Phase diagrams in inflating balloon

TL;DR

This paper analyzes the phase transition behavior of an inflating rubber balloon under external force using non-linear elastic theory, revealing conditions for uniform or coexistence inflation states.

Contribution

It introduces a theoretical framework for understanding volume transitions in inflating rubber balloons considering external force and material stretchability.

Findings

Critical force depends on rubber material properties

Discontinuous inflation transition occurs with sufficient stretchability

Coexistence of inflated and weakly inflated regions identified

Abstract

Volume transition of an inflating cylindrical balloon made of rubber under external force $F$ is studied based on the non-linear elastic theory for rubber. The pressure difference $\Delta P$ between inside and outside of the balloon is calculated as a function of the volume $V$ of the fluid inside the balloon. It is shown that if $F$ is smaller than a critical value $F_c$, the inflation of the balloon takes place with coexistence of strongly inflated region and weakly inflated region, while if $F$ is larger than $F_c$, the inflation takes place uniformly. It is shown that the critical force $F_c$ depends on the material parameter of the rubber, and that the discontinuous transition for finite stretching force can take place only when the rubber has enough stretchability