Abstract

The present contribution deals with thermofluidynamical features occurring during the drawing of capillaries for microstructured optical fibres. Here, the process stability depends strongly on flow and thermal processes taking place as a preform is heated and drawn in the furnace. This is the case particularly for hollow fibres for which the existence of the inner hole directly depends on material parameters such as the surface tension and the rheological properties and on process parameter such as hole internal pressure and the process temperature. A fluid-mechanics model suggested in the literature that makes use of asymptotic analysis based on small aspect ratio of the micro capillaries, has been revisited and improved recently and the leading-order equations have been then examined in some asymptotic limits by Luzi et al. . Starting from the novel class of solutions of the simplified equations of motion the present paper focuses on the effect of both surface tension and internal hole pressure since those are of essential importance during drawing. Thus, comparisons with experimental data are performed, in order to validate the analytical model developed in , which will be briefly presented here. The theoretical model gives very accurate predictions both when the internal hole is pressurized or when no pressure is applied, as long as the temperature does not reach too high values.

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  1. A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, "Modeling the fabrication of hollow fibres: Capillary drawing," J. Lightw. Technol. 19, 1924-1931 (2001).
  2. C. J. Voyce, A. D. Fitt, T. M. Monro, "Mathematical modeling as an accurate predictive tool in capillary and microstructured fibre manufacture: The effects of preform rotation," J. Lightw. Technol. 26, 791-798 (2008).
  3. I. M. Griffiths, P. D. Howell, "The surface-tension-driven evolution of a two-dimensional annular viscous tube," J. Fluid Mechanic 593, 181-208 (2007).
  4. I. M. Griffiths, P. D. Howell, "Mathematical modelling of non-axisymmetric capillary tube drawing," J. Fluid Mechan. 605, 181-206 (2008).
  5. P. D. Howell, P. Willmott, "Slender viscous fibres with inertia and gravity," J. Mech. Appl. Math. 47, 4541-548 (1994).
  6. C. J. Voyce, A. D. Fitt, J. R. Hayes, T. M. Monro, "Mathematical modeling of the self-pressurizing mechanism for microstructured fibre drawing," J. Lightw. Technol. 27, 871-878 (2009).
  7. G. Luzi, P. Epple, M. Scharrer, K. Fujimoto, C. Rauh, A. Delgado, "Asymptotic analysis of flow processes at drawing of single optical microfibres," J. Theoretical Comput. Fluid Dynamic .
  8. A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, D. J. Richardson, "The mathematical modeling of capillary drawing for holey fibre manufacture," J. Eng. Math. 43, 201-227 (2002).
  9. S. C. Xue, R. I. Tanner, G. W. Barton, R. Lwin, M. C. J. Large, Poladin, "Fabrication of microstructured optical fibres—Part II: Problem formulation and numerical modeling of transient draw process," J. Lightw. Technol. 23, 2255-2266 (2005).
  10. S. C. Xue, M. C. J. Large, G. W. Barton, R. I. Tanner, L. Poladin, R. Lwin, "Role of material properties and drawing conditions in the fabrication of microstructured optical fibres," J. Lightw. Technol. 24, (2006).
  11. S. C. Xue, L. Poladin, G. W. Barton, M. C. J. Large, "Radiative heat transfer in preforms for microstructured oprtical fibres," Int. J. Heat Mass Transfer 50, 1569-1576 (2007).
  12. Z. Yin, Y. Jaluria, "Thermal transport and flow in high-speed optical fibre drawing," ASME J. Heat Transfer 120, 916-930 (1998).
  13. G. Gupta, W. W. Schultz, "Non-isothermal flows of newtonian slender glass fibers," Int. J. Non-Linear Mech. 3, 1151-163 (1998).
  14. H. Huang, R. M. Miura, J. J. Wylie, "Optical fiber drawing and dopant transport," SIAM J. Appl. Math. 69, 330-347 (2008).
  15. S. R. Chodhury, Y. Jaluria, "Thermal transport due to material gas flow in a furnace for drawing an optical fiber," J. Mater. Res. 13, 494-503.
  16. S. R. Chodhury, Y. Jaluria, "Practical aspects in the drawing an optical fiber," J. Mater. Res. 13, 483-493.
  17. Z. Yin, Y. Jaluria, "Thermal transport and flow in high-speed optical fiber drawing," Trans. ASME Heat Transfer Div. 120, 916-930 (1998).
  18. G. Urbain, Y. Bottinga, P. Richet, "Viscosity of liquid silica, silicates and alumino-silicates," Geochimica Cosmochimica Acta 46, 1061-1072 (1982).

2009 (1)

C. J. Voyce, A. D. Fitt, J. R. Hayes, T. M. Monro, "Mathematical modeling of the self-pressurizing mechanism for microstructured fibre drawing," J. Lightw. Technol. 27, 871-878 (2009).

2008 (3)

C. J. Voyce, A. D. Fitt, T. M. Monro, "Mathematical modeling as an accurate predictive tool in capillary and microstructured fibre manufacture: The effects of preform rotation," J. Lightw. Technol. 26, 791-798 (2008).

I. M. Griffiths, P. D. Howell, "Mathematical modelling of non-axisymmetric capillary tube drawing," J. Fluid Mechan. 605, 181-206 (2008).

H. Huang, R. M. Miura, J. J. Wylie, "Optical fiber drawing and dopant transport," SIAM J. Appl. Math. 69, 330-347 (2008).

2007 (2)

S. C. Xue, L. Poladin, G. W. Barton, M. C. J. Large, "Radiative heat transfer in preforms for microstructured oprtical fibres," Int. J. Heat Mass Transfer 50, 1569-1576 (2007).

I. M. Griffiths, P. D. Howell, "The surface-tension-driven evolution of a two-dimensional annular viscous tube," J. Fluid Mechanic 593, 181-208 (2007).

2006 (1)

S. C. Xue, M. C. J. Large, G. W. Barton, R. I. Tanner, L. Poladin, R. Lwin, "Role of material properties and drawing conditions in the fabrication of microstructured optical fibres," J. Lightw. Technol. 24, (2006).

2005 (1)

S. C. Xue, R. I. Tanner, G. W. Barton, R. Lwin, M. C. J. Large, Poladin, "Fabrication of microstructured optical fibres—Part II: Problem formulation and numerical modeling of transient draw process," J. Lightw. Technol. 23, 2255-2266 (2005).

2002 (1)

A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, D. J. Richardson, "The mathematical modeling of capillary drawing for holey fibre manufacture," J. Eng. Math. 43, 201-227 (2002).

2001 (1)

A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, "Modeling the fabrication of hollow fibres: Capillary drawing," J. Lightw. Technol. 19, 1924-1931 (2001).

1998 (3)

Z. Yin, Y. Jaluria, "Thermal transport and flow in high-speed optical fibre drawing," ASME J. Heat Transfer 120, 916-930 (1998).

G. Gupta, W. W. Schultz, "Non-isothermal flows of newtonian slender glass fibers," Int. J. Non-Linear Mech. 3, 1151-163 (1998).

Z. Yin, Y. Jaluria, "Thermal transport and flow in high-speed optical fiber drawing," Trans. ASME Heat Transfer Div. 120, 916-930 (1998).

1994 (1)

P. D. Howell, P. Willmott, "Slender viscous fibres with inertia and gravity," J. Mech. Appl. Math. 47, 4541-548 (1994).

1982 (1)

G. Urbain, Y. Bottinga, P. Richet, "Viscosity of liquid silica, silicates and alumino-silicates," Geochimica Cosmochimica Acta 46, 1061-1072 (1982).

ASME J. Heat Transfer (1)

Z. Yin, Y. Jaluria, "Thermal transport and flow in high-speed optical fibre drawing," ASME J. Heat Transfer 120, 916-930 (1998).

Geochimica Cosmochimica Acta (1)

G. Urbain, Y. Bottinga, P. Richet, "Viscosity of liquid silica, silicates and alumino-silicates," Geochimica Cosmochimica Acta 46, 1061-1072 (1982).

Int. J. Heat Mass Transfer (1)

S. C. Xue, L. Poladin, G. W. Barton, M. C. J. Large, "Radiative heat transfer in preforms for microstructured oprtical fibres," Int. J. Heat Mass Transfer 50, 1569-1576 (2007).

Int. J. Non-Linear Mech. (1)

G. Gupta, W. W. Schultz, "Non-isothermal flows of newtonian slender glass fibers," Int. J. Non-Linear Mech. 3, 1151-163 (1998).

J. Eng. Math. (1)

A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, D. J. Richardson, "The mathematical modeling of capillary drawing for holey fibre manufacture," J. Eng. Math. 43, 201-227 (2002).

J. Fluid Mechan. (1)

I. M. Griffiths, P. D. Howell, "Mathematical modelling of non-axisymmetric capillary tube drawing," J. Fluid Mechan. 605, 181-206 (2008).

J. Fluid Mechanic (1)

I. M. Griffiths, P. D. Howell, "The surface-tension-driven evolution of a two-dimensional annular viscous tube," J. Fluid Mechanic 593, 181-208 (2007).

J. Lightw. Technol. (5)

A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, "Modeling the fabrication of hollow fibres: Capillary drawing," J. Lightw. Technol. 19, 1924-1931 (2001).

C. J. Voyce, A. D. Fitt, T. M. Monro, "Mathematical modeling as an accurate predictive tool in capillary and microstructured fibre manufacture: The effects of preform rotation," J. Lightw. Technol. 26, 791-798 (2008).

S. C. Xue, R. I. Tanner, G. W. Barton, R. Lwin, M. C. J. Large, Poladin, "Fabrication of microstructured optical fibres—Part II: Problem formulation and numerical modeling of transient draw process," J. Lightw. Technol. 23, 2255-2266 (2005).

S. C. Xue, M. C. J. Large, G. W. Barton, R. I. Tanner, L. Poladin, R. Lwin, "Role of material properties and drawing conditions in the fabrication of microstructured optical fibres," J. Lightw. Technol. 24, (2006).

C. J. Voyce, A. D. Fitt, J. R. Hayes, T. M. Monro, "Mathematical modeling of the self-pressurizing mechanism for microstructured fibre drawing," J. Lightw. Technol. 27, 871-878 (2009).

J. Mater. Res. (2)

S. R. Chodhury, Y. Jaluria, "Thermal transport due to material gas flow in a furnace for drawing an optical fiber," J. Mater. Res. 13, 494-503.

S. R. Chodhury, Y. Jaluria, "Practical aspects in the drawing an optical fiber," J. Mater. Res. 13, 483-493.

J. Mech. Appl. Math. (1)

P. D. Howell, P. Willmott, "Slender viscous fibres with inertia and gravity," J. Mech. Appl. Math. 47, 4541-548 (1994).

J. Theoretical Comput. Fluid Dynamic (1)

G. Luzi, P. Epple, M. Scharrer, K. Fujimoto, C. Rauh, A. Delgado, "Asymptotic analysis of flow processes at drawing of single optical microfibres," J. Theoretical Comput. Fluid Dynamic .

SIAM J. Appl. Math. (1)

H. Huang, R. M. Miura, J. J. Wylie, "Optical fiber drawing and dopant transport," SIAM J. Appl. Math. 69, 330-347 (2008).

Trans. ASME Heat Transfer Div. (1)

Z. Yin, Y. Jaluria, "Thermal transport and flow in high-speed optical fiber drawing," Trans. ASME Heat Transfer Div. 120, 916-930 (1998).

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