Drawing and Nonlinear Stability of Non-Newtonian Fibres with Internal Holes

There are various applications that require the production of narrow fibres with internal holes running parallel to the axis of the fibre. One notable example is Microstructured Optical Fibres (MOFs), also known as ‘holey’ fibres. MOFs have gained significant attention in recent decades due to their numerous advantages, including customizable optical properties, compact size, lightweight, high flexibility, and cost-effectiveness. MOFs are created by passing a macroscopic preform with a specific hole structure through a nozzle and then stretching it into fibres using a take-up roller. One of the main challenges in these fabrication processes is that the size and shape of the internal holes can be significantly altered by surface tension during stretching. This is particularly critical in the production of MOFs, as the optical properties are highly sensitive to the hole geometry. Another issue is the potential instability of the drawing process, resulting in oscillations in the thread’s geometry that make it unsuitable for most applications. While most MOFs are made from glass materials, which can be approximated as having Newtonian rheology with temperature-dependent viscosity, there has been growing interest in using polymer materials for fibre production. Polymer fibres offer advantages such as lower processing temperatures and ease of preform creation, and a wide range of polymers have been found suitable for the fabrication process. This has led to the question of whether non-Newtonian polymer materials can be utilized to achieve the manufacturing goals of preserving internal hole structures and controlling instabilities. This proposal is motivated by this question and will explore the drawing of a thread composed of a viscoelastic fluid with internal holes. However, as we will show in the proposal, deriving and analysing long-wavelength equations for these types of non-Newtonian rheologies is significantly more challenging than in the Newtonian case or in the case of non-Newtonian threads without interior holes. Nevertheless, the goal of this proposal is to overcome these challenges, gain a solid understanding of the fundamental mechanics in play and hence determine how non-Newtonian rheology can be leveraged to improve the fabrication process for the drawing of ‘holey’ fibres and other related applications.