Effects of Surface Tension, Inertia, Cooling and Internal Pressurization in the Drawing of Fibres with Internal Hole Structure

Abstract

The main focus of this study is determining the steady states and stability of the drawing process of fibers with internal hole structure. Using an asymptotic approach we develop the governing equations of mass, momentum, heat and the details of the internal structure. The momentum and heat equations are coupled because the viscosity is a strongly varying function of temperature. We begin by considering the isothermal case with no internal pressure and use linear stability analysis to show that the presence of an axisymmetric hole destabilises the flow for finite capillary number and thereby directly addresses a question raised in the literature. However, our formulation allows us to go much further and consider arbitrary hole structures or non-axisymmetric shapes and show that any structure with holes will be less stable than the case of a solid axisymmetric thread. For a solid axisymmetric thread we also determine a closed-form expression that delineates the unconditional instability boundary in which case the thread is unstable for all draw ratios. We also consider the effects of cooling and internal pressure for an axisymmetric tube and examine how the presence of the hole affects the system. We consider how the presence of a hole affects the stability when there is non-zero surface tension. When there is no cooling the presence of the hole is always destabilising. This is also true for sufficiently weak cooling or sufficiently small hole sizes. However, for sufficiently strong cooling and large hole sizes the presence of the hole is stabilising. We also consider how internal pressure affects the dynamics of a hole when surface tension and cooling are important. For non-zero surface tension with cooling and internal pressure and small hole sizes increasing the hole size is destabilising.

Date of Award	9 Aug 2023
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Jonathan James WYLIE (Supervisor)