Inflation and deflation dynamics of water-filled balloons

This work presents simplified modelling of the fully coupled behavior of a spherical, hyperelastic balloon exhibiting bi-stability, under a time-dependent externally-dictated input pressure. The reduced order model, derived under the assumption of laminar flow at high Reynolds numbers, distinguish between the flow regime during deflation, where the potential flow theory can be applied, and inflation where boundary layer separation occurs, giving rise to an internal jet. Combining the bi-stable elasticity of the balloon and the effects of the entrapped fluid, yields a non-linear oscillator equation describing the extensional motion of the balloon, assuming the latter does not deviate significantly from sphericity.

A two-step model verification, based on finite element computations is presented. First, the different forces applied by the entrapped fluid on the balloon are examined separately utilizing several degenerated simulations, where the elasticity of the balloon is ignored. Next, a fully coupled finite element simulation is executed and compared to the reduced order model, showing a good correlation.

A possible application of the suggested system could be serving as a building block for soft robots, exploiting multiple bi-stable elements.