Physics Behind the Snapping of a Twisted Balloon

Yu-Chuan Cheng^1*, Tzay-Ming Hong¹

¹物理學系, 國立清華大學, 新竹, Taiwan

* Presenter:Yu-Chuan Cheng, email:s103022207@gmail.com

It is common childhood experience to twist balloons and turn them into hats, dogs, and flower etc. In this presentation we investigate the process that leads up to the snap of a cylindrical balloon.

For a twisted short balloon (1≦L/D≦7 where L, D denotes length and diameter), its phase transits from (1) being sheared and wrinkle-free while torque τ is linear to θ, (2) appearance of a neck without wrinkles, while radius and shear angle is found to obey r³dθ/dx=const, (3) development of parallel wrinkles whose number ~12 is insensitive to L, D, and thickness. Torque increases concavely with θ, to (4) wrinkles cross one another eventually and are followed by a sudden snap into separate segments, as for a bended drinking straw. For a medium-size balloon (7≦L/D≦15), (a) similar to (1), (b) skip (2, 3) to become curled with a low-amplitude oscillation in τ(θ), (c) similar to (4).
When the balloon is long (15≦L/D), (i) similar to (1) (ii) similar to (b), but develop a supercoil while accompanied by a suddenly drop in τ, (iii) repeat (i, ii) where the number of repetition varied with L/D.

Heuristic models are proposed to understand the physics behind different phases and their transitions. Molecular Dynamics simulation is also performed to reveal the energetics, unavailable in experiments. Furthermore, to verify whether the above properties are unique to a quasi-1D object as balloons, we also studied the twisting of a thread (real 1D) and ribbon (2D).

Keywords: twisting, DNA supercoiling, MD simulation, complex systems, ribbon