Abstract

A series of six experiments drawing tubular fibres are compared to some recent mathematical modelling of this fabrication process. The importance of fibre tension in determining the internal geometry of the fibre is demonstrated, confirming a key prediction of the models. There is evidence of self-pressurisation of the internal channel, where an additional pressure is induced in the internal channel as the fibre is drawn, and the dependence of the magnitude of this pressure on fibre tension is discussed. Additionally, there is evidence that the difference between the glass and furnace temperatures is proportional to the furnace temperature and dependent on the preform geometry.

© 2015 Optical Society of America

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References

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  1. Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Drawing of micro-structured fibres: circular and non-circular tubes,” J. Fluid Mech. 755, 176–203 (2014).
    [Crossref]
  2. P. Buchak, D. G. Crowdy, Y. M. Stokes, and H. Ebendorff-Heidepriem, “Elliptical pore regularization of the inverse problem for microstructure optical fibre fabrication,” J. Fluid Mech. 778, 5–38 (2015).
    [Crossref]
  3. M. J. Chen, Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Microstructured optical fibre drawing with active channel pressurisation,” J. Fluid Mech. 783, 137–165 (2015).
    [Crossref]
  4. H. Tronnolone, Y. M. Stokes, H. T. C. Foo, and H. Ebendorff-Heidepriem, “Gravitational extension of a fluid cylinder with internal structure,” J. Fluid Mech. submitted (2015).
  5. T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Ann. Rev. Materials Res. 36, 467–495 (2006).
    [Crossref]
  6. S. Xue, R. Tanner, G. Barton, R. Lwin, M. Large, and L. Poladian, “Fabrication of Microstructured Optical Fibres Part I: Problem Formulation and Numerical Modelling of Transient Draw Process,” J. Lightwave Technol. 23, 2245–2254 (2005).
    [Crossref]
  7. G. Luzi, P. Epple, M. Scharrer, K. Fujimoto, C. Rauh, and A. Delgado, “Numerical Solution and Experimental Validation of the Drawing Process of Six-Hole Optical Fibers Including the Effects of Inner Pressure and Surface Tension,” J. Lightwave Technol. 30, 1306–1311 (2012).
    [Crossref]
  8. G. T. Jasion, J. S. Shrimpton, Y. Chen, T. Bradley, D. J. Richardson, and F. Poletti, “MicroStructure Element Method (MSEM): viscous flow model for the virtual draw of microstructured optical fibers,” Opt. Express 23, 312–329 (2015).
    [Crossref] [PubMed]
  9. A. D. Fitt, K. Furusawa, T. M. Monro, and C. P. Please, “Modelling the Fabrication of Hollow Fibers: Capillary Drawing,” J. Lightwave Technol. 19, 1924–1931 (2001).
    [Crossref]
  10. A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, and D. J. Richardson, “The mathematical modelling of capillary drawing for holey fibre manufacture,” Journal of Engineering Mathematics 43, 201–227 (2002).
    [Crossref]
  11. Y. Chen and T. Birks, “Predicting hole sizes after fibre drawing without knowing the viscosity,” Optical Materials Express 3, 346–356 (2013).
    [Crossref]
  12. A. L. Yarin, P. Gospodinov, and V. I. Roussinov, “Stability loss and sensitivity in hollow fiber drawing,” Phys Fluids 6, 1454–1463 (1994).
    [Crossref]
  13. P. Gospodinov and A. L. Yarin, “Draw resonance of optical microcapillaries in non-isothermal drawing,” Intl J. Multiphase Flow 23, 967–976 (1997).
    [Crossref]
  14. C. J. Voyce, A. D. Fitt, and T. M. Monro, “Mathematical Modeling as an Accurate Predictive Tool in Capillary and Microstructured Fiber Manufacture: The Effects of Preform Rotation,” J. Lightwave Technol. 26, 791–798 (2008).
    [Crossref]
  15. C. J. Voyce, A. D. Fitt, J. R. Hayes, and T. M. Monro, “Mathematical Modeling of the Self-Pressurizing Mechanism for Microstructured Fiber Drawing,” J. Lightwave Technol. 27, 871–878 (2009).
    [Crossref]
  16. R. Kostecki, H. Ebendorff-Heidepriem, S. C. Warren-Smith, and T. M. Monro, “Predicting the drawing conditions for microstructured optical fiber fabrication,” Optical Materials Express 4, 29–40 (2014).
    [Crossref]
  17. L. Cummings and P. Howell, “On the evolution of non-axisymmetric viscous fibres with surface tension, inertia and gravity,” Journal of Fluid Mechanics 389, 361–389 (1999).
    [Crossref]
  18. Schott Glass Company, Optical Glass (2014).
  19. M. Trabelssi, H. Ebendorff-Heidepriem, K. C. Richardson, T. M. Monro, and P. F. Joseph, “Computational modeling of die swell of extruded glass preforms at high viscosity,” J. Am. Ceram. Soc. 97, 1572—1581 (2014).
    [Crossref]

2015 (3)

P. Buchak, D. G. Crowdy, Y. M. Stokes, and H. Ebendorff-Heidepriem, “Elliptical pore regularization of the inverse problem for microstructure optical fibre fabrication,” J. Fluid Mech. 778, 5–38 (2015).
[Crossref]

M. J. Chen, Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Microstructured optical fibre drawing with active channel pressurisation,” J. Fluid Mech. 783, 137–165 (2015).
[Crossref]

G. T. Jasion, J. S. Shrimpton, Y. Chen, T. Bradley, D. J. Richardson, and F. Poletti, “MicroStructure Element Method (MSEM): viscous flow model for the virtual draw of microstructured optical fibers,” Opt. Express 23, 312–329 (2015).
[Crossref] [PubMed]

2014 (3)

Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Drawing of micro-structured fibres: circular and non-circular tubes,” J. Fluid Mech. 755, 176–203 (2014).
[Crossref]

R. Kostecki, H. Ebendorff-Heidepriem, S. C. Warren-Smith, and T. M. Monro, “Predicting the drawing conditions for microstructured optical fiber fabrication,” Optical Materials Express 4, 29–40 (2014).
[Crossref]

M. Trabelssi, H. Ebendorff-Heidepriem, K. C. Richardson, T. M. Monro, and P. F. Joseph, “Computational modeling of die swell of extruded glass preforms at high viscosity,” J. Am. Ceram. Soc. 97, 1572—1581 (2014).
[Crossref]

2013 (1)

Y. Chen and T. Birks, “Predicting hole sizes after fibre drawing without knowing the viscosity,” Optical Materials Express 3, 346–356 (2013).
[Crossref]

2012 (1)

2009 (1)

2008 (1)

2006 (1)

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Ann. Rev. Materials Res. 36, 467–495 (2006).
[Crossref]

2005 (1)

2002 (1)

A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, and D. J. Richardson, “The mathematical modelling of capillary drawing for holey fibre manufacture,” Journal of Engineering Mathematics 43, 201–227 (2002).
[Crossref]

2001 (1)

1999 (1)

L. Cummings and P. Howell, “On the evolution of non-axisymmetric viscous fibres with surface tension, inertia and gravity,” Journal of Fluid Mechanics 389, 361–389 (1999).
[Crossref]

1997 (1)

P. Gospodinov and A. L. Yarin, “Draw resonance of optical microcapillaries in non-isothermal drawing,” Intl J. Multiphase Flow 23, 967–976 (1997).
[Crossref]

1994 (1)

A. L. Yarin, P. Gospodinov, and V. I. Roussinov, “Stability loss and sensitivity in hollow fiber drawing,” Phys Fluids 6, 1454–1463 (1994).
[Crossref]

Barton, G.

Birks, T.

Y. Chen and T. Birks, “Predicting hole sizes after fibre drawing without knowing the viscosity,” Optical Materials Express 3, 346–356 (2013).
[Crossref]

Bradley, T.

Buchak, P.

P. Buchak, D. G. Crowdy, Y. M. Stokes, and H. Ebendorff-Heidepriem, “Elliptical pore regularization of the inverse problem for microstructure optical fibre fabrication,” J. Fluid Mech. 778, 5–38 (2015).
[Crossref]

M. J. Chen, Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Microstructured optical fibre drawing with active channel pressurisation,” J. Fluid Mech. 783, 137–165 (2015).
[Crossref]

Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Drawing of micro-structured fibres: circular and non-circular tubes,” J. Fluid Mech. 755, 176–203 (2014).
[Crossref]

Chen, M. J.

M. J. Chen, Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Microstructured optical fibre drawing with active channel pressurisation,” J. Fluid Mech. 783, 137–165 (2015).
[Crossref]

Chen, Y.

Crowdy, D. G.

P. Buchak, D. G. Crowdy, Y. M. Stokes, and H. Ebendorff-Heidepriem, “Elliptical pore regularization of the inverse problem for microstructure optical fibre fabrication,” J. Fluid Mech. 778, 5–38 (2015).
[Crossref]

M. J. Chen, Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Microstructured optical fibre drawing with active channel pressurisation,” J. Fluid Mech. 783, 137–165 (2015).
[Crossref]

Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Drawing of micro-structured fibres: circular and non-circular tubes,” J. Fluid Mech. 755, 176–203 (2014).
[Crossref]

Cummings, L.

L. Cummings and P. Howell, “On the evolution of non-axisymmetric viscous fibres with surface tension, inertia and gravity,” Journal of Fluid Mechanics 389, 361–389 (1999).
[Crossref]

Delgado, A.

Ebendorff-Heidepriem, H.

P. Buchak, D. G. Crowdy, Y. M. Stokes, and H. Ebendorff-Heidepriem, “Elliptical pore regularization of the inverse problem for microstructure optical fibre fabrication,” J. Fluid Mech. 778, 5–38 (2015).
[Crossref]

M. J. Chen, Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Microstructured optical fibre drawing with active channel pressurisation,” J. Fluid Mech. 783, 137–165 (2015).
[Crossref]

Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Drawing of micro-structured fibres: circular and non-circular tubes,” J. Fluid Mech. 755, 176–203 (2014).
[Crossref]

R. Kostecki, H. Ebendorff-Heidepriem, S. C. Warren-Smith, and T. M. Monro, “Predicting the drawing conditions for microstructured optical fiber fabrication,” Optical Materials Express 4, 29–40 (2014).
[Crossref]

M. Trabelssi, H. Ebendorff-Heidepriem, K. C. Richardson, T. M. Monro, and P. F. Joseph, “Computational modeling of die swell of extruded glass preforms at high viscosity,” J. Am. Ceram. Soc. 97, 1572—1581 (2014).
[Crossref]

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Ann. Rev. Materials Res. 36, 467–495 (2006).
[Crossref]

H. Tronnolone, Y. M. Stokes, H. T. C. Foo, and H. Ebendorff-Heidepriem, “Gravitational extension of a fluid cylinder with internal structure,” J. Fluid Mech. submitted (2015).

Epple, P.

Fitt, A. D.

Foo, H. T. C.

H. Tronnolone, Y. M. Stokes, H. T. C. Foo, and H. Ebendorff-Heidepriem, “Gravitational extension of a fluid cylinder with internal structure,” J. Fluid Mech. submitted (2015).

Fujimoto, K.

Furusawa, K.

A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, and D. J. Richardson, “The mathematical modelling of capillary drawing for holey fibre manufacture,” Journal of Engineering Mathematics 43, 201–227 (2002).
[Crossref]

A. D. Fitt, K. Furusawa, T. M. Monro, and C. P. Please, “Modelling the Fabrication of Hollow Fibers: Capillary Drawing,” J. Lightwave Technol. 19, 1924–1931 (2001).
[Crossref]

Gospodinov, P.

P. Gospodinov and A. L. Yarin, “Draw resonance of optical microcapillaries in non-isothermal drawing,” Intl J. Multiphase Flow 23, 967–976 (1997).
[Crossref]

A. L. Yarin, P. Gospodinov, and V. I. Roussinov, “Stability loss and sensitivity in hollow fiber drawing,” Phys Fluids 6, 1454–1463 (1994).
[Crossref]

Hayes, J. R.

Howell, P.

L. Cummings and P. Howell, “On the evolution of non-axisymmetric viscous fibres with surface tension, inertia and gravity,” Journal of Fluid Mechanics 389, 361–389 (1999).
[Crossref]

Jasion, G. T.

Joseph, P. F.

M. Trabelssi, H. Ebendorff-Heidepriem, K. C. Richardson, T. M. Monro, and P. F. Joseph, “Computational modeling of die swell of extruded glass preforms at high viscosity,” J. Am. Ceram. Soc. 97, 1572—1581 (2014).
[Crossref]

Kostecki, R.

R. Kostecki, H. Ebendorff-Heidepriem, S. C. Warren-Smith, and T. M. Monro, “Predicting the drawing conditions for microstructured optical fiber fabrication,” Optical Materials Express 4, 29–40 (2014).
[Crossref]

Large, M.

Luzi, G.

Lwin, R.

Monro, T. M.

R. Kostecki, H. Ebendorff-Heidepriem, S. C. Warren-Smith, and T. M. Monro, “Predicting the drawing conditions for microstructured optical fiber fabrication,” Optical Materials Express 4, 29–40 (2014).
[Crossref]

M. Trabelssi, H. Ebendorff-Heidepriem, K. C. Richardson, T. M. Monro, and P. F. Joseph, “Computational modeling of die swell of extruded glass preforms at high viscosity,” J. Am. Ceram. Soc. 97, 1572—1581 (2014).
[Crossref]

C. J. Voyce, A. D. Fitt, J. R. Hayes, and T. M. Monro, “Mathematical Modeling of the Self-Pressurizing Mechanism for Microstructured Fiber Drawing,” J. Lightwave Technol. 27, 871–878 (2009).
[Crossref]

C. J. Voyce, A. D. Fitt, and T. M. Monro, “Mathematical Modeling as an Accurate Predictive Tool in Capillary and Microstructured Fiber Manufacture: The Effects of Preform Rotation,” J. Lightwave Technol. 26, 791–798 (2008).
[Crossref]

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Ann. Rev. Materials Res. 36, 467–495 (2006).
[Crossref]

A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, and D. J. Richardson, “The mathematical modelling of capillary drawing for holey fibre manufacture,” Journal of Engineering Mathematics 43, 201–227 (2002).
[Crossref]

A. D. Fitt, K. Furusawa, T. M. Monro, and C. P. Please, “Modelling the Fabrication of Hollow Fibers: Capillary Drawing,” J. Lightwave Technol. 19, 1924–1931 (2001).
[Crossref]

Please, C. P.

A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, and D. J. Richardson, “The mathematical modelling of capillary drawing for holey fibre manufacture,” Journal of Engineering Mathematics 43, 201–227 (2002).
[Crossref]

A. D. Fitt, K. Furusawa, T. M. Monro, and C. P. Please, “Modelling the Fabrication of Hollow Fibers: Capillary Drawing,” J. Lightwave Technol. 19, 1924–1931 (2001).
[Crossref]

Poladian, L.

Poletti, F.

Rauh, C.

Richardson, D. J.

G. T. Jasion, J. S. Shrimpton, Y. Chen, T. Bradley, D. J. Richardson, and F. Poletti, “MicroStructure Element Method (MSEM): viscous flow model for the virtual draw of microstructured optical fibers,” Opt. Express 23, 312–329 (2015).
[Crossref] [PubMed]

A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, and D. J. Richardson, “The mathematical modelling of capillary drawing for holey fibre manufacture,” Journal of Engineering Mathematics 43, 201–227 (2002).
[Crossref]

Richardson, K. C.

M. Trabelssi, H. Ebendorff-Heidepriem, K. C. Richardson, T. M. Monro, and P. F. Joseph, “Computational modeling of die swell of extruded glass preforms at high viscosity,” J. Am. Ceram. Soc. 97, 1572—1581 (2014).
[Crossref]

Roussinov, V. I.

A. L. Yarin, P. Gospodinov, and V. I. Roussinov, “Stability loss and sensitivity in hollow fiber drawing,” Phys Fluids 6, 1454–1463 (1994).
[Crossref]

Scharrer, M.

Shrimpton, J. S.

Stokes, Y. M.

P. Buchak, D. G. Crowdy, Y. M. Stokes, and H. Ebendorff-Heidepriem, “Elliptical pore regularization of the inverse problem for microstructure optical fibre fabrication,” J. Fluid Mech. 778, 5–38 (2015).
[Crossref]

M. J. Chen, Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Microstructured optical fibre drawing with active channel pressurisation,” J. Fluid Mech. 783, 137–165 (2015).
[Crossref]

Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Drawing of micro-structured fibres: circular and non-circular tubes,” J. Fluid Mech. 755, 176–203 (2014).
[Crossref]

H. Tronnolone, Y. M. Stokes, H. T. C. Foo, and H. Ebendorff-Heidepriem, “Gravitational extension of a fluid cylinder with internal structure,” J. Fluid Mech. submitted (2015).

Tanner, R.

Trabelssi, M.

M. Trabelssi, H. Ebendorff-Heidepriem, K. C. Richardson, T. M. Monro, and P. F. Joseph, “Computational modeling of die swell of extruded glass preforms at high viscosity,” J. Am. Ceram. Soc. 97, 1572—1581 (2014).
[Crossref]

Tronnolone, H.

H. Tronnolone, Y. M. Stokes, H. T. C. Foo, and H. Ebendorff-Heidepriem, “Gravitational extension of a fluid cylinder with internal structure,” J. Fluid Mech. submitted (2015).

Voyce, C. J.

Warren-Smith, S. C.

R. Kostecki, H. Ebendorff-Heidepriem, S. C. Warren-Smith, and T. M. Monro, “Predicting the drawing conditions for microstructured optical fiber fabrication,” Optical Materials Express 4, 29–40 (2014).
[Crossref]

Xue, S.

Yarin, A. L.

P. Gospodinov and A. L. Yarin, “Draw resonance of optical microcapillaries in non-isothermal drawing,” Intl J. Multiphase Flow 23, 967–976 (1997).
[Crossref]

A. L. Yarin, P. Gospodinov, and V. I. Roussinov, “Stability loss and sensitivity in hollow fiber drawing,” Phys Fluids 6, 1454–1463 (1994).
[Crossref]

Ann. Rev. Materials Res. (1)

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Ann. Rev. Materials Res. 36, 467–495 (2006).
[Crossref]

Intl J. Multiphase Flow (1)

P. Gospodinov and A. L. Yarin, “Draw resonance of optical microcapillaries in non-isothermal drawing,” Intl J. Multiphase Flow 23, 967–976 (1997).
[Crossref]

J. Am. Ceram. Soc. (1)

M. Trabelssi, H. Ebendorff-Heidepriem, K. C. Richardson, T. M. Monro, and P. F. Joseph, “Computational modeling of die swell of extruded glass preforms at high viscosity,” J. Am. Ceram. Soc. 97, 1572—1581 (2014).
[Crossref]

J. Fluid Mech. (3)

Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Drawing of micro-structured fibres: circular and non-circular tubes,” J. Fluid Mech. 755, 176–203 (2014).
[Crossref]

P. Buchak, D. G. Crowdy, Y. M. Stokes, and H. Ebendorff-Heidepriem, “Elliptical pore regularization of the inverse problem for microstructure optical fibre fabrication,” J. Fluid Mech. 778, 5–38 (2015).
[Crossref]

M. J. Chen, Y. M. Stokes, P. Buchak, D. G. Crowdy, and H. Ebendorff-Heidepriem, “Microstructured optical fibre drawing with active channel pressurisation,” J. Fluid Mech. 783, 137–165 (2015).
[Crossref]

J. Lightwave Technol. (5)

Journal of Engineering Mathematics (1)

A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, and D. J. Richardson, “The mathematical modelling of capillary drawing for holey fibre manufacture,” Journal of Engineering Mathematics 43, 201–227 (2002).
[Crossref]

Journal of Fluid Mechanics (1)

L. Cummings and P. Howell, “On the evolution of non-axisymmetric viscous fibres with surface tension, inertia and gravity,” Journal of Fluid Mechanics 389, 361–389 (1999).
[Crossref]

Opt. Express (1)

Optical Materials Express (2)

Y. Chen and T. Birks, “Predicting hole sizes after fibre drawing without knowing the viscosity,” Optical Materials Express 3, 346–356 (2013).
[Crossref]

R. Kostecki, H. Ebendorff-Heidepriem, S. C. Warren-Smith, and T. M. Monro, “Predicting the drawing conditions for microstructured optical fiber fabrication,” Optical Materials Express 4, 29–40 (2014).
[Crossref]

Phys Fluids (1)

A. L. Yarin, P. Gospodinov, and V. I. Roussinov, “Stability loss and sensitivity in hollow fiber drawing,” Phys Fluids 6, 1454–1463 (1994).
[Crossref]

Other (2)

H. Tronnolone, Y. M. Stokes, H. T. C. Foo, and H. Ebendorff-Heidepriem, “Gravitational extension of a fluid cylinder with internal structure,” J. Fluid Mech. submitted (2015).

Schott Glass Company, Optical Glass (2014).

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Figures (9)

Fig. 1
Fig. 1

A schematic diagram of an annular preform (left) and a microscope image of a drawn tubular fibre (right). The outer radius of the preform is denoted r0 and the radius of the fibre is rL. The ratio between the inner and outer radii of the preform is ρ0 and the ratio between the inner and outer radii of the fibre is ρL.

Fig. 2
Fig. 2

The preform outer diameter 2r0 shows taper and was calculated for the six experiments using Eq. (19). Figure 2(a) shows the calculated preform outer diameter versus fibre tension for experiments 1 (black), 2 (red), 3 (blue) and 4 (green). Figure 2(b) shows the calculated preform outer diameter versus draw speed for experiment 5. Figure 2(c) shows the calculated preform outer diameter versus applied pressure for experiment 6.

Fig. 3
Fig. 3

Comparison between experimental measurements (crosses) and model output (circles) for experiments 1 and 2. Figures 3(a) and (c) show the outer diameter and the fibre diameter ratio, respectively, versus tension for experiment 1. Figures 3(b) and (d) show the outer diameter and fibre diameter ratio for experiment 2. The dashed lines in Figs. 3(c) and (d) represent the preform diameter ratio.

Fig. 4
Fig. 4

Comparison between experimental measurements (crosses) and model output (circles) for experiments 3 and 4. Figures 4(a) and (c) show the outer diameter and the fibre diameter ratio, respectively, versus fibre tension for experiment 3. Figures 4(b) and (d) show the outer diameter and fibre diameter ratio for experiment 4. The dashed lines in Figs. 4(c) and (d) represent the preform diameter ratio.

Fig. 5
Fig. 5

Comparison between experimental measurements (crosses) and model output (circles) for experiment 5. Figure 5(a)–(b) show the outer diameter and the fibre diameter ratio, respectively, versus draw speed, with the preform diameter ratio shown as a dashed line in Fig. 5(b). Figure 5(c) shows the relationship between draw speed and the measured fibre tension. Note that the measurement error (not shown) on Udraw is ±0.1 m/min.

Fig. 6
Fig. 6

Comparison between experimental measurements (crosses) and model (circles) output for experiment 6. Figures 6(a)–(b) show the outer diameter and the fibre diameter ratio, respectively, versus the applied channel pressurisation, with the preform diameter ratio shown as a dashed line in Fig. 6(b). Figure 6(c) shows the relationship between pressurisation and the measured fibre tension. Note that the measurement error (not shown) on the pressurisation is ±10 Pa.

Fig. 7
Fig. 7

Calculated pressurisation required for the model to exactly match the experimental data. Figures 7(a)–(d) are for experiments 1–4 and show the calculated pressure versus fibre tension. Figure 7(e) shows the calculated pressure for experiment 5 versus draw speed. Figure 7(f) shows the difference between calculated pressure and the applied pressure for experiment 6 versus the applied channel pressurisation.

Fig. 8
Fig. 8

A microscope image showing the cross-section of a fibre from a recent experiment (left) and a schematic of the preform from which it was drawn (right). Note that the relative sizes of the holes in the fibre are larger than those in the preform. Since this fibre was produced from an unpressurised draw, this is further evidence of self-pressurisation.

Fig. 9
Fig. 9

Difference between measured furnace temperature and calculated glass temperature expressed as a percentage of furnace temperature for each experimental point. Note that for experiment 5 the relationship between draw speed and tension is given in Fig. 5(c) and for experiment 6 the relationship between pressurisation and tension is given in Fig. 6(c).

Tables (1)

Tables Icon

Table 1 Summary of the dimensions of the preform and the operational parameter values used in the six experiments. Additionally, the surface tension parameter for F2 glass, which was used in all the above experiments, is γ = 0.23Nm−1 and the neck down length was approximately L = 0.03m. The numbers in brackets which follow the ranges for Tfurnace, Udraw and pH indicate the number of incremental steps taken to vary these operational parameters between the stated values during the course of a given experiment.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

D = U L / U 0 = S 0 / S L ,
σ = 6 γ S 0 𝒯 ,
μ 0 L = γ U 0 S 0 .
α 0 = α ( ρ 0 ) , α L = α ( ρ L ) , where α ( ρ ) = 1 π 1 ρ 1 + ρ .
ρ L = 1 π α L 2 1 + π α L 2 .
r L = S 0 π D ( 1 ρ L 2 ) = r 0 1 ρ 0 2 D ( 1 ρ L 2 ) ,
S S 0 = ( α α 0 ) 1 / 3 ( 1 + 3 α 0 𝒯 ) 3 α 0 𝒯 ( α α 0 ) .
( α L α 0 ) ( α L α 0 ) 1 / 3 ( 1 3 α 0 + 1 ) + 1 D 1 3 α 0 = 0 ,
α L = 8 α 0 3 3 ( 1 3 α 0 𝒯 + 1 ) 3 / 2 cos 3 θ 3 ,
θ = arctan ( 4 D 27 ( 1 + 3 α 0 𝒯 ) 3 3 α 0 𝒯 1 ) + π .
α L α 0 ( 1 + 1 3 α 0 𝒯 1 2 D 1 1 + 3 α 0 𝒯 + ) 3 .
= 𝒯 log Q , with Q = D ( α L α 0 ) 1 / 3 ,
p H = γ S 0 𝒫 .
d α d τ = 1 2 1 8 π α ( 1 π 2 α 4 ) 𝒫 χ ,
d χ d τ = 1 6 χ α 𝒯 ,
𝒫 > 8 π 3 α 0 ( 3 𝒯 α 0 + 1 ) .
𝒫 < a 2 D 9 ( D 1 ) ( a ( α 0 1 / π ) + 3 ( D 1 ) ) + 2 3 π D ( 1 + 3 D π 𝒯 ) ,
T glass = 137 + 4065.2 log 10 μ 0 + 2.314 .
2 r 0 = 2 r L D 1 ρ L 2 1 ρ 0 2 ,

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