Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/124787
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Type: Journal article
Title: Coupled fluid and energy flow in fabrication of microstructured optical fibres
Author: Stokes, Y.M.
Wylie, J.J.
Chen, M.J.
Citation: Journal of Fluid Mechanics, 2019; 874:548-572
Publisher: Cambridge University Press
Issue Date: 2019
ISSN: 0022-1120
1469-7645
Statement of
Responsibility: 
Yvonne M. Stokes, Jonathan J. Wylie and M.J. Chen
Abstract: We consider the role of heating and cooling in the steady drawing of a long and thin viscous thread with an arbitrary number of internal holes of arbitrary shape. The internal holes and the external boundary evolve as a result of the axial drawing and surface-tension effects. The heating and cooling affects the evolution of the thread because both the viscosity and surface tension of the thread are assumed to be functions of the temperature. We use asymptotic techniques to show that, under a suitable transformation, this complicated three-dimensional free boundary problem can be formulated in such a way that the transverse aspect of the flow can be reduced to the solution of a standard Stokes flow problem in the absence of axial stretching. The solution of this standard problem can then be substituted into a system of three ordinary differential equations that completely determine the flow. We use this approach to develop a very simple numerical method that can determine the way that thermal effects impact on the drawing of threads by devices that either specify the fibre tension or the draw ratio. We also develop a numerical method to solve the inverse problem of determining the initial cross-sectional geometry, draw tension and, importantly, heater temperature to obtain a desired cross-sectional shape and change in cross-sectional area at the device exit. This precisely allows one to determine the pattern of air holes in the preform that will achieve the desired hole pattern in the stretched fibre.
Keywords: Capillary flows; lubrication theory
Rights: © Cambridge University Press 2019
RMID: 0030130998
DOI: 10.1017/jfm.2019.466
Grant ID: http://purl.org/au-research/grants/arc/DP130101541
http://purl.org/au-research/grants/arc/FT160100108
Appears in Collections:Mathematical Sciences publications

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