On the inflation and deflation dynamics of liquid-filled, hyperelastic balloons

TL;DR

This paper develops a reduced-order, hybrid model for the inflation and deflation dynamics of liquid-filled hyperelastic balloons, capturing flow regimes and validating results with finite element simulations.

Contribution

It introduces a piecewise fluid pressure model and a nonlinear oscillator equation for balloon dynamics, integrating flow separation effects and validating with finite element analysis.

Findings

Model accurately predicts inflation and deflation behavior.

Flow separation leads to jet formation during inflation.

Excellent agreement with finite element simulations.

Abstract

We derive a reduced-order model describing the inflation and deflation dynamics of a liquid-filled hyperelastic balloon, focusing on inviscid laminar flow and the extensional motion of the balloon. We initially study the flow and pressure fields for dictated motion of the solid, which throughout deflation are obtained by solving the potential problem. However, during inflation, flow separation creates a jet within the balloon, requiring a different approach. The analyses of both flow regimes lead to a simple piecewise model, describing the fluidic pressure during inflation and deflation, which is then verified by finite element computations. We then use a variational approach to derive the equation governing the balloon's dynamics, yielding a nonlinear hybrid oscillator equation, describing the interaction between the extensional mode of the balloon, and the entrapped fluid. Analytical and graphical investigations of the suggested model are presented, shedding light on its static and dynamic behaviour under different operating conditions. Our suggested model and its underlying assumptions are verified utilizing a fully coupled finite element scheme, showing excellent agreement.