Phase Diagram and Snap-Off Transition for a Twisted Party Balloon

TL;DR

This paper investigates the phase diagram and snap-off transition in twisted party balloons, revealing multiple shape states, hysteresis effects, and providing heuristic models for phase boundaries.

Contribution

It introduces a comprehensive phase diagram for twisted balloons, identifying multiple stable shapes and hysteresis, with heuristic models for phase boundary predictions.

Findings

Five distinct balloon shapes identified: straight, necking, wrinkled, helix, supercoil.

Hysteresis effects influence phase boundaries and shape transitions.

Heuristic models successfully predict phase boundaries.

Abstract

All children enjoy inflating balloons and twisting them into different shapes and animals. Snapping the balloon into two separate compartments is a necessary step that bears resemblance to the pinch-off phenomenon for water droplet detached from the faucet. In addition to testing whether balloons exhibit the properties of self-similarity and memory effect that are often associated with the latter event, we determine their phase diagram by experiments. It turns out that a common party balloon does not just snap. They in fact can assume five more shapes, i.e., straight, necking, wrinkled, helix, and supercoil, depending on the twist angle and ratio of its length and diameter. Moreover, history also matters due to their prominent hysteresis. One may shift the phase boundary or/and reshuffle the phases by untwisting or lengthening the balloon at different twist angle and initial length. Heuristic models are provided to obtain analytic expressions for the phase boundaries.