The impact and rupture of a water-filled balloon on a rigid surface
Lund, Hugh Michael
University of Cambridge
Department of Applied Mathematics and Theoretical Physics
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Lund, H. M. (2014). The impact and rupture of a water-filled balloon on a rigid surface (doctoral thesis).
The dropping of a water-ﬁlled latex balloon onto a ﬂat, rigid surface is an experiment that is known and has been performed by many, but on which there is no existing published work. High-speed images taken of the process revealed a range of phenomena, many of which had not been previously observed. After release, a water-ﬁlled balloon accelerates down and impacts with the tank ﬂoor. Upon impact, the balloon deforms through the propagation of waves up the balloon from the impact point. If the balloon does not rupture during this deformation, it then bounces up oﬀ the surface, the whole process similar to that when a water droplet bounces on a hydrophobic surface. Often, however, the balloon ruptures. This occurs through the propagation of one or more cracks through the balloon, leading to the rapid retraction of the membrane over the water’s surface, and consequent ejection of a ﬁne spray of water droplets behind it. If there are any waves on the balloon at the moment of rupture, a larger-scale growth of the interfacial amplitude occurs, of the same wavelength as the preburst waves. Eventually, gravity dominates, as the water slumps down and spreads over the ﬂat surface. In this thesis, the process described above is examined in detail, both experimentally and theoretically. To gain some insight into the behaviour of the latex balloons, their static and quasi-static behaviour is examined. A experimental method better than simply dropping the balloons was derived, permitting the accurate quantitative measurement of the process. In this new method, the balloons were held stationary, forced at a set frequency, then ruptured with a pin. The pre-burst waves are then shown to be accurately modelled by linear theory, with tension in the membrane acting much like a ﬂuid surface tension. The behaviour of the rubber in retraction from large initial stretches is shown to be disperse, in contrast with that observed for retractions from small initial stretches, due to both non-linearity in the rubber and drag from the water on the strip. The spray ejected behind the rubber is explained as consequence of the inherent instability of the Gaussian velocity ﬁeld in the wake. Finally, the late-time growth of the interfacial amplitude is examined, and argued to be closely-related to the Richtmyer-Meshkov instability. A model is then derived for the case of a balloon oscillated and burst with water both inside and outside, and is shown to be in approximate agreement with experiments.
Fluid instabilities, Water balloon
This research was supported by EPSRC studentship grant number EP/P504120/1.
This record's URL: http://www.repository.cam.ac.uk/handle/1810/245343