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Bursting water balloons

Published online by Cambridge University Press:  04 September 2014

Hugh M. Lund  and
Stuart B. Dalziel
Hugh M. Lund*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Stuart B. Dalziel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: hugh.lund@gmail.com
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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.

JFM classification

Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , pp. 771 - 815
Copyright
© 2014 Cambridge University Press 

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References

Acheson, D. J. 1990 Elementary Fluid Dynamics. Oxford University Press.Google Scholar
Anderson, T. L. 2004 Fracture Mechanics: Fundamentals and Applications, 3rd edn. Taylor and Francis.Google Scholar
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, 79–94.Google Scholar
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), 170–196.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Broberg, K. B. 1999 Cracks and Fracture. Academic Press.Google Scholar
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445–468.CrossRefGoogle Scholar
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, 60–84.Google Scholar
Carruthers, A. & Filippone, A. 2005 Aerodynamic drag of streamers and flags. J. Aircraft 42 (4), 976–982.Google Scholar
Chapman, P. R. & Jacobs, J. W. 2006 Experiments on the three-dimensional incompressible Richtmyer–Meshkov instability. Phys. Fluids 18, 074101.Google Scholar
Christensen, K. H. 2005 Transient and steady drift currents in waves damped by surfactants. Phys. Fluids 17, 042102.CrossRefGoogle Scholar
Craik, A. D. D. 1985 Wave Interactions and Fluid Flows. Cambridge University Press.Google Scholar
Dutta, S., Glimm, J., Grove, J. W., Sharp, D. & Zhang, Y. 2004 Spherical Richtmyer–Meshkov instability for axisymmetric flow. Maths Comput. Simul. 65, 417–430.Google Scholar
Gere, J. M. & Timoshenko, S. P. 1997 Mechanics of Materials, 4th edn. PWS.Google Scholar
Glimm, J., Grove, J. W. & Zhang, Y. 2000 Three dimensional axisymmetric simulations of fluid instabilities in curved geometry. Adv. Fluid Mech 26, 643–652.Google Scholar
Greenhill, A. G. 1878 Plane vortex motion. Q. J. Pure Appl. Maths 15, 10–29.Google Scholar
Hoyt, J. W. & Taylor, J. J. 1977 Waves on water jets. J. Fluid Mech. 83 (1), 119–127.Google Scholar
Jacobs, J. W. & Sheeley, J. M. 1996 Experimental study of incompressible Richtmyer–Meshkov instability. Phys. Fluids 8, 405–415.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.Google Scholar
Likhachev, O. A. & Jacobs, J. W. 2005 A vortex model for Richtmyer–Meshkov instability accounting for finite Atwood number. Phys. Fluids 17, 031704.CrossRefGoogle Scholar
Lucassen-Reynders, E. H. & Lucassen, J. 1969 Properties of capillary waves. Adv. Colloid Interface Sci. 2, 347–395.Google Scholar
Mark, J. E. 2009 Polymer Data Handbook, 2nd edn. Oxford University Press.Google Scholar
Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave. Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza 4, 151–157.Google Scholar
Miller, C. A. & Scriven, L. E. 1968 The oscillations of a fluid droplet immersed in another fluid. J. Fluid Mech. 32, 417–425.Google Scholar
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), 815–830.CrossRefGoogle Scholar
Mullins, L. 1969 Softening of rubber by deformation. Rubber Chem. Technol. 42, 339–362.Google Scholar
Niederhaus, C. E. & Jacobs, J. W. 2003 Experimental study of the Richtmyer–Meshkov instability of incompressible fluids. J. Fluid Mech. 485, 243–277.Google Scholar
Paidoussis, M. P. 2003 Fluid Structure Interactions: Slender Structures and Axial Flow, vol. vol. 2. Elsevier Academic Press.Google Scholar
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.CrossRefGoogle Scholar
Rayleigh, L. 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. 29, 71–97.Google Scholar
Richard, D. & Quere, D. 2000 Bouncing water drops. Europhys. Lett. 50, 769–775.Google Scholar
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.Google Scholar
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), 77–106.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Sato, H. 1960 The stability and transition of a two-dimensional jet. J. Fluid Mech. 7 (01), 53–80.Google Scholar
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), 321–352.Google Scholar
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.Google Scholar
Taneda, S. 1968 Waving motions of flags. J. Phys. Soc. Japan 24 (2), 392–401.Google Scholar
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), 192–196.Google Scholar
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, 1662–1671.CrossRefGoogle Scholar
Vermorel, R., Vandenberghe, N. & Villermaux, E. 2007 Rubber band recoil. Proc. R. Soc. A 463, 641–658.Google Scholar

Lund and Dalziel supplementary movie

A 300mm water-filled balloon is dropped from a height of 1m onto a flat, rigid surface. After impact at t=0, the balloon deforms, causing it to rupture. The video was recorded at 5400fps.

Download Lund and Dalziel supplementary movie(Video)
Video 2 MB

Lund and Dalziel supplementary movie

A 130mm water-filled balloon is oscillated in air at 120hz, before being ruptured by a pin at time t=0. The video was recorded at 5400fps.

Download Lund and Dalziel supplementary movie(Video)
Video 2.3 MB

Lund and Dalziel supplementary movie

A 130mm water-filled balloon is submerged in water and oscillated at 170hz, before being ruptured by a pin a t=0. The video was recorded at 5400fps.

Download Lund and Dalziel supplementary movie(Video)
Video 3.4 MB