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Coupled fluid and energy flow in fabrication of microstructured optical fibres

Published online by Cambridge University Press:  11 July 2019

Yvonne M. Stokes Open the ORCID record for Yvonne M. Stokes [Opens in a new window] ,
Jonathan J. Wylie  and
M. J. Chen Open the ORCID record for M. J. Chen [Opens in a new window]
Yvonne M. Stokes*
Affiliation:
School of Mathematical Sciences and Institute for Photonics and Advanced Sensing, The University of Adelaide, SA 5005, Australia
Jonathan J. Wylie
Affiliation:
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong SAR Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
M. J. Chen
Affiliation:
School of Mathematical Sciences and Institute for Photonics and Advanced Sensing, The University of Adelaide, SA 5005, Australia
*
†Email address for correspondence: yvonne.stokes@adelaide.edu.au
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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.

JFM classification

Interfacial Flows (free surface): Capillary flows Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 548 - 572
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Copyright
© 2019 Cambridge University Press 

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