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Type: Theses
Title: Extensional and surface-tension-driven fluid flows in microstructured optical fibre fabrication
Author: Tronnolone, Hayden
Issue Date: 2016
School/Discipline: School of Mathematical Sciences
Abstract: Microstructured optical fibres (MOFs) are a design of optical fibre comprising a series of longitudinal air channels within a thread of material that form a waveguide for light. The flexibility of this design allows optical fibres to be created with adaptable and previously unrealised optical properties. A MOF is typically constructed by first creating a macroscopic version of the design, known as a preform, with a centimetre-scale diameter that is later drawn into a fibre with a micrometer-scale diameter. There are several methods for constructing a preform. In the extrusion method molten material is forced through a die containing an array of blocking elements that match the required pattern of channels. Preforms may also be constructed by stacking tubes and fusing them together with heat. In both processes the fluid flow that arises can deform the air channels, rendering the fibre useless. At present there is only a limited understanding of the relative importance of the various physical parameters in determining the final preform geometry, which means that the development of new MOF technology requires time-consuming and costly experimentation. This thesis develops mathematical models of the fluid flows that occur during the extrusion and stacking methods of MOF preform fabrication. These models are used to determine which physical mechanisms are important during the manufacturing process so as to inform the fabrication of MOF preforms. A model is constructed of a fixed slender fluid cylinder with internal structure stretching under gravity and with surface-tension-driven deformation. The molten material is modelled as a Newtonian fluid with a temperature-dependent viscosity, which is assumed known. The variables are expanded as series in powers of a slenderness parameter so that, after dropping higher-order terms, the resulting equations partially decouple into a one-dimensional model for the axial ow and a two-dimensional model for the transverse flow. Under a suitable transformation of variables the transverse equations are precisely the Stokes equations with unit surface tension. After reviewing the use of complex variables to represent the transverse problem, three numerical solution methods are considered: two based upon spectral methods and one using the method of fundamental solutions (MFS). These methods are compared for their efficiency and accuracy. Several example solutions for stretching cylinders are presented and the role of surface tension is investigated using approximate solutions derived for zero and small surface tension. The model is validated against experimental data and found to be in good agreement. The stretching model is extended to the case of an extruded fluid cylinder, neglecting extrudate-swell effects, where again the fluid flow decouples in axial and transverse models. The results are compared with experimental observations and the model used to analyse the formation of distortions during preform extrusion and how these may be controlled. Two problems related to preform fabrication are considered that feature cross sections with non-circular initial outer boundaries. A technique is developed for deriving initial conformal maps describing such domains, which are used in the stretching and extrusion models to analyse the proposed problems.
Advisor: Stokes, Yvonne Marie
Finn, Matt
Crowdy, Darren
Dissertation Note: Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2016.
Keywords: microstructured optical fibres
slenderness approximations
complex variables
Stokes flow
conformal maps
spectral methods
fluid mechanics
preform extrusion
capillary stacking
Provenance: This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at:
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