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Gravitational extension of a fluid cylinder with internal structure

Published online by Cambridge University Press:  03 February 2016

Hayden Tronnolone ,
Yvonne M. Stokes ,
Herbert Tze Cheung Foo  and
Heike Ebendorff-Heidepriem
Hayden Tronnolone*
Affiliation:
School of Mathematical Sciences, The University of Adelaide, North Terrace, Adelaide, SA 5005, Australia
Yvonne M. Stokes
Affiliation:
School of Mathematical Sciences, The University of Adelaide, North Terrace, Adelaide, SA 5005, Australia
Herbert Tze Cheung Foo
Affiliation:
Institute for Photonics and Advanced Sensing, School of Chemistry and Physics, The University of Adelaide, North Terrace, Adelaide, SA 5005, Australia
Heike Ebendorff-Heidepriem
Affiliation:
Institute for Photonics and Advanced Sensing, School of Chemistry and Physics, The University of Adelaide, North Terrace, Adelaide, SA 5005, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Motivated by the fabrication of microstructured optical fibres, a model is presented for the extension under gravity of a slender fluid cylinder with internal structure. It is shown that the general problem decouples into a two-dimensional surface-tension-driven Stokes flow that governs the transverse shape and an axial problem that depends upon the transverse flow. The problem and its solution differ from those obtained for fibre drawing, because the problem is unsteady and the fibre tension depends on axial position. Solutions both with and without surface tension are developed and compared, which show that the relative importance of surface tension depends upon both the parameter values and the geometry under consideration. The model is compared with experimental data and is shown to be in good agreement. These results also show that surface-tension effects are essential to accurately describing the cross-sectional shape.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Slender-body theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 790 , 10 March 2016 , pp. 308 - 338
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Copyright
© 2016 Cambridge University Press 

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