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Dynamics of collapse of free-surface bubbles: effects of gravity and viscosity
Published online by Cambridge University Press: 06 February 2024
Abstract
The rupture of the thin film at the top of a bubble at a liquid–gas interface leads to an axisymmetric collapse of the bubble cavity. We present scaling laws for such a cavity collapse, established from experiments conducted with bubbles spanning a wide range of Bond (
${10^{-3}< Bo\leq 1}$) and Ohnesorge numbers (
${10^{-3}< Oh<10^{-1}}$), defined with the bubble radius 
$R$. The cavity collapse is a capillary-driven process, with a dependency on viscosity and gravity, affecting respectively, precursory capillary waves on the cavity boundary and the static bubble shape. The collapse is characterised by the normal interface velocity (
$U_n$) and by the tangential wave propagation velocity of the kink (
$U_t$), defined by the intersection of the concave cavity boundary formed after the rupture of the thin film with the convex boundary of the bubble cavity. During the collapse, 
$U_t$ remains constant and is shown to be 
$U_t=4.5U_c{\mathcal {W}}_R$, where 
$U_c$ is the capillary velocity and 
${\mathcal {W}}_R(Oh,Bo)={(1-\sqrt {Oh {\mathscr {L}}} )^{-1/2}}$ is the wave resistance factor due to the precursory capillary waves, with 
$\mathscr {L}(Bo)$ being the path correction of the kink motion. The movement of the kink in the normal direction is part of the inward shrinkage of the whole cavity due to the sudden reduction of gas pressure inside the bubble cavity after the thin film rupture. This normal velocity is shown to scale as 
$U_c$ in the equatorial plane, while at the bottom of the cavity 
$\bar {U}_{nb}=U_c(Z_c/R)({\mathcal {W}_R}/ {\mathscr {L}})$, where 
$Z_c(Bo)$ is the static cavity depth. The filling rate of the cavity, which remains a constant throughout the collapse, is shown to be entirely determined by the shrinking velocity and scales as 
${Q_T\simeq 2{\rm \pi} R Z_c U_c}$. From 
$Q_T$ we recover the jet velocity scaling, thereby relating the cavity collapse with the jet velocity scaling.
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- JFM Papers
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- © The Author(s), 2024. Published by Cambridge University Press
References
Bartolo, D., Josserand, C. & Bonn, D. 2006 Singular jets and bubbles in drop impact. Phys. Rev. Lett. 96, 124501.Google Scholar
Benusiglio, A., Quéré, D. & Clanet, C. 2014 Explosions at the water surface. J. Fluid Mech. 752, 123–139.Google Scholar
Bergmann, R., van der Meer, D., Stijnman, M., Sandtke, M., Prosperetti, A. & Lohse, D. 2006 Giant bubble pinch-off. Phys. Rev. Lett. 96, 154505.Google Scholar
Blanchard, D.C. 1963 The electrification of the atmosphere by particles from bubbles in the sea. Prog. Oceanogr. 1, 71–202.Google Scholar
Blanco-Rodríguez, F.J. & Gordillo, J.M. 2020 On the sea spray aerosol originated from bubble bursting jets. J. Fluid Mech. 886, R2.Google Scholar
Blanco-Rodríguez, F.J. & Gordillo, J.M. 2021 On the jets produced by drops impacting a deep liquid pool and by bursting bubbles. J. Fluid Mech. 916, A37.Google Scholar
Boulton-Stone, J.M. & Blake, J.R. 1993 Gas bubbles bursting at a free surface. J. Fluid Mech. 254, 437–466.CrossRefGoogle Scholar
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 3, 074001.Google Scholar
Burton, J.C., Waldrep, R. & Taborek, P. 2005 Scaling and instabilities in bubble pinch-off. Phys. Rev. Lett. 94 (18), 184502.Google Scholar
Das, S.P. & Hopfinger, E.J. 2008 Parametrically forced gravity waves in a circular cylinder and finite-time singularity. J. Fluid Mech. 599, 205–228.Google Scholar
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, 013603.Google Scholar
Doshi, P., Cohen, I., Zhang, W.W., Siegel, M., Howell, P., Basaran, O.A. & Nagel, S.R. 2003 Persistence of memory in drop breakup: the breakdown of universality. Science 302 (5648), 1185–1188.Google Scholar
Duchemin, L., Popinet, S., Josserand, C. & Zaleski, S. 2002 Jet formation in bubbles bursting at a free surface. Phys. Fluids 14 (9), 3000–3008.Google Scholar
Duclaux, V., Caille, F., Duez, C., Ybert, C., Bocquet, L. & Clanet, C. 2007 Dynamics of transient cavities. J. Fluid Mech. 591, 1–19.Google Scholar
Eggers, J. & Fontelos, M.A. 2015 Singularities: Formation, Structure, and Propagation. Cambridge University Press.Google Scholar
Eggers, J., Fontelos, M.A., Leppinen, D. & Snoeijer, J.H. 2007 Theory of the collapsing axisymmetric cavity. Phys. Rev. Lett. 98 (9), 094502.Google Scholar
Feng, J., Roché, M., Vigolo, D., Arnaudov, L.N., Stoyanov, S.D., Gurkov, T.D., Tsutsumanova, G.G. & Stone, H.A. 2014 Nanoemulsions obtained via bubble-bursting at a compound interface. Nat. Phys. 10 (8), 606–612.Google Scholar
Gañán Calvo, A.M. 2017 Revision of bubble bursting: universal scaling laws of top jet drop size and speed. Phys. Rev. Lett. 119, 204502.Google Scholar
Gañán Calvo, A.M. 2018 Scaling laws of top jet drop size and speed from bubble bursting including gravity and inviscid limit. Phys. Rev. Fluids 3, 091601.Google Scholar
Gañán Calvo, A.M. & López-Herrera, J.M. 2021 On the physics of transient ejection from bubble bursting. J. Fluid Mech. 929, A12.Google Scholar
Ghabache, E., Antkowiak, A., Josserand, C. & Séon, T. 2014 On the physics of fizziness: how bubble bursting controls droplets ejection. Phys. Fluids 26 (12), 121701.Google Scholar
Gordillo, J.M. & Blanco-Rodríguez, F.J. 2023 Theory of the jets ejected after the inertial collapse of cavities with applications to bubble bursting jets. Phys. Rev. Fluids 8, 073606.Google Scholar
Gordillo, J.M. & Rodríguez-Rodríguez, J. 2019 Capillary waves control the ejection of bubble bursting jets. J. Fluid Mech. 867, 556–571.Google Scholar
Ismail, A.S., Gañán Calvo, A.M., Castrejón-Pita, J.R., Herrada, M.A. & Castrejón-Pita, A.A. 2018 Controlled cavity collapse: scaling laws of drop formation. Soft Matt. 14, 7671–7679.Google Scholar
Ji, B., Yang, Z. & Feng, J. 2021 Compound jetting from bubble bursting at an air–oil–water interface. Nat. Commun. 12 (1), 6305.Google Scholar
Joung, Y.S., Ge, Z. & Buie, C.R. 2017 Bioaerosol generation by raindrops on soil. Nat. Commun. 8, 14668.Google Scholar
Kientzler, C.F., Arons, A.B., Blanchard, D.C. & Woodcock, A.H. 1954 Photographic investigation of the projection of droplets by bubbles bursting at a water surface. Tellus 6 (1), 1–7.CrossRefGoogle Scholar
Krishnan, S., Bharadwaj, S.V. & Vasan, V. 2022 Impact of freely falling liquid containers and subsequent jetting. Exp. Fluids 63 (7), 1–20.Google Scholar
Krishnan, S., Hopfinger, E.J. & Puthenveettil, B.A. 2017 On the scaling of jetting from bubble collapse at a liquid surface. J. Fluid Mech. 822, 791–812.Google Scholar
Krishnan, S. & Puthenveettil, B.A. 2015 Dynamics of collapse of free surface bubbles. Procedia IUTAM 15, 207–214.Google Scholar
Krishnan, S., Puthenveettil, B.A. & Hopfinger, E.J. 2020 Hole expansion from a bubble at a liquid surface. Phys. Fluids 32 (3), 032108.Google Scholar
Lai, C.Y., Eggers, J. & Deike, L. 2018 Bubble bursting: universal cavity and jet profiles. Phys. Rev. Lett. 121, 144501.Google Scholar
Lee, J.S., Weon, B.M., Park, S.J., Je, J.H., Fezzaa, K. & Lee, W.K. 2011 Size limits the formation of liquid jets during bubble bursting. Nat. Commun. 2, 367.Google Scholar
MacIntyre, F. 1972 Flow patterns in breaking bubbles. J. Geophys. Res. 77 (27), 5211–5228.Google Scholar
Oguz, H.N. & Prosperetti, A. 1993 Dynamics of bubble growth and detachment from a needle. J. Fluid Mech. 257, 111–145.Google Scholar
Perlin, M., Lin, H. & Ting, C.L. 1993 On parasitic capillary waves generated by steep gravity waves: an experimental investigation with spatial and temporal measurements. J. Fluid Mech. 255, 597–620.Google Scholar
Puthenveettil, B.A. & Hopfinger, E.J. 2009 Evolution and breaking of parametrically forced capillary waves in a circular cylinder. J. Fluid Mech. 633, 355–379.Google Scholar
Puthenveettil, B.A., Saha, A., Krishnan, S. & Hopfinger, E.J. 2018 Shape parameters of a floating bubble. Phys. Fluids 30 (11), 112105.Google Scholar
Renardy, Y., Popinet, S., Duchemin, L., Renardy, M., Zaleski, S., Josserand, C., Drumright-Clarke, M.A., Richard, D., Clanet, C. & Quéré, D. 2003 Pyramidal and toroidal water drops after impact on a solid surface. J. Fluid Mech. 484, 69–83.Google Scholar
Sampath, K., Afshar-Mohajer, N., Chandrala, L.D., Heo, W.S., Gilbert, J., Austin, D., Koehler, K. & Katz, J. 2019 Aerosolization of crude oil-dispersant slicks due to bubble bursting. J. Geophys. Res. 124 (10), 5555–5578.Google Scholar
Spiel, D.E. 1995 On the births of jet drops from bubbles bursting on water surfaces. J. Geophys. Res. 100 (C3), 4995–5006.Google Scholar
Thoroddsen, S.T., Takehara, K., Nguyen, H.D. & Etoh, T.G. 2018 Singular jets during the collapse of drop-impact craters. J. Fluid Mech. 848, R3.Google Scholar
Walls, P.L.L., Henaux, L. & Bird, J.C. 2015 Jet drops from bursting bubbles: how gravity and viscosity couple to inhibit droplet production. Phys. Rev. E 92, 021002.Google Scholar
Walls, P.L.L., McRae, O., Natarajan, V., Johnson, C., Antoniou, C. & Bird, J.C. 2017 Quantifying the potential for bursting bubbles to damage suspended cells. Sci. Rep. 7 (1), 15102.Google Scholar
Woodcock, A.H., Kientzler, C.F., Arons, A.B. & Blanchard, D.C. 1953 Giant condensation nuclei from bursting bubbles. Nature 172, 1144–1145.Google Scholar
Yang, Z., Ji, B., Ault, J.T. & Feng, J. 2023 Enhanced singular jet formation in oil-coated bubble bursting. Nat. Phys. 19, 1–7.Google Scholar
Yang, Z.Q., Tian, Y.S. & Thoroddsen, S.T. 2020 Multitude of dimple shapes can produce singular jets during the collapse of immiscible drop-impact craters. J. Fluid Mech. 904, A19.Google Scholar
Zeff, B.W., Kleber, B., Fineberg, J. & Lathrop, D.P. 2000 Singularity dynamics in curvature collapse and jet eruption on a fluid surface. Nature 403 (6768), 401–404.Google Scholar
Krishnan et al. supplementary movie 1
Cavity collapse from a free-surface bubble of radius R=0.47mm in water (Bo=0.03; Oh=0.0055) (figure 3). A bubble pinch-off from the precursory wave focusing at the bottom of the cavity is also seen. The video is captured at 20000 fps.
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Krishnan et al. supplementary movie 2
Cavity collapse from a free-surface bubble of radius R=0.7mm in GW55 (Bo=0.08; Oh=0.034) (figure 4) free of any precursory capillary waves. The video is captured at 20000 fps.
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Krishnan et al. supplementary movie 3
Cavity collapse from a free-surface bubble of radius R=0.175mm in water (Bo=0.0042; Oh=0.0099) (figure 10a). The video is captured at 100000 fps.
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