Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/86149
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Type: Journal article
Title: Drawing of micro-structured fibres: circular and non-circular tubes
Author: Stokes, Y.
Buchak, P.
Crowdy, D.
Ebendorff-Heidepriem, H.
Citation: Journal of Fluid Mechanics, 2014; 755:176-203
Publisher: Cambridge University Press
Issue Date: 2014
ISSN: 0022-1120
1469-7645
Statement of
Responsibility: 
Yvonne M. Stokes, Peter Buchak, Darren G. Crowdy and Heike Ebendor-Heidepriem
Abstract: A general mathematical framework is presented for modelling the pulling of optical glass fibres in a draw tower. The only modelling assumption is that the fibres are slender; cross-sections along the fibre can have general shape, including the possibility of multiple holes or channels. A key result is to demonstrate how a so-called reduced time variable τ serves as a natural parameter in describing how an axial-stretching problem interacts with the evolution of a general surface-tension-driven transverse flow via a single important function of τ, herein denoted by H (τ), derived from the total rescaled cross-plane perimeter. For any given preform geometry, this function H (τ) may be used to calculate the tension required to produce a given fibre geometry, assuming only that the surface tension is known. Of principal practical interest in applications is the ‘inverse problem’ of determining the initial cross-sectional geometry, and experimental draw parameters, necessary to draw a desired final cross-section. Two case studies involving annular tubes are presented in detail: one involves a cross-section comprising an annular concatenation of sintering near-circular discs, the cross-section of the other is a concentric annulus. These two examples allow us to exemplify and explore two features of the general inverse problem. One is the question of the uniqueness of solutions for a given set of experimental parameters, the other concerns the inherent ill-posedness of the inverse problem. Based on these examples we also give an experimental validation of the general model and discuss some experimental matters, such as buckling and stability. The ramifications for modelling the drawing of fibres with more complicated geometries, and multiple channels, are discussed.
Rights: © Cambridge University Press 2014 The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence <http://creativecommons.org/licenses/by/3.0/>.
RMID: 0030008065
DOI: 10.1017/jfm.2014.408
Grant ID: http://purl.org/au-research/grants/arc/DP130101541
Appears in Collections:Mathematical Sciences publications

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