Viscous flow-fields in hyperelastic Chambers

Abstract

Viscous flows in hyperelastic chambers are relevant to many biological phenomena such as inhalation into the lung's acinar region and medical applications such as the inflation of a small balloon in minimally invasive procedures. In this work, we analytically study the viscous flow and elastic deformation created due to inflation of such spherical chambers from one or two inlets. Our investigation considers the constitutive hyperelastic law coupled with the flow dynamics inside the chamber. We derive a closed-form expression for the inflation dynamics, accounting for the effect of elastic bi-stability. Interestingly, the obtained pressure distribution shows that the maximal pressure on the chamber's surface is greater than the pressure at the entrance to the chamber. The analytically calculated velocity-and pressure-fields during inflation are compared to a fully coupled finite element scheme, showing excellent agreement. Our results allow capturing the balloon's viscous resistance to inflation/deflation, thus enabling us to model the process of inflation/deflation and the induced stress fields.