Skip to main content Accessibility help
×
Home

Bursting water balloons

  • Hugh M. Lund (a1) and Stuart B. Dalziel (a1)

Abstract

The impact and rupture of a water-filled latex balloon on a flat, rigid surface is investigated using high-speed photography. Three distinct stages of the flow are observed, for which physical explanations are given. As the balloon lands and deforms, waves are formed on the balloon’s surface for which the restoring force is tension in the latex. These waves are shown to closely obey linear potential theory for constant surface tension. Should the balloon rupture, a crack forms, from which the membrane retracts. Spray is simultaneously ejected from the water’s surface, a consequence of a shear instability in the wake behind the retracting membrane. At later times, a larger-scale growth of the interfacial amplitude is observed, for which the generation mechanism is momentum in the water due to the preburst waves. However, it is argued that this is also a manifestation of the same mechanism that drives Richtmyer–Meshkov instability (RMI). Further, it is shown experimentally that this growth of the interface may also occur when there is no density difference across the balloon, a situation that does not arise for the standard RMI. An analytical model is then derived to predict the interfacial growth for such an interface, and is shown to predict the asymptotic growth rate of the interface accurately.

Copyright

Corresponding author

Email address for correspondence: hugh.lund@gmail.com

References

Hide All
Acheson, D. J. 1990 Elementary Fluid Dynamics. Oxford University Press.
Anderson, T. L. 2004 Fracture Mechanics: Fundamentals and Applications, 3rd edn. Taylor and Francis.
Archer, P. J., Thomas, T. G. & Coleman, G. N. 2010 The instability of a vortex ring impinging on a free surface. J. Fluid Mech. 642, 7994.
Balasubramanian, S., Orlicz, G. C. & Prestridge, K. P. 2013 Experimental study of initial condition dependence on turbulent mixing in shock-accelerated Richtmyer–Meshkov fluid layers. J. Turbul. 14 (3), 170196.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Broberg, K. B. 1999 Cracks and Fracture. Academic Press.
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445468.
Buttler, W. T., Oró, D. M., Preston, D. L., Mikaelian, K. O., Cherne, F. J., Hixson, R. S., Mariam, F. G., Morris, C., Stone, J. B., Terrones, G. & Tupa, D. 2012 Unstable Richtmyer–Meshkov growth of solid and liquid metals in vacuum. J. Fluid Mech. 703, 6084.
Carruthers, A. & Filippone, A. 2005 Aerodynamic drag of streamers and flags. J. Aircraft 42 (4), 976982.
Chapman, P. R. & Jacobs, J. W. 2006 Experiments on the three-dimensional incompressible Richtmyer–Meshkov instability. Phys. Fluids 18, 074101.
Christensen, K. H. 2005 Transient and steady drift currents in waves damped by surfactants. Phys. Fluids 17, 042102.
Craik, A. D. D. 1985 Wave Interactions and Fluid Flows. Cambridge University Press.
Dutta, S., Glimm, J., Grove, J. W., Sharp, D. & Zhang, Y. 2004 Spherical Richtmyer–Meshkov instability for axisymmetric flow. Maths Comput. Simul. 65, 417430.
Gere, J. M. & Timoshenko, S. P. 1997 Mechanics of Materials, 4th edn. PWS.
Glimm, J., Grove, J. W. & Zhang, Y. 2000 Three dimensional axisymmetric simulations of fluid instabilities in curved geometry. Adv. Fluid Mech 26, 643652.
Greenhill, A. G. 1878 Plane vortex motion. Q. J. Pure Appl. Maths 15, 1029.
Hoyt, J. W. & Taylor, J. J. 1977 Waves on water jets. J. Fluid Mech. 83 (1), 119127.
Jacobs, J. W. & Sheeley, J. M. 1996 Experimental study of incompressible Richtmyer–Meshkov instability. Phys. Fluids 8, 405415.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Likhachev, O. A. & Jacobs, J. W. 2005 A vortex model for Richtmyer–Meshkov instability accounting for finite Atwood number. Phys. Fluids 17, 031704.
Lucassen-Reynders, E. H. & Lucassen, J. 1969 Properties of capillary waves. Adv. Colloid Interface Sci. 2, 347395.
Mark, J. E. 2009 Polymer Data Handbook, 2nd edn. Oxford University Press.
Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave. Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza 4, 151157.
Miller, C. A. & Scriven, L. E. 1968 The oscillations of a fluid droplet immersed in another fluid. J. Fluid Mech. 32, 417425.
Morris-Thomas, M. T. & Steen, S. 2009 Experiments on the stability and drag of a flexible sheet under in-plane tension in uniform flow. J. Fluids Struct. 25 (5), 815830.
Mullins, L. 1969 Softening of rubber by deformation. Rubber Chem. Technol. 42, 339362.
Niederhaus, C. E. & Jacobs, J. W. 2003 Experimental study of the Richtmyer–Meshkov instability of incompressible fluids. J. Fluid Mech. 485, 243277.
Paidoussis, M. P. 2003 Fluid Structure Interactions: Slender Structures and Axial Flow, vol. vol. 2. Elsevier Academic Press.
Petersan, P. J., Deegan, R. D., Marder, M. & Swinney, H. L. 2004 Cracks in rubber under tension exceed the shear wave speed. Phys. Rev. Lett. 93, 015504.
Rayleigh, L. 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. 29, 7197.
Richard, D. & Quere, D. 2000 Bouncing water drops. Europhys. Lett. 50, 769775.
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297319.
Rollin, B. & Andrews, M. J. 2013 On generating initial conditions for turbulence models: the case of Rayleigh–Taylor instability turbulent mixing. J. Turbul. 14 (3), 77106.
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.
Sato, H. 1960 The stability and transition of a two-dimensional jet. J. Fluid Mech. 7 (01), 5380.
Sato, H. & Kuriki, K. 1961 The mechanism of transition in the wake of a thin flat plate placed parallel to a uniform flow. J. Fluid Mech. 11 (Pt 3), 321352.
Stanaway, S. K., Cantwell, B. J. & Spalart, P. R.1988 A numerical study of viscous vortex rings using a spectral method. NASA STI/Recon Tech. Rep. N 89, 23820.
Taneda, S. 1968 Waving motions of flags. J. Phys. Soc. Japan 24 (2), 392401.
Taylor, G. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. Lond. A 201 (1065), 192196.
Velikovich, A. L., Dahlburg, J. P., Schmitt, A. J., Gardner, J. H., Phillips, L., Cochran, F. L., Chong, Y. K., Dimonte, G. & Metzler, N. 2000 Richtmyer–Meshkov-like instabilities and early-time perturbation growth in laser targets and $Z$ -pinch loads. Phys. Plasmas 7, 16621671.
Vermorel, R., Vandenberghe, N. & Villermaux, E. 2007 Rubber band recoil. Proc. R. Soc. A 463, 641658.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

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