Dynamics of Pressurised Viscoelastic Tubes

There are a number of manufacturing processes in which one must pressurize the hole of a tube composed of viscoelastic material. In the blown film process, sufficient pressure is required to cause the hole to expand and ultimately generate a thin film. In the production of micro-structured optical fibers, pressurization is necessary to prevent surface-tension-driven hole closure. Unfortunately, a range of issues plagues such manufacturing techniques, such as instabilities and high sensitivity to defects. Polymeric materials are typically used in the blown film process, while recent work has shown significant promise for using polymeric materials in the manufacture of microstructured optical fibers. It is therefore of paramount importance to consider how viscoelasticity inherent in polymeric materials interacts with surface tension, inertia, and viscous forces to control the flow. This proposal is motivated by the goal of understanding how the viscoelastic properties of the fluid can be best utilized to achieve the main manufacturing objectives. We will address these questions by deriving a set of long-wavelength equations that describe the flow. This represents a serious challenge because the pressure in the hole drives a radial flow that precludes the use of previous techniques employed in the literature for threads without holes. Nevertheless, we will derive a new method based on a weakly elastic assumption to obtain a relevant system of equations. Once we have derived the long-wavelength equations, we will determine how hole closure and stability issues in drawing are affected by viscoelastic effects. We will also examine the linear and nonlinear stability of a uniform thread and explore how to leverage viscoelastic rheology to achieve the manufacturing goals for the blown film process.