The interaction between floating particles. Math. Proc. Cambridge 45 (2), 288–295.CrossRefGoogle Scholar
Oolman, T.O. & Blanch, H.W. 1986 Bubble coalescence in stagnant liquids. Chem. Engng Commun. 43 (4–6), 237–261.CrossRefGoogle Scholar
Patankar, S., Farsoiya, P.K. & Dasgupta, R. 2018 Faraday waves on a cylindrical fluid filament-generalised equation and simulations. J. Fluid Mech. 857, 80–110.CrossRefGoogle Scholar
Paulsen, J.D., Burton, J.C., Nagel, S.R., Appathurai, S., Harris, M.T. & Basaran, O.A. 2012 The inexorable resistance of inertia determines the initial regime of drop coalescence. Proc. Natl Acad. Sci. USA 109 (18), 6857–6861.CrossRefGoogle ScholarPubMed
Paulsen, J.D., Carmigniani, R., Kannan, A., Burton, J.C. & Nagel, S.R. 2014 Coalescence of bubbles and drops in an outer fluid. Nat. Commun. 5 (3182), 1–7.CrossRefGoogle Scholar
Poulain, S., Villermaux, E. & Bourouiba, L. 2018 Ageing and burst of surface bubbles. J. Fluid Mech. 851, 636–671.CrossRefGoogle Scholar
Princen, H.M. 1963 Shape of a fluid drop at a liquid-liquid interface. J. Colloid Sci. 18, 178–195.CrossRefGoogle Scholar
Ristenpart, W.D., McCalla, P.M., Roy, R.V. & Stone, H.A. 2006 Coalescence of spreading droplets on a wettable substrate. Phys. Rev. Lett. 97 (6), 1–4.CrossRefGoogle ScholarPubMed
Sadhal, S.S., Ayyaswamy, P.S. & Chung, J.N. 1977 Transport Phenomena with Drops and Bubbles. Springer.Google Scholar
Samanta, S. & Ghosh, P. 2011 Coalescence of bubbles and stability of foams in aqueous solutions of Tween surfactants. Chem. Engng Res. Des. 89 (11), 2344–2355.CrossRefGoogle Scholar
Stover, R.L., Tobias, C.W. & Denn, M.M. 1997 Bubble coalescence dynamics. AIChE J. 43 (10), 2385–2392.CrossRefGoogle Scholar
Taki, K., Tabata, K., Kihara, S. & Ohshima, M. 2006 Bubble coalescence in foaming process of polymers. Polym. Engng Sci. 46 (5), 680–690.CrossRefGoogle Scholar
Thoroddsen, S.T., Etoh, T.G., Takehara, K. & Ootsuka, N. 2005 On the coalescence speed of bubbles. Phys. Fluids 17 (7), 1–4.CrossRefGoogle Scholar
Toba, Y. 1959 Drop production by bursting of air bubbles on the sea surface (II) theoretical study on the shape of floating bubbles. J. Oceanogr. Soc. Japan 15 (3), 121–130.CrossRefGoogle Scholar
Vella, D. & Mahadevan, L. 2005 The ‘Cheerios effect’. Am. J. Phys. 73 (9), 817–825.CrossRefGoogle Scholar
Veron, F. 2015 Ocean spray. Annu. Rev. Fluid Mech. 47, 507–538.CrossRefGoogle Scholar
Wang, X., et al. 2017 The role of jet and film drops in controlling the mixing state of submicron sea spray aerosol particles. Proc. Natl Acad. Sci. USA 114 (27), 6978–6983.CrossRefGoogle ScholarPubMed
Xia, X., He, C. & Zhang, P. 2019 Universality in the viscous-to-inertial coalescence of liquid droplets. Proc. Natl Acad. Sci. USA 116 (47), 23467–23472.CrossRefGoogle ScholarPubMed
Yang, Y.M. & Maa, J.R. 1984 Bubble coalescence in dilute surfactant solutions. J. Colloid Interface Sci. 98 (1), 120–125.CrossRefGoogle Scholar
Zhang, F.H., Thoraval, M.J., Thoroddsen, S.T. & Taborek, P. 2015 Partial coalescence from bubbles to drops. J. Fluid Mech. 782, 209–239.CrossRefGoogle Scholar
Zheng, Q.A., Klemas, V. & Hsu, Y.-H.H.L. 1983 Laboratory measurement of water surface bubble life time. J. Geophys. Res. 88 (C1), 701–706.CrossRefGoogle Scholar

Shaw and Deike supplemementay movie 1

Surface bubble coalescence as viewed from above and below the free surface.

Download Shaw and Deike supplemementay movie 1(Video)
Video 44.2 MB

Shaw and Deike supplemementay movie 2

Retraction of the film separating two parent surface bubbles at the start of coalescence.

Download Shaw and Deike supplemementay movie 2(Video)
Video 5.4 MB