Skip to main content Accessibility help

Dynamics of expansion and collapse of explosive two-dimensional bubbles

  • Jérôme Duplat (a1)


An explosive gas mixture of hydrogen and oxygen is introduced in liquid water between two horizontal walls, forming a flat cylindrical bubble. Ignition and explosion of the bubble lead to a large depressurized cavity that finally implodes. We investigate the dynamics of the bubble collapse, which is qualitatively similar to the collapse of a spherical bubble. It exhibits a slightly weaker singularity than for spherical bubbles. We also analyse the explosion process. Starting with an initial radius $R_{0}$ , the bubble reaches a maximal radius $R_{max}$ that depends on the gap thickness $h$ between the two walls: for a thinner gap, the condensation of water vapour is more efficient, the overpressure consecutive to the combustion is weaker, and its duration is shorter. This leads to a smaller maximal radius $R_{max}$ . An indirect measurement of the transport coefficient of hot water vapour can be inferred from this observation.


Corresponding author

Email address for correspondence:


Hide All
Blaik, M. & Christian, E. A. 1965 Near-surface measurements of deep explosions. Part I. Pressure pulses from small charges. J. Acoust. Soc. Am. 38 (1), 5056.
Brenner, M. P., Hilgenfeldt, S. & Lohse, D. 2002 Single-bubble sonoluminescence. Rev. Mod. Phys. 74 (2), 425484.
Chapman, N. R. 1988 Source levels of shallow explosive charges. J. Acoust. Soc. Am. 84 (2), 697702.
Cole, R. H. 1948 Underwater Explosions. Princeton University Press.
Duplat, J. & Villermaux, E. 2015 Luminescence from collapsing centimeter bubbles expanded by chemical reaction. Phys. Rev. Lett. 115, 094501.
Flannigan, D. J. & Suslick, K. S. 2005 Plasma formation and temperature measurement during single-bubble cavitation. Nature 434 (7029), 5255.
Hurricane, O. A. et al. 2014 Fuel gain exceeding unity in an inertially confined fusion implosion. Nature 506, 343348.
Landau, L. & Lifshitz, E. M. 1987 Fluid Mechanics. Pergamon.
Lauterborn, W. 1974 Laser-induced cavitation. Acustica 31 (2), 5178.
Li, J., Zhao, Z. W., Kazakov, A. & Dryer, F. L. 2004 An updated comprehensive kinetic model of hydrogen combustion. Intl J. Chem. Kinet. 36 (10), 566575.
Lide, D. R.(Ed.) 2005 Handbook of Chemistry and Physics, 86th edn. CRC Press, Taylor & Francis.
Lindl, J. D. et al. 2011 Progress towards ignition on the national ignition facility. Nucl. Fusion 51, 094024.
Meyer, E. & Kuttruff, H. 1959 On the phase relation between sonoluminescence and the cavitation process with periodic excitation. Z. Angew. Phys. 11, 325333.
Morley, C.2005 Gaseq: A Chemical Equilibrium Software for Windows (
Oguz, H. N. & Prosperetti, A. 1993 Dynamics of bubble growth and detachment from a needle. J. Fluid Mech. 257, 111145.
Ohl, C. D., Lindau, O. & Lauterborn, W. 1998 Luminescence from spherically and aspherically collapsing laser induced bubbles. Phys. Rev. Lett. 80 (2), 393396.
Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Annu. Rev. Fluid Mech. 9, 145185.
Rayleigh, Lord 1917 On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 34 (200), 9498.
Séon, T. & Antkowiak, A. 2012 Large bubble rupture sparks fast liquid jet. Phys. Rev. Lett. 109, 014501.
Storey, B. D. & Szeri, A. J. 2000 Water vapour, sonoluminescence and sonochemistry. Proc. R. Soc. Lond. A 456 (1999), 16851709.
Vledouts, A., Quinard, J., Vandenberghe, N. & Villermaux, E. 2016 Explosive fragmentation of liquid shells. J. Fluid Mech. 788, 246273.
Walker, R. E. & Westenberg, A. A. 1960 Molecular diffusion studies in gases at high temperature. Part IV. Results and interpretation of the CO2 –O2 , CH4 –O2 , H2 –O2 , CO–O2 , and H2O–O2 systems. J. Chem. Phys. 32 (2), 436442.
Zeldovich, Y. B. & Frank-Kamenetskii, D. A. 1938 On the theory of uniform flame propagation. Dokl. Akad. Nauk SSSR 19, 693798.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Dynamics of expansion and collapse of explosive two-dimensional bubbles

  • Jérôme Duplat (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed