Abstract

We propose a new method to accurately model the structural evolution of a microstructured fiber (MOF) during its drawing process, given its initial preform structure and draw conditions. The method, applicable to a broad range of MOFs with high air-filling fraction and thin glass membranes, is an extension of the Discrete Element Method; it determines forces on the nodes in the microstructure to progressively update their position along the neck-down region, until the fiber reaches a final frozen state. The model is validated through simulation of 6 Hollow Core Photonic Band Gap Fibers (HC-PBGFs) and is shown to predict accurately the final fiber dimensions and cross-sectional distortions. The model is vastly more capable than other state of the art models and allows fast exploration of wide drawing parameter spaces, eliminating the need for expensive and time-consuming empirical parameter scans.

© 2015 Optical Society of America

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References

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  17. S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97(2), 023603 (2006).
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  22. J. Ramos, “Drawing of annular liquid jets at low reynolds numbers,” Comput. Theor. Polym. Sci. 11(6), 429–443 (2001).
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  23. 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).
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  24. F. Geyling, “Basic fluid‐dynamic considerations in the drawing of optical fibers,” Bell Syst. Tech. J. 55(8), 1011–1056 (1976).
    [Crossref]
  25. Y. Chen and T. A. Birks, “Predicting hole sizes after fibre drawing without knowing the viscosity,” Opt. Mater. Express 3(3), 346–356 (2013).
    [Crossref]
  26. G. Luzi, P. Epple, C. Rauh, and A. Delgado, “Study of the effects of inner pressure and surface tension on the fibre drawing process with the aid of an analytical asymptotic fibre drawing model and the numerical solution of the full n.–st. Equations,” Arch. Appl. Mech. 83(11), 1607–1636 (2013).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  40. S.-C. Xue, L. Poladian, G. Barton, and M. Large, “Radiative heat transfer in preforms for microstructured optical fibres,” Int. J. Heat Mass Tran. 50(7-8), 1569–1576 (2007).
    [Crossref]
  41. 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]
  42. Z. Yin and Y. Jaluria, “Neck down and thermally induced defects in high-speed optical fiber drawing,” J. Heat Transfer 122(2), 351–362 (2000).
    [Crossref]
  43. J. Yang and Y. Jaluria, “Transport processes governing the drawing of a hollow optical fiber,” J. Heat Transfer 131(7), 072102 (2009).
    [Crossref]

2014 (5)

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8(4), 278–286 (2014).
[Crossref]

V. Sleiffer, Y. Jung, N. Baddela, J. Surof, M. Kuschnerov, V. Veljanovski, J. Hayes, N. Wheeler, E. Numkam Fokoua, J. Wooler, D. Gray, N. Wong, F. Parmigiani, S. Alam, M. Petrovich, F. Poletti, D. Richardson, and H. de Waardt, “High capacity mode-division multiplexed optical transmission in a novel 37-cell hollow-core photonic bandgap fiber,” J. Lightwave Technol. 32(4), 854–863 (2014).
[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,” Opt. Mater. Express 4(1), 29–40 (2014).
[Crossref]

E. N. Fokoua, D. J. Richardson, and F. Poletti, “Impact of structural distortions on the performance of hollow-core photonic bandgap fibers,” Opt. Express 22(3), 2735–2744 (2014).
[Crossref] [PubMed]

2013 (8)

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

E. N. Fokoua, M. N. Petrovich, N. K. Baddela, N. V. Wheeler, J. R. Hayes, F. Poletti, and D. J. Richardson, “Real-time prediction of structural and optical properties of hollow-core photonic bandgap fibers during fabrication,” Opt. Lett. 38(9), 1382–1384 (2013).
[Crossref] [PubMed]

G. Luzi, P. Epple, C. Rauh, and A. Delgado, “Study of the effects of inner pressure and surface tension on the fibre drawing process with the aid of an analytical asymptotic fibre drawing model and the numerical solution of the full n.–st. Equations,” Arch. Appl. Mech. 83(11), 1607–1636 (2013).
[Crossref]

Y. Kim and Y. Seol, “Numerical simulations of two-dimensional wet foam by the immersed boundary method,” Comput. Struc. 122, 259–269 (2013).
[Crossref]

G. Jasion, J. Shrimpton, Z. Li, and S. Yang, “On the bridging mechanism in vibration controlled dispensing of pharmaceutical powders from a micro hopper,” Powder Technol. 249, 24–37 (2013).
[Crossref]

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. K. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, Z. Li, R. Slavik, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7(4), 279–284 (2013).
[Crossref]

F. Poletti, M. N. Petrovich, and D. J. Richardson, “Hollow-core photonic bandgap fibers: Technology and applications,” Nanophotonics 2(5-6), 315–340 (2013).
[Crossref]

Y. Maalej, M. El Ghezal, and I. Doghri, “Micromechanical approach for the behaviour of open cell foams,” Eur. J. Comp. Mech. 22, 198–208 (2013).

2012 (1)

2009 (3)

J. Yang and Y. Jaluria, “Transport processes governing the drawing of a hollow optical fiber,” J. Heat Transfer 131(7), 072102 (2009).
[Crossref]

A. M. Cubillas, J. M. Lazaro, O. M. Conde, M. N. Petrovich, and J. M. Lopez-Higuera, “Gas sensor based on photonic crystal fibres in the 2ν3 and ν2+ 2ν3 vibrational bands of methane,” Sensors (Basel) 9(8), 6261–6272 (2009).
[Crossref] [PubMed]

S. S. Chakravarthy and W. K. Chiu, “Boundary integral method for the evolution of slender viscous fibres containing holes in the cross-section,” J. Fluid Mech. 621, 155–182 (2009).
[Crossref]

2007 (1)

S.-C. Xue, L. Poladian, G. Barton, and M. Large, “Radiative heat transfer in preforms for microstructured optical fibres,” Int. J. Heat Mass Tran. 50(7-8), 1569–1576 (2007).
[Crossref]

2006 (1)

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97(2), 023603 (2006).
[Crossref] [PubMed]

2005 (2)

2004 (1)

Z. Wei, K.-M. Lee, S. W. Tchikanda, Z. Zhou, and S.-P. Hong, “Free surface flow in high speed fiber drawing with large-diameter glass preforms,” J. Heat Transfer 126(5), 713–722 (2004).
[Crossref]

2003 (3)

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

Q. Sun, “Discrete modelling of two-dimensional liquid foams,” China Part. 1(5), 206–211 (2003).
[Crossref]

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[Crossref] [PubMed]

2002 (3)

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]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002).
[Crossref] [PubMed]

R. H. Doremus, “Viscosity of silica,” J. Appl. Phys. 92(12), 7619–7629 (2002).
[Crossref]

2001 (1)

J. Ramos, “Drawing of annular liquid jets at low reynolds numbers,” Comput. Theor. Polym. Sci. 11(6), 429–443 (2001).
[Crossref]

2000 (2)

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000).
[Crossref] [PubMed]

Z. Yin and Y. Jaluria, “Neck down and thermally induced defects in high-speed optical fiber drawing,” J. Heat Transfer 122(2), 351–362 (2000).
[Crossref]

1999 (2)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
[Crossref] [PubMed]

S. R. Choudhury, “A computational method for generating the free-surface neck-down profile for glass flow in optical fiber drawing,” Numer. Heat Tr. Anal. Appl. 35, 1–24 (1999).

1997 (2)

P. Gospodinov and A. Yarin, “Draw resonance of optical microcapillaries in non-isothermal drawing,” Int. J. Multiph. Flow 23(5), 967–976 (1997).
[Crossref]

S. H. K. Lee and Y. Jaluria, “Simulation of the transport processes in the neck-down region of a furnace drawn optical fiber,” Int. J. Heat Mass Tran. 40(4), 843–856 (1997).
[Crossref]

1996 (1)

1988 (1)

W. Warren and A. Kraynik, “The linear elastic properties of open-cell foams,” J. Appl. Mech. 55(2), 341–346 (1988).
[Crossref]

1979 (1)

P. A. Cundall and O. D. Strack, “A discrete numerical model for granular assemblies,” Geotechnique 29(1), 47–65 (1979).
[Crossref]

1976 (1)

F. Geyling, “Basic fluid‐dynamic considerations in the drawing of optical fibers,” Bell Syst. Tech. J. 55(8), 1011–1056 (1976).
[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. Character 77(519), 426–440 (1906).
[Crossref]

Abdolvand, A.

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8(4), 278–286 (2014).
[Crossref]

Ahmad, F. R.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[Crossref] [PubMed]

Alam, S.

V. Sleiffer, Y. Jung, N. Baddela, J. Surof, M. Kuschnerov, V. Veljanovski, J. Hayes, N. Wheeler, E. Numkam Fokoua, J. Wooler, D. Gray, N. Wong, F. Parmigiani, S. Alam, M. Petrovich, F. Poletti, D. Richardson, and H. de Waardt, “High capacity mode-division multiplexed optical transmission in a novel 37-cell hollow-core photonic bandgap fiber,” J. Lightwave Technol. 32(4), 854–863 (2014).
[Crossref]

Allan, D. C.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
[Crossref] [PubMed]

Antonopoulos, G.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002).
[Crossref] [PubMed]

Atkin, D. M.

Baddela, N.

V. Sleiffer, Y. Jung, N. Baddela, J. Surof, M. Kuschnerov, V. Veljanovski, J. Hayes, N. Wheeler, E. Numkam Fokoua, J. Wooler, D. Gray, N. Wong, F. Parmigiani, S. Alam, M. Petrovich, F. Poletti, D. Richardson, and H. de Waardt, “High capacity mode-division multiplexed optical transmission in a novel 37-cell hollow-core photonic bandgap fiber,” J. Lightwave Technol. 32(4), 854–863 (2014).
[Crossref]

Baddela, N. K.

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. K. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, Z. Li, R. Slavik, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7(4), 279–284 (2013).
[Crossref]

E. N. Fokoua, M. N. Petrovich, N. K. Baddela, N. V. Wheeler, J. R. Hayes, F. Poletti, and D. J. Richardson, “Real-time prediction of structural and optical properties of hollow-core photonic bandgap fibers during fabrication,” Opt. Lett. 38(9), 1382–1384 (2013).
[Crossref] [PubMed]

Barton, G.

S.-C. Xue, L. Poladian, G. Barton, and M. Large, “Radiative heat transfer in preforms for microstructured optical fibres,” Int. J. Heat Mass Tran. 50(7-8), 1569–1576 (2007).
[Crossref]

S.-C. Xue, R. Tanner, G. Barton, R. Lwin, M. Large, and L. Poladian, “Fabrication of microstructured optical fibers-part ii: Numerical modeling of steady-state draw process,” J. Lightwave Technol. 23(7), 2255–2266 (2005).
[Crossref]

Benabid, F.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002).
[Crossref] [PubMed]

Bhagwat, A. R.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97(2), 023603 (2006).
[Crossref] [PubMed]

Birks, T. A.

Borrelli, N. F.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

Buchak, P.

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]

Chakravarthy, S. S.

S. S. Chakravarthy and W. K. Chiu, “Boundary integral method for the evolution of slender viscous fibres containing holes in the cross-section,” J. Fluid Mech. 621, 155–182 (2009).
[Crossref]

Chang, W.

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8(4), 278–286 (2014).
[Crossref]

Chen, Y.

Chiu, W. K.

S. S. Chakravarthy and W. K. Chiu, “Boundary integral method for the evolution of slender viscous fibres containing holes in the cross-section,” J. Fluid Mech. 621, 155–182 (2009).
[Crossref]

Choudhury, S. R.

S. R. Choudhury, “A computational method for generating the free-surface neck-down profile for glass flow in optical fiber drawing,” Numer. Heat Tr. Anal. Appl. 35, 1–24 (1999).

Conde, O. M.

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S. H. K. Lee and Y. Jaluria, “Simulation of the transport processes in the neck-down region of a furnace drawn optical fiber,” Int. J. Heat Mass Tran. 40(4), 843–856 (1997).
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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,” Opt. Mater. Express 4(1), 29–40 (2014).
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[Crossref] [PubMed]

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
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F. Poletti, N. V. Wheeler, M. N. Petrovich, N. K. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, Z. Li, R. Slavik, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7(4), 279–284 (2013).
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D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
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A. M. Cubillas, J. M. Lazaro, O. M. Conde, M. N. Petrovich, and J. M. Lopez-Higuera, “Gas sensor based on photonic crystal fibres in the 2ν3 and ν2+ 2ν3 vibrational bands of methane,” Sensors (Basel) 9(8), 6261–6272 (2009).
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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).
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S.-C. Xue, L. Poladian, G. Barton, and M. Large, “Radiative heat transfer in preforms for microstructured optical fibres,” Int. J. Heat Mass Tran. 50(7-8), 1569–1576 (2007).
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S.-C. Xue, R. Tanner, G. Barton, R. Lwin, M. Large, and L. Poladian, “Fabrication of microstructured optical fibers-part ii: Numerical modeling of steady-state draw process,” J. Lightwave Technol. 23(7), 2255–2266 (2005).
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F. Poletti, M. N. Petrovich, and D. J. Richardson, “Hollow-core photonic bandgap fibers: Technology and applications,” Nanophotonics 2(5-6), 315–340 (2013).
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F. Poletti, N. V. Wheeler, M. N. Petrovich, N. K. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, Z. Li, R. Slavik, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7(4), 279–284 (2013).
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E. N. Fokoua, M. N. Petrovich, N. K. Baddela, N. V. Wheeler, J. R. Hayes, F. Poletti, and D. J. Richardson, “Real-time prediction of structural and optical properties of hollow-core photonic bandgap fibers during fabrication,” Opt. Lett. 38(9), 1382–1384 (2013).
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S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97(2), 023603 (2006).
[Crossref] [PubMed]

Richardson, D.

V. Sleiffer, Y. Jung, N. Baddela, J. Surof, M. Kuschnerov, V. Veljanovski, J. Hayes, N. Wheeler, E. Numkam Fokoua, J. Wooler, D. Gray, N. Wong, F. Parmigiani, S. Alam, M. Petrovich, F. Poletti, D. Richardson, and H. de Waardt, “High capacity mode-division multiplexed optical transmission in a novel 37-cell hollow-core photonic bandgap fiber,” J. Lightwave Technol. 32(4), 854–863 (2014).
[Crossref]

Richardson, D. J.

E. N. Fokoua, D. J. Richardson, and F. Poletti, “Impact of structural distortions on the performance of hollow-core photonic bandgap fibers,” Opt. Express 22(3), 2735–2744 (2014).
[Crossref] [PubMed]

E. N. Fokoua, M. N. Petrovich, N. K. Baddela, N. V. Wheeler, J. R. Hayes, F. Poletti, and D. J. Richardson, “Real-time prediction of structural and optical properties of hollow-core photonic bandgap fibers during fabrication,” Opt. Lett. 38(9), 1382–1384 (2013).
[Crossref] [PubMed]

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. K. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, Z. Li, R. Slavik, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7(4), 279–284 (2013).
[Crossref]

F. Poletti, M. N. Petrovich, and D. J. Richardson, “Hollow-core photonic bandgap fibers: Technology and applications,” Nanophotonics 2(5-6), 315–340 (2013).
[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]

Roberts, P. J.

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. Express 13(1), 236–244 (2005).
[Crossref] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
[Crossref] [PubMed]

Russell, P. S.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
[Crossref] [PubMed]

J. C. Knight, T. A. Birks, P. S. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996).
[Crossref] [PubMed]

Russell, P. S. J.

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8(4), 278–286 (2014).
[Crossref]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002).
[Crossref] [PubMed]

Sabert, H.

Scharrer, M.

Seol, Y.

Y. Kim and Y. Seol, “Numerical simulations of two-dimensional wet foam by the immersed boundary method,” Comput. Struc. 122, 259–269 (2013).
[Crossref]

Shrimpton, J.

G. Jasion, J. Shrimpton, Z. Li, and S. Yang, “On the bridging mechanism in vibration controlled dispensing of pharmaceutical powders from a micro hopper,” Powder Technol. 249, 24–37 (2013).
[Crossref]

Silcox, J.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[Crossref] [PubMed]

Slavik, R.

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. K. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, Z. Li, R. Slavik, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7(4), 279–284 (2013).
[Crossref]

Sleiffer, V.

V. Sleiffer, Y. Jung, N. Baddela, J. Surof, M. Kuschnerov, V. Veljanovski, J. Hayes, N. Wheeler, E. Numkam Fokoua, J. Wooler, D. Gray, N. Wong, F. Parmigiani, S. Alam, M. Petrovich, F. Poletti, D. Richardson, and H. de Waardt, “High capacity mode-division multiplexed optical transmission in a novel 37-cell hollow-core photonic bandgap fiber,” J. Lightwave Technol. 32(4), 854–863 (2014).
[Crossref]

Smith, C. M.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

St J Russell, P.

Stentz, A. J.

Stokes, Y. M.

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]

Strack, O. D.

P. A. Cundall and O. D. Strack, “A discrete numerical model for granular assemblies,” Geotechnique 29(1), 47–65 (1979).
[Crossref]

Sun, Q.

Q. Sun, “Discrete modelling of two-dimensional liquid foams,” China Part. 1(5), 206–211 (2003).
[Crossref]

Surof, J.

V. Sleiffer, Y. Jung, N. Baddela, J. Surof, M. Kuschnerov, V. Veljanovski, J. Hayes, N. Wheeler, E. Numkam Fokoua, J. Wooler, D. Gray, N. Wong, F. Parmigiani, S. Alam, M. Petrovich, F. Poletti, D. Richardson, and H. de Waardt, “High capacity mode-division multiplexed optical transmission in a novel 37-cell hollow-core photonic bandgap fiber,” J. Lightwave Technol. 32(4), 854–863 (2014).
[Crossref]

Tanner, R.

Tchikanda, S. W.

Z. Wei, K.-M. Lee, S. W. Tchikanda, Z. Zhou, and S.-P. Hong, “Free surface flow in high speed fiber drawing with large-diameter glass preforms,” J. Heat Transfer 126(5), 713–722 (2004).
[Crossref]

Thomas, M. G.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[Crossref] [PubMed]

Tomlinson, A.

Travers, J.

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8(4), 278–286 (2014).
[Crossref]

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. Character 77(519), 426–440 (1906).
[Crossref]

Veljanovski, V.

V. Sleiffer, Y. Jung, N. Baddela, J. Surof, M. Kuschnerov, V. Veljanovski, J. Hayes, N. Wheeler, E. Numkam Fokoua, J. Wooler, D. Gray, N. Wong, F. Parmigiani, S. Alam, M. Petrovich, F. Poletti, D. Richardson, and H. de Waardt, “High capacity mode-division multiplexed optical transmission in a novel 37-cell hollow-core photonic bandgap fiber,” J. Lightwave Technol. 32(4), 854–863 (2014).
[Crossref]

Venkataraman, N.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[Crossref] [PubMed]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

Warren, W.

W. Warren and A. Kraynik, “The linear elastic properties of open-cell foams,” J. Appl. Mech. 55(2), 341–346 (1988).
[Crossref]

Warren-Smith, S. C.

Wei, Z.

Z. Wei, K.-M. Lee, S. W. Tchikanda, Z. Zhou, and S.-P. Hong, “Free surface flow in high speed fiber drawing with large-diameter glass preforms,” J. Heat Transfer 126(5), 713–722 (2004).
[Crossref]

West, J. A.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

Wheeler, N.

V. Sleiffer, Y. Jung, N. Baddela, J. Surof, M. Kuschnerov, V. Veljanovski, J. Hayes, N. Wheeler, E. Numkam Fokoua, J. Wooler, D. Gray, N. Wong, F. Parmigiani, S. Alam, M. Petrovich, F. Poletti, D. Richardson, and H. de Waardt, “High capacity mode-division multiplexed optical transmission in a novel 37-cell hollow-core photonic bandgap fiber,” J. Lightwave Technol. 32(4), 854–863 (2014).
[Crossref]

Wheeler, N. V.

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. K. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, Z. Li, R. Slavik, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7(4), 279–284 (2013).
[Crossref]

E. N. Fokoua, M. N. Petrovich, N. K. Baddela, N. V. Wheeler, J. R. Hayes, F. Poletti, and D. J. Richardson, “Real-time prediction of structural and optical properties of hollow-core photonic bandgap fibers during fabrication,” Opt. Lett. 38(9), 1382–1384 (2013).
[Crossref] [PubMed]

Williams, D. P.

Windeler, R. S.

Wong, N.

V. Sleiffer, Y. Jung, N. Baddela, J. Surof, M. Kuschnerov, V. Veljanovski, J. Hayes, N. Wheeler, E. Numkam Fokoua, J. Wooler, D. Gray, N. Wong, F. Parmigiani, S. Alam, M. Petrovich, F. Poletti, D. Richardson, and H. de Waardt, “High capacity mode-division multiplexed optical transmission in a novel 37-cell hollow-core photonic bandgap fiber,” J. Lightwave Technol. 32(4), 854–863 (2014).
[Crossref]

Wooler, J.

V. Sleiffer, Y. Jung, N. Baddela, J. Surof, M. Kuschnerov, V. Veljanovski, J. Hayes, N. Wheeler, E. Numkam Fokoua, J. Wooler, D. Gray, N. Wong, F. Parmigiani, S. Alam, M. Petrovich, F. Poletti, D. Richardson, and H. de Waardt, “High capacity mode-division multiplexed optical transmission in a novel 37-cell hollow-core photonic bandgap fiber,” J. Lightwave Technol. 32(4), 854–863 (2014).
[Crossref]

Xue, S.-C.

S.-C. Xue, L. Poladian, G. Barton, and M. Large, “Radiative heat transfer in preforms for microstructured optical fibres,” Int. J. Heat Mass Tran. 50(7-8), 1569–1576 (2007).
[Crossref]

S.-C. Xue, R. Tanner, G. Barton, R. Lwin, M. Large, and L. Poladian, “Fabrication of microstructured optical fibers-part ii: Numerical modeling of steady-state draw process,” J. Lightwave Technol. 23(7), 2255–2266 (2005).
[Crossref]

Yang, J.

J. Yang and Y. Jaluria, “Transport processes governing the drawing of a hollow optical fiber,” J. Heat Transfer 131(7), 072102 (2009).
[Crossref]

Yang, S.

G. Jasion, J. Shrimpton, Z. Li, and S. Yang, “On the bridging mechanism in vibration controlled dispensing of pharmaceutical powders from a micro hopper,” Powder Technol. 249, 24–37 (2013).
[Crossref]

Yarin, A.

P. Gospodinov and A. Yarin, “Draw resonance of optical microcapillaries in non-isothermal drawing,” Int. J. Multiph. Flow 23(5), 967–976 (1997).
[Crossref]

Yin, Z.

Z. Yin and Y. Jaluria, “Neck down and thermally induced defects in high-speed optical fiber drawing,” J. Heat Transfer 122(2), 351–362 (2000).
[Crossref]

Zhou, Z.

Z. Wei, K.-M. Lee, S. W. Tchikanda, Z. Zhou, and S.-P. Hong, “Free surface flow in high speed fiber drawing with large-diameter glass preforms,” J. Heat Transfer 126(5), 713–722 (2004).
[Crossref]

Arch. Appl. Mech. (1)

G. Luzi, P. Epple, C. Rauh, and A. Delgado, “Study of the effects of inner pressure and surface tension on the fibre drawing process with the aid of an analytical asymptotic fibre drawing model and the numerical solution of the full n.–st. Equations,” Arch. Appl. Mech. 83(11), 1607–1636 (2013).
[Crossref]

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F. Geyling, “Basic fluid‐dynamic considerations in the drawing of optical fibers,” Bell Syst. Tech. J. 55(8), 1011–1056 (1976).
[Crossref]

China Part. (1)

Q. Sun, “Discrete modelling of two-dimensional liquid foams,” China Part. 1(5), 206–211 (2003).
[Crossref]

Comput. Struc. (1)

Y. Kim and Y. Seol, “Numerical simulations of two-dimensional wet foam by the immersed boundary method,” Comput. Struc. 122, 259–269 (2013).
[Crossref]

Comput. Theor. Polym. Sci. (1)

J. Ramos, “Drawing of annular liquid jets at low reynolds numbers,” Comput. Theor. Polym. Sci. 11(6), 429–443 (2001).
[Crossref]

Eur. J. Comp. Mech. (1)

Y. Maalej, M. El Ghezal, and I. Doghri, “Micromechanical approach for the behaviour of open cell foams,” Eur. J. Comp. Mech. 22, 198–208 (2013).

Geotechnique (1)

P. A. Cundall and O. D. Strack, “A discrete numerical model for granular assemblies,” Geotechnique 29(1), 47–65 (1979).
[Crossref]

Int. J. Heat Mass Tran. (2)

S. H. K. Lee and Y. Jaluria, “Simulation of the transport processes in the neck-down region of a furnace drawn optical fiber,” Int. J. Heat Mass Tran. 40(4), 843–856 (1997).
[Crossref]

S.-C. Xue, L. Poladian, G. Barton, and M. Large, “Radiative heat transfer in preforms for microstructured optical fibres,” Int. J. Heat Mass Tran. 50(7-8), 1569–1576 (2007).
[Crossref]

Int. J. Multiph. Flow (1)

P. Gospodinov and A. Yarin, “Draw resonance of optical microcapillaries in non-isothermal drawing,” Int. J. Multiph. Flow 23(5), 967–976 (1997).
[Crossref]

J. Appl. Mech. (1)

W. Warren and A. Kraynik, “The linear elastic properties of open-cell foams,” J. Appl. Mech. 55(2), 341–346 (1988).
[Crossref]

J. Appl. Phys. (1)

R. H. Doremus, “Viscosity of silica,” J. Appl. Phys. 92(12), 7619–7629 (2002).
[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. Fluid Mech. (2)

S. S. Chakravarthy and W. K. Chiu, “Boundary integral method for the evolution of slender viscous fibres containing holes in the cross-section,” J. Fluid Mech. 621, 155–182 (2009).
[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]

J. Heat Transfer (3)

Z. Yin and Y. Jaluria, “Neck down and thermally induced defects in high-speed optical fiber drawing,” J. Heat Transfer 122(2), 351–362 (2000).
[Crossref]

J. Yang and Y. Jaluria, “Transport processes governing the drawing of a hollow optical fiber,” J. Heat Transfer 131(7), 072102 (2009).
[Crossref]

Z. Wei, K.-M. Lee, S. W. Tchikanda, Z. Zhou, and S.-P. Hong, “Free surface flow in high speed fiber drawing with large-diameter glass preforms,” J. Heat Transfer 126(5), 713–722 (2004).
[Crossref]

J. Lightwave Technol. (3)

S.-C. Xue, R. Tanner, G. Barton, R. Lwin, M. Large, and L. Poladian, “Fabrication of microstructured optical fibers-part ii: Numerical modeling of steady-state draw process,” J. Lightwave Technol. 23(7), 2255–2266 (2005).
[Crossref]

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(9), 1306–1311 (2012).
[Crossref]

V. Sleiffer, Y. Jung, N. Baddela, J. Surof, M. Kuschnerov, V. Veljanovski, J. Hayes, N. Wheeler, E. Numkam Fokoua, J. Wooler, D. Gray, N. Wong, F. Parmigiani, S. Alam, M. Petrovich, F. Poletti, D. Richardson, and H. de Waardt, “High capacity mode-division multiplexed optical transmission in a novel 37-cell hollow-core photonic bandgap fiber,” J. Lightwave Technol. 32(4), 854–863 (2014).
[Crossref]

Nanophotonics (1)

F. Poletti, M. N. Petrovich, and D. J. Richardson, “Hollow-core photonic bandgap fibers: Technology and applications,” Nanophotonics 2(5-6), 315–340 (2013).
[Crossref]

Nat. Photonics (2)

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. K. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, Z. Li, R. Slavik, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7(4), 279–284 (2013).
[Crossref]

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8(4), 278–286 (2014).
[Crossref]

Nature (1)

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

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[Crossref] [PubMed]

Powder Technol. (1)

G. Jasion, J. Shrimpton, Z. Li, and S. Yang, “On the bridging mechanism in vibration controlled dispensing of pharmaceutical powders from a micro hopper,” Powder Technol. 249, 24–37 (2013).
[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. Character 77(519), 426–440 (1906).
[Crossref]

Science (3)

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[Crossref] [PubMed]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002).
[Crossref] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
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Figures (10)

Fig. 1
Fig. 1 The 3 stages of fiber production; (a) first stage preform, Ø ~2-4cm (illustration), (b) cane, Ø ~2-5mm without jacket glass (optical micrograph), (c) final fiber, Ø ~150 μm (enhanced SEM).
Fig. 2
Fig. 2 Schematic of a second stage draw. Three regions are indicated; the preform which is the initial condition, the neck-down which is inside the furnace and is where all the geometry changes take place, and the fiber which is the final result.
Fig. 3
Fig. 3 The relationship between the microstructure solution and the Fitt solution of the Jacket glass. The external boundary of the microstructure solution is bound by the internal diameter of the jacket, h1, as it marches in z. The jacket tube is solved using the Fitt model.
Fig. 4
Fig. 4 Geometry representation and force resolution around a node. (a) The microstructure is represented by a triangular lattice of cells. This generates a grid of nodes (red points) connected by struts (black lines). (b) Forces: surface tension, Ft, acts on the node directly and is a function of the angle turned in the fillet, ψ; the viscous, Fv, and pressure, Fp, forces act parallel and normal to the struts respectively. In this example the 3 left most nodes are adjacent to the core. The total force acting on the node is Fn.
Fig. 5
Fig. 5 A strut element represented as a Lagrangian fluid volume, the strut has length and width of l and w respectively and the direction parallel and normal to the strut is given by the unit vectors s ^ and n ^ . PA and PB are the gas pressures on either side of the strut, and τss is the viscous stress, acting on the element.
Fig. 6
Fig. 6 A neck down profile generated by the Fitt model (bottom) and temperature profile of furnace and preform / fiber (top). The draw diameter and draw speed are relative to the initial diameter and feed speed. The ‘node transect’ shows the positions of a selection of nodes from the microstructure as they are evolved through the draw, (data from simulated fiber 1 – see Table 3).
Fig. 7
Fig. 7 The cane as used in the experiments, (a), and simulation, (b), without the jacket glass.
Fig. 8
Fig. 8 Evolution of the microstructure through simulated draw 1 (Table 3). Left: the axial temperature profile of fiber and furnace. Center: complete neck down shape across the whole computational domain with initial and final geometries shown above and below respectively. Right: the microstructure at specified positions in the neck down, with fiber OD and cladding expansion ratio at that position, and relative force vectors indicated. Microstructure changes are concentrated between z = 10 and 50%.
Fig. 9
Fig. 9 Comparison of optical micrographs of Experimental fibers A, B & C (top) with Simulated fibers 1, 2 & 3 (bottom).
Fig. 10
Fig. 10 Core size as a result of different core pressures, comparing the experimental results with the simulated results of all fibers.

Tables (3)

Tables Icon

Table 1 Experimental draw parameters.

Tables Icon

Table 2 Material parameters

Tables Icon

Table 3 Virtual draw parameters

Equations (20)

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

F v,s = τ ss w=2μ ( u 2 u 1 ) s ^ l w s ^
F p,s =( P B P A )l n ^
Δ p t =γ 1 R c
F t,n,i =γ 1 R c ψ R c θ ^ =γψ θ ^
F v,n = i F v,s,i
F p,n = 1 2 i F p,s,i
F t,n = i F t,n,i
F n = F v,n + F p,n + F t,n
u 1 = u 1 + a F
x 1 = x 0 ( h 1 1 h 1 0 ) + Δ t   u 1
F < C ( F v , n 2 + F p , n 2 + F s , n 2 ) 1 / 2
x ext 1 = 1 2 B h 1 x ^ ext 0
u ext =0
B=1( 1 R ext,cane h 10 ) h 1 / h 2 1 h 1 0 / h 20 1
e= h 1 / h 2
ρ( h 2 2 h 1 2 )[ w 0t  +  w 0 w 0z   g] =  [ 3μ( h 2 2   h 1 2 ) w 0z  + γ ( h 1  +  h 2 ) ] z
( h 1 2 ) t + ( h 1 2 w 0 ) z =  p 0 h 1 2 h 2 2 γ h 1 h 2 ( h 1 + h 2 ) μ( h 2 2 + h 1 2 )
( h 2 2 ) t + ( h 2 2 w 0 ) z =  p 0 h 1 2 h 2 2 γ h 1 h 2 ( h 1 + h 2 ) μ( h 2 2 + h 1 2 )
( h 2 2 h 1 2 ) 2 [ ρ c p ( T 0t + w 0 T 0z )k ( T 0z ) z ] h 2 σα( T a 4 T 0 4 )= h 2 N( T a T 0 )
μ=0.58× 10 7 exp( 515400 R(T+273.15) ),

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