Hostname: page-component-7c8c6479df-ws8qp Total loading time: 0 Render date: 2024-03-29T13:40:09.464Z Has data issue: false hasContentIssue false

Explosive fragmentation of liquid shells

Published online by Cambridge University Press:  05 January 2016

A. Vledouts
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384 Marseille, France
J. Quinard
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384 Marseille, France
N. Vandenberghe
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384 Marseille, France
E. Villermaux*
Affiliation:
Institut Universitaire de France, Paris, France
*
Email address for correspondence: villermaux@irphe.univ-mrs.fr

Abstract

The forced radial expansion of a spherical liquid shell by an exothermic chemical reaction is a prototypical configuration for the explosion of cohesive materials in three dimensions. The shell is formed by the capillary pinch off of a thin liquid annular jet surrounding a jet of reactive gaseous mixture at ambient pressure. The encapsulated gas in the resulting liquid bubble is a mixture of hydrogen and oxygen in controlled relative proportions, which is ignited by a laser plasma aimed at the centre of the bubble. The strongly exothermic combustion of the mixture induces the expansion of the hot burnt gas, pushing the shell radially outwards in a violently accelerated motion. That motion triggers the instability of the shell, developing thickness modulations ultimately piercing it in a number of places. The capillary retraction of the holes concentrates the liquid constituting the shell into a web of ligaments, whose breakup leads to stable drops. We offer a comprehensive description of the overall process, from the kinematics of the shell initial expansion, to the final drop size distribution as a function of the composition of the gas mixture, the initial shell radius and thickness.

Type
Papers
Copyright
© 2016 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

Bradley, D., Sheppard, C. G. W., Suardjaja, I. M. & Wooley, R. 2004 Fundamentals of high-energy spark ignition with lasers. Combust. Flame 138, 5577.Google Scholar
Bremond, N. & Villermaux, E. 2005 Bursting thin liquid films. J. Fluid Mech. 524, 121130.Google Scholar
Bremond, N. & Villermaux, E. 2006 Atomization by jet impact. J. Fluid Mech. 549, 273306.Google Scholar
Buff, F. P., Lowett, R. A. & Stillinger, F. H. Jr 1965 Interfacial density profile for fluids in the critical region. Phys. Rev. Lett. 15 (15), 621623.Google Scholar
Burrows, A. 2000 Supernovae explosions in the universe. Nature 403, 727733.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover.Google Scholar
Cole, R. H. 1948 Underwater Explosions. Princeton University Press.Google Scholar
Culick, F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 11281129.Google Scholar
Duplat, J. & Villermaux, E. 2015 Luminescence from collapsing centimeter bubbles expanded by chemical reaction. Phys. Rev. Lett. 115, 094501.Google Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.Google Scholar
Frost, D. L. 1988 Dynamics of explosive boiling of a droplet. Phys. Fluids 31 (9), 25542561.Google Scholar
Frost, D. L., Ornthanalai, C., Zarei, Z., Tanguay, V. & Zhang, F. 2007 Particle momentum effects from the detonation of heterogeneous explosives. J. Appl. Phys. 101, 113529.Google Scholar
Grady, D. E. 1982 Local inertial effects in dynamic fragmentation. J. Appl. Phys. 53, 322325.Google Scholar
Grady, D. E. 2007 Fragmentation of Rings and Shells: The Legacy of N. F. Mott. Springer.Google Scholar
Hassett, M. O., Fischer, M. W. F., Sugawara, Z. T., Stolze-Rybczynski, J. & Money, N. P. 2013 Splash and grab: biomechanics of peridiole ejection and function of the funicular cord in bird’s nest fungi. Fungal Biol. 117, 708714.Google Scholar
Ingold, C. T. 1933 Spore discharge in the ascomycetes. New Physiologist 3, 175196.Google Scholar
Ingold, C. T. 1971 Fungal Spores: Their Liberation and Dispersal. Clarendon.Google Scholar
Kedrinskii, V. K. 2005 Hydrodynamics of Explosions. Springer.Google Scholar
Kedrinskii, V. K. 2009 Hydrodynamic aspects of explosive eruptions of volcanoes: simulation problems. Shock Waves 18, 451464.Google Scholar
Keller, J. B. & Kolodner, I. 1954 Instability of liquid surfaces and the formation of drops. J. Appl. Phys. 25, 918921.Google Scholar
Kendall, J. M. 1986 Experiments on annular liquid jet instability and on the formation of liquid shells. Phys. Fluids 29, 20862094.Google Scholar
Krichevsky, O. & Stavans, J. 1994 Surfactant–polymer interactions in freely suspended lyotropic films. Phys. Rev. Lett. 73, 696699.Google Scholar
Landau, L. & Lifshitz, E. M. 1987 Fluid Mechanics. Pergamon.Google Scholar
Leblanc, L., Manoubi, M., Dennis, K., Liang, Z. & Radulescu, M. I. 2013 Dynamics of unconfined spherical flames: influence of buoyancy. Phys. Fluids 25, 091106.Google Scholar
Lewis, B. & von Elbe, G. 1961 Combustion, Flames and Explosions of Gases. Academic.Google Scholar
Lhuissier, H. & Villermaux, E. 2012 Crumpled water bells. J. Fluid Mech. 693, 508540.Google Scholar
Lhuissier, H. & Villermaux, E. 2013 ‘Effervescent’ atomization in two dimensions. J. Fluid Mech. 714, 361392.Google Scholar
Lide, D. R. 2004 CRC Handbook of Chemistry and Physics. CRC Press.Google Scholar
Marangoni, C. & Stefanelli, P. 1873 Monografia delle bolle liquide. Nuovo Cimento 9 (1), 236256.Google Scholar
Morley, C.2005 Gaseq (http://www.gaseq.co.uk).Google Scholar
Mott, N. F. 1947 Fragmentation of shell cases. Proc. R. Soc. Lond. A 189, 300308.Google Scholar
Plesset, M. S. 1954 On the stability of fluid flows with spherical symmetry. J. Appl. Phys. 25, 9698.Google Scholar
Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Annu. Rev. Fluid Mech. 9, 145185.Google Scholar
Rayleigh, L. 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. A 29, 7197.Google Scholar
Rayleigh, L. 1917 On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 34, 9498.Google Scholar
von Rittinger, P. R. 1867 Lehrbuch der Aufbereitungskunde: in ihrer neuesten Entwicklung und Ausbildung systematisch dargestellt. Ernst und Korn.Google Scholar
Sedov, L. I. 1946 Le mouvement d’air en cas d’une forte explosion. C. R. Acad. Sci. URSS 52, 1720.Google Scholar
Senior, D. A. 1961 Burning velocities of hydrogen-air and hydrogen-oxygen mixtures: Determination by burner method with schlieren photography. Combust. Flame 5, 710.Google Scholar
Settles, G. S. 2001 Schlieren and Shadowgraph Techniques. Springer.Google Scholar
Spiglanin, T. A., McIlroy, A., Fournier, E. W., Cohen, R. B. & Syage, J. A. 1995 Time-resolved imaging of flame kernels: laser spark ignition of H $_{2}$ /O $_{2}$ /Ar mixtures. Combust. Flame 102, 310328.Google Scholar
Srivastava, D., Weinrotter, M., Iskra, K., Agarwal, A. & Wintner, E. 2009 Characterisation of laser ignition in hydrogen–air mixtures in a combustion bomb. Int. J. Hydrog. Energy 34, 24752482.Google Scholar
Stebnovskii, S. V. 1982 Development of initial perturbations of the external boundary of an expanding gas–liquid ring. J. Appl. Mech. Tech. Phys. 23 (5), 633637.Google Scholar
Strehlow, R. A., Luckritz, R. T., Adamczyk, A. A. & Shimpi, S. A. 1979 The blast wave generated by spherical flames. Combust. Flame 35, 297310.Google Scholar
Sultanov, F. M. & Yarin, A. L. 1990 Droplet size distribution in a percolation model for explosive dispersal. J. Appl. Mech. Tech. Phys. 31 (5), 708713.Google Scholar
Takeno, T. 1985 Pressure distribution in flame propagating in a soap bubble. Combust. Flame 62, 9599.Google Scholar
Taylor, G. I. 1946 The air wave surrounding an expanding sphere. Proc. R. Soc. Lond. A 186, 273292.Google Scholar
Taylor, G. I. 1950 The formation of a blast wave by a very intense explosion. ii. The atomic explosion of 1945. Proc. R. Soc. Lond. A 201, 175186.Google Scholar
Taylor, G. I. 1959 The dynamics of thin sheets of fluid. iii. Disintegration of fluid sheets. Proc. R. Soc. Lond. A 253, 313321.Google Scholar
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39, 419446.Google Scholar
Villermaux, E. & Bossa, B. 2011 Drop fragmentation on impact. J. Fluid Mech. 668, 412435.Google Scholar
Zeldovich, Y. B., Barenblatt, G. I., Librovich, V. B. & Makhviladze, G. M. 1985 The Mathematical Theory of Combustion and Explosions. Consultants Bureau.Google Scholar
Zeldovich, Y. B. & Frank-Kamenetskii, D. A. 1938 On the theory of uniform flame propagation. Dokl. Akad. Nauk SSSR 19, 693798.Google Scholar
Zeldovich, Y. B. & Raizer, Y. P. 2002 Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover.Google Scholar
Zhang, H. & Ravi-Chandar, K. 2007 On the dynamics of necking and fragmentation – I. Real-time and post-mortem observations in Al 6061-O. Intl J. Fract. 142 (3–4), 183217.Google Scholar
Zhang, H. & Ravi-Chandar, K. 2008 On the dynamics of necking and fragmentation – II. Effect of material properties, geometrical constraints and absolute size. Intl J. Fract. 150 (1–2), 336.Google Scholar
Zhao, H., Liu, H. F., Xu, J. L. & Li, W. F. 2011 Experimental study of drop size distribution in the bag breakup regime. Ind. Engng Chem. Res. 50 (16), 97679773.Google Scholar
Zitoun, R. & Deshaies, B. 1997 Burning velocities of rich H $_{2}$ /O $_{2}$ flames under cryogenic conditions. Combust. Flame 109, 427435.Google Scholar