Abstract

We report the first analytical description of the drawing of fibres with holes that does not require knowledge of the viscosity (or temperature) of the glass in the furnace. The model yields expressions for the size of a hole that is isolated from other holes and small compared to the outer diameter of the fibre, but includes the effects of surface tension, pressurisation and arbitrary viscosity profiles. The effect of viscosity is represented by the fibre draw tension which, unlike viscosity, can readily be measured in practice by the fibre fabricator. The model matches experiments without recourse to any adjustable fitting parameters.

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  1. A. L. Yarin, P. Gospodinov, and V. I. Roussinov, “Stability loss and sensitivity in hollow fiber drawing,” Phys. Fluids6(4), 1454–1463 (1994).
    [CrossRef]
  2. 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,” J. Eng. Math.43(2/4), 201–227 (2002).
    [CrossRef]
  3. S. C. Xue, R. I. Tanner, G. W. Barton, R. Lwin, M. C. J. Large, and L. Poladian, “Fabrication of microstructured optical fibers - Part I: problem formulation and numerical modeling of transient draw process,” J. Lightwave Technol.23(7), 2245–2254 (2005).
    [CrossRef]
  4. S. C. Xue, M. C. J. Large, G. W. Barton, R. I. Tanner, L. Poladian, and R. Lwin, “Role of material properties and drawing conditions in the fabrication of microstructured optical fibers,” J. Lightwave Technol.24(2), 853–860 (2006).
    [CrossRef]
  5. R. M. Wynne, “A fabrication process for microstructured optical fibers,” J. Lightwave Technol.24(11), 4304–4313 (2006).
    [CrossRef]
  6. 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(7), 791–798 (2008).
    [CrossRef]
  7. F. T. Trouton, “On the coefficient of viscous traction and its relation to that of viscosity,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character77(519), 426–440 (1906).
    [CrossRef]
  8. R. T. Knapp, J. W. Daily, and F. G. Hammitt, Cavitation (McGraw-Hill, 1970), p. 108.
  9. S. Wolfram, The Mathematica Book, 5th ed. (Wolfram Media, 2003).
  10. P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express13(1), 236–244 (2005).
    [CrossRef] [PubMed]
  11. S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express12(13), 2864–2869 (2004).
    [CrossRef] [PubMed]
  12. W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express10(14), 609–613 (2002).
    [CrossRef] [PubMed]

2008 (1)

2006 (2)

2005 (2)

2004 (1)

2002 (2)

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,” J. Eng. Math.43(2/4), 201–227 (2002).
[CrossRef]

W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express10(14), 609–613 (2002).
[CrossRef] [PubMed]

1994 (1)

A. L. Yarin, P. Gospodinov, and V. I. Roussinov, “Stability loss and sensitivity in hollow fiber drawing,” Phys. Fluids6(4), 1454–1463 (1994).
[CrossRef]

1906 (1)

F. T. Trouton, “On the coefficient of viscous traction and its relation to that of viscosity,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character77(519), 426–440 (1906).
[CrossRef]

Barton, G. W.

Birks, T. A.

Couny, F.

Farr, L.

Fitt, A. D.

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(7), 791–798 (2008).
[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,” J. Eng. Math.43(2/4), 201–227 (2002).
[CrossRef]

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,” J. Eng. Math.43(2/4), 201–227 (2002).
[CrossRef]

Gospodinov, P.

A. L. Yarin, P. Gospodinov, and V. I. Roussinov, “Stability loss and sensitivity in hollow fiber drawing,” Phys. Fluids6(4), 1454–1463 (1994).
[CrossRef]

Knight, J. C.

Large, M. C. J.

Leon-Saval, S. G.

Lwin, R.

Mangan, B. J.

Mason, M. W.

Monro, T. M.

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(7), 791–798 (2008).
[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,” J. Eng. Math.43(2/4), 201–227 (2002).
[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,” J. Eng. Math.43(2/4), 201–227 (2002).
[CrossRef]

Poladian, L.

Reeves, W. H.

Richardson, D. J.

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,” J. Eng. Math.43(2/4), 201–227 (2002).
[CrossRef]

Roberts, P. J.

Roussinov, V. I.

A. L. Yarin, P. Gospodinov, and V. I. Roussinov, “Stability loss and sensitivity in hollow fiber drawing,” Phys. Fluids6(4), 1454–1463 (1994).
[CrossRef]

Russell, P. St. J.

Sabert, H.

Tanner, R. I.

Tomlinson, A.

Trouton, F. T.

F. T. Trouton, “On the coefficient of viscous traction and its relation to that of viscosity,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character77(519), 426–440 (1906).
[CrossRef]

Voyce, C. J.

Wadsworth, W. J.

Williams, D. P.

Wynne, R. M.

Xue, S. C.

Yarin, A. L.

A. L. Yarin, P. Gospodinov, and V. I. Roussinov, “Stability loss and sensitivity in hollow fiber drawing,” Phys. Fluids6(4), 1454–1463 (1994).
[CrossRef]

J. Eng. Math. (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,” J. Eng. Math.43(2/4), 201–227 (2002).
[CrossRef]

J. Lightwave Technol. (4)

Opt. Express (3)

Phys. Fluids (1)

A. L. Yarin, P. Gospodinov, and V. I. Roussinov, “Stability loss and sensitivity in hollow fiber drawing,” Phys. Fluids6(4), 1454–1463 (1994).
[CrossRef]

Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character (1)

F. T. Trouton, “On the coefficient of viscous traction and its relation to that of viscosity,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character77(519), 426–440 (1906).
[CrossRef]

Other (2)

R. T. Knapp, J. W. Daily, and F. G. Hammitt, Cavitation (McGraw-Hill, 1970), p. 108.

S. Wolfram, The Mathematica Book, 5th ed. (Wolfram Media, 2003).

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