Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T06:15:26.410Z Has data issue: false hasContentIssue false
  • English
  • Français

Microstructured optical fibre drawing with active channel pressurisation

Published online by Cambridge University Press:  13 October 2015

Michael J. Chen ,
Yvonne M. Stokes ,
Peter Buchak ,
Darren G. Crowdy  and
Heike Ebendorff-Heidepriem
Michael J. Chen*
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
Peter Buchak
Affiliation:
Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK
Darren G. Crowdy
Affiliation:
Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK
Heike Ebendorff-Heidepriem
Affiliation:
ARC Centre of Excellence for Nanoscale BioPhotonics, Institute for Photonics and Advanced Sensing, School of Physical Sciences, The University of Adelaide, North Terrace, Adelaide, SA 5005, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The use of channel pressurisation in drawing microstructured optical fibres (MOFs) potentially allows for fine control of the internal structure of the fibre. By applying extra pressure inside the channels it is possible to counteract the effect of surface tension which would otherwise act to close the channels in the fibre as it is drawn. This paper extends the modelling approach of Stokes et al. (J. Fluid Mech., vol. 755, 2014, pp. 176–203) to include channel pressurisation. This approach treats the problem as two submodels for the flow, one in the axial direction along the fibre and another in the plane perpendicular to that direction. In the absence of channel pressurisation these models decoupled and were solved independently; we show that they become fully coupled when the internal channels are pressurised. The fundamental case of a fibre with an annular cross-section (containing one central channel) will be examined in detail. In doing this we consider both a forward problem to determine the shape of fibre from a known preform and an inverse problem to design a preform such that when drawn it will give a desired fibre geometry. Criteria on the pressure corresponding to fibre explosion and closure of the channel will be given that represent an improvement over similar criteria in the literature. A comparison between our model and a recent experiment is presented to demonstrate the effectiveness of the modelling approach. We make use of some recent work by Buchak et al. (J. Fluid Mech., vol. 778, 2015, pp. 5–38) to examine more complicated fibre geometries, where the cross-sectional shape of the internal channels is assumed to be elliptical and multiple channels are present. The examples presented here demonstrate the versatility of our modelling approach, where the subtleties of the interaction between surface tension and pressurisation can be revealed even for complex patterns of cross-sectional channels.

JFM classification

Interfacial Flows (free surface): Capillary flows Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Lubrication theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 783 , 25 November 2015 , pp. 137 - 165
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Boyd, K., Ebendorff-Heidepriem, H., Monro, T. M. & Munch, J. 2012 Surface tension and viscosity measurement of optical glasses using a scanning $\text{CO}_{2}$ laser. Opt. Mater. Express 2 (8), 1101–1110.CrossRefGoogle Scholar
Buchak, P. & Crowdy, D. G.2014 Fluid dynamics of MOF fabrication: elliptical cross-sections. Available at: http://wwwf.imperial.ac.uk/∼dgcrowdy/.Google Scholar
Buchak, P., Crowdy, D. G., Stokes, Y. M. & Ebendorff-Heidepriem, H. 2015 Elliptical pore regularisation of the inverse problem for microstructured optical fibre fabrication. J. Fluid Mech. 778, 5–38.CrossRefGoogle Scholar
Chen, Y. & Birks, T. A. 2013 Predicting hole sizes after fibre drawing without knowing the viscosity. Opt. Mater. Express 3 (3), 346–356.CrossRefGoogle Scholar
Crowdy, D. G. 2004 An elliptical-pore model of late-stage planar viscous sintering. J. Fluid Mech. 501, 251–277.CrossRefGoogle Scholar
Cummings, L. J. & Howell, P. D. 1999 On the evolution of non-axisymmetric viscous fibres with surface tension, inertia and gravity. J. Fluid Mech. 389, 361–389.CrossRefGoogle Scholar
Dewynne, J. N., Howell, P. D. & Wilmott, P. 1994 Slender viscous fibres with inertia and gravity. Q. J. Mech. Appl. Maths 47 (4), 541–555.CrossRefGoogle Scholar
Dewynne, J. N., Ockendon, J. R. & Wilmott, P. 1992 A systematic derivation of the leading-order equations for extensional flows in slender geometries. J. Fluid Mech. 244, 323–338.CrossRefGoogle Scholar
Fitt, A. D., Furusawa, K., Monro, T. M., Please, C. P. & Richardson, D. J. 2002 The mathematical modelling of capillary drawing for holey fibre manufacture. J. Engng Maths 43, 201–227.CrossRefGoogle Scholar
Griffiths, I. M. & Howell, P. D. 2007 The surface-tension-driven evolution of a two-dimensional annular viscous tube. J. Fluid Mech. 593, 181–208.CrossRefGoogle Scholar
Griffiths, I. M. & Howell, P. D. 2008 Mathematical modelling of non-axisymmetric capillary tube drawing. J. Fluid Mech. 605, 181–206.CrossRefGoogle Scholar
Kostecki, R., Ebendorff-Heidepriem, H., Warren-Smith, S. C. & Monro, T. M. 2014 Predicting the drawing conditions for microstructured optical fiber fabrication. Opt. Mater. Express 4, 29–40.CrossRefGoogle Scholar
Monro, T. M. & Ebendorff-Heidepriem, H. 2006 Progress in microstructured optical fibers. Annu. Rev. Mater. Res. 36, 467–495.CrossRefGoogle Scholar
Monro, T. M., Warren-Smith, S., Schartner, E. P., François, A., Heng, S., Ebendorff-Heidepriem, H. & Afshar, S. 2010 Sensing with suspended-core optical fibre. Opt. Fiber Technol. 16 (6), 343–356.CrossRefGoogle Scholar
Ruan, Y., Schartner, E. P., Ebendorff-Heidepriem, H., Hoffmann, P. & Monro, T.M. 2007 Detection of quantum-dot labeled proteins using soft glass microstructured optical fibers. Opt. Express 15 (26), 17819–17826.CrossRefGoogle ScholarPubMed
Schott Glass Company2015 Optical Glass Data Sheets. Available at: http://www.schott.com/advanced_optics/english/products/optical-components/optical-filters/optical-filter-glass/.Google Scholar
Stokes, Y. M., Buchak, P., Crowdy, D. G. & Ebendorff-Heidepriem, H. 2014 Drawing of micro-structured fibres: circular and non-circular tubes. J. Fluid Mech. 755, 176–203.CrossRefGoogle Scholar
Stokes, Y. M., Tuck, E. O. & Schwartz, L. W. 2000 Extensional fall of a very viscous fluid drop. Q. J. Mech. Appl. Maths 53, 565–582.CrossRefGoogle Scholar
Taroni, M., Breward, C. J. W., Cummings, L. J. & Griffiths, I. M. 2013 Asymptotic solutions of glass temperature profiles during steady optical fibre drawing. J. Engng Maths 80, 1–20.CrossRefGoogle Scholar
Voyce, C. J., Fitt, A. D., Hayes, J. R. & Monro, T. M. 2009 Mathematical modeling of the self-pressurizing mechanism for microstructured fiber drawing. J. Lightwave Technol. 27 (7), 871–878.CrossRefGoogle Scholar
Wilson, S. D. R. 1988 The slow dripping of a viscous fluid. J. Fluid Mech. 190, 561–570.CrossRefGoogle Scholar
Wylie, J. J., Huang, H. & Miura, R. M. 2011 Stretching of viscous threads at low Reynolds numbers. J. Fluid Mech. 683, 212–234.CrossRefGoogle Scholar
Yarin, A. L. 1993 Free Liquid Jets and Films: Hydrodynamics and Rheology. Longman Scientific & Technical and Wiley & Sons.Google Scholar
Yarin, A. L., Gospodinov, P. & Roussinov, V. I. 1994 Stability loss and sensitivity in hollow fiber drawing. Phys. Fluids 6, 1454–1463.CrossRefGoogle Scholar