Abstract

Drawing of the hollow all-polymer Bragg fibers based on PMMA/PS and PVDF/PC materials combinations are demonstrated. Hole collapse during drawing effects the uniformity of a photonic crystal reflector in the resultant fiber. We first investigate how the hole collapse effects fiber transmission properties. We then present modelling of fluid dynamics of hollow multilayer polymer fiber drawing. Particularly, hole collapse during drawing and layer thickness non-uniformity are investigated as a function of draw temperature, draw ratio, feeding speed, core pressurization and mismatch of material properties in a multilayer. Both the newtonian and generalized newtonian cases are considered assuming slender geometries.

© 2006 Optical Society of America

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2006 (2)

2005 (4)

2004 (3)

2003 (4)

P. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

J. Canning, E. Buckley, and K. Lyytikainen "Propagation in air by field superposition of scattered light within a Fresnel fiber," Opt. Lett. 28, 230-232 (2003).
[CrossRef] [PubMed]

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

M.A. van Eijkelenborg, A. Argyros, G. Barton, I.M. Bassett, M. Fellew, G. Henry, N.A. Issa, M.C.J. Large, S. Manos, W. Padden, L. Poladian, J. Zagari, "Recent progress in microstructured polymer optical fibre fabrication and characterisation," Opt. Fiber Techn. 9, 199-209 (2003).
[CrossRef]

2002 (3)

J. Canning, E. Buckley, K. Lyttikainen, and T. Ryan, "Wavelength dependent leakage in a Fresnel-based air-silica structured optical fibre," Optics Communications 207, 35 (2002).
[CrossRef]

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, Y. Fink "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650 (2002).
[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," J. Eng. Math. 43, 201-227 (2002).
[CrossRef]

2001 (1)

2000 (1)

J.A. Harrington, "A review of IR transmitting, hollow waveguides," Fib. Integr. Opt. 19, 211 (2000).
[CrossRef]

1999 (1)

L.J. Cummings, P.D. Howell, "On the evolution of non-axisymmetric viscous fibres with surface tension, inertia and gravity," J. Fluid mech. 389, 361-389 (1999).
[CrossRef]

1997 (1)

M. Saito and K. Kikuchi, "Infrared optical fiber sensors," Opt. Rev. 4, 527-538 (1997).
[CrossRef]

1986 (1)

B.D. Freeman, M.M. Denn, R. Keunings, G.E. Molau and J. Ramos, "Profile development in drawn hollow tubes," J. Polym. Eng. 6, 171-186 (1986).
[CrossRef]

1976 (1)

F.T. Geyling, "Basic fluid dynamic consideration in the drawing of optical fibers," Bell Sys. Tech. J. 55, 1011-1056 (1976).

1972 (1)

Y.T. Shah and J.R.A. Pearson, "On the stability of nonisothermal fiber spinning," Ind. Eng. Chem. Fundam. 11, 145-149 (1972).
[CrossRef]

1970 (2)

J.A. Burgman "Liquid glass jets in the forming of continuous fibers," Glass Technol. 11, 110-116 (1970).

S. Wu, "Surface and interfacial tensions of polymer melts. II. Poly(methylmethacrylate), poly(nbutylmethacrylate), and polystyrene," J. Phys. Chem. 74, 632-638 (1970).
[CrossRef]

1969 (1)

M.R. Matovich and J.R.A. Pearson, "Spinning a molten threadline - Steady-state isothermal viscous flows," Ind. Eng. Chem. Fundam. 8, 512-520 (1969).
[CrossRef]

Allan, D.C.

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

Argyros, A.

M.A. van Eijkelenborg, A. Argyros, G. Barton, I.M. Bassett, M. Fellew, G. Henry, N.A. Issa, M.C.J. Large, S. Manos, W. Padden, L. Poladian, J. Zagari, "Recent progress in microstructured polymer optical fibre fabrication and characterisation," Opt. Fiber Techn. 9, 199-209 (2003).
[CrossRef]

Barton, G.

M.A. van Eijkelenborg, A. Argyros, G. Barton, I.M. Bassett, M. Fellew, G. Henry, N.A. Issa, M.C.J. Large, S. Manos, W. Padden, L. Poladian, J. Zagari, "Recent progress in microstructured polymer optical fibre fabrication and characterisation," Opt. Fiber Techn. 9, 199-209 (2003).
[CrossRef]

Barton, G.W.

Bassett, I.M.

M.A. van Eijkelenborg, A. Argyros, G. Barton, I.M. Bassett, M. Fellew, G. Henry, N.A. Issa, M.C.J. Large, S. Manos, W. Padden, L. Poladian, J. Zagari, "Recent progress in microstructured polymer optical fibre fabrication and characterisation," Opt. Fiber Techn. 9, 199-209 (2003).
[CrossRef]

Benoit, G.

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, Y. Fink "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650 (2002).
[CrossRef] [PubMed]

Bjarklev, A.

Borrelli, N.F.

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

Broeng, J.

Buckley, E.

J. Canning, E. Buckley, and K. Lyytikainen "Propagation in air by field superposition of scattered light within a Fresnel fiber," Opt. Lett. 28, 230-232 (2003).
[CrossRef] [PubMed]

J. Canning, E. Buckley, K. Lyttikainen, and T. Ryan, "Wavelength dependent leakage in a Fresnel-based air-silica structured optical fibre," Optics Communications 207, 35 (2002).
[CrossRef]

Burgman, J.A.

J.A. Burgman "Liquid glass jets in the forming of continuous fibers," Glass Technol. 11, 110-116 (1970).

Canning, J.

J. Canning, E. Buckley, and K. Lyytikainen "Propagation in air by field superposition of scattered light within a Fresnel fiber," Opt. Lett. 28, 230-232 (2003).
[CrossRef] [PubMed]

J. Canning, E. Buckley, K. Lyttikainen, and T. Ryan, "Wavelength dependent leakage in a Fresnel-based air-silica structured optical fibre," Optics Communications 207, 35 (2002).
[CrossRef]

Cummings, L.J.

L.J. Cummings, P.D. Howell, "On the evolution of non-axisymmetric viscous fibres with surface tension, inertia and gravity," J. Fluid mech. 389, 361-389 (1999).
[CrossRef]

Denn, M.M.

B.D. Freeman, M.M. Denn, R. Keunings, G.E. Molau and J. Ramos, "Profile development in drawn hollow tubes," J. Polym. Eng. 6, 171-186 (1986).
[CrossRef]

Deyerl, H.J.

Emery, A.F.

H.M. Reeve, A.M. Mescher and A.F. Emery, "Investigation of steady-state drawing force and heat transfer in polymer optical fiber manufacturing," J. Heat Transfer 126, 236-243 (2004).
[CrossRef]

Fellew, M.

M.A. van Eijkelenborg, A. Argyros, G. Barton, I.M. Bassett, M. Fellew, G. Henry, N.A. Issa, M.C.J. Large, S. Manos, W. Padden, L. Poladian, J. Zagari, "Recent progress in microstructured polymer optical fibre fabrication and characterisation," Opt. Fiber Techn. 9, 199-209 (2003).
[CrossRef]

Fink, Y.

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, Y. Fink "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650 (2002).
[CrossRef] [PubMed]

Fitt, A.D.

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, 201-227 (2002).
[CrossRef]

Freeman, B.D.

B.D. Freeman, M.M. Denn, R. Keunings, G.E. Molau and J. Ramos, "Profile development in drawn hollow tubes," J. Polym. Eng. 6, 171-186 (1986).
[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, 201-227 (2002).
[CrossRef]

Gallagher, M.T.

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

Geyling, F.T.

F.T. Geyling, "Basic fluid dynamic consideration in the drawing of optical fibers," Bell Sys. Tech. J. 55, 1011-1056 (1976).

Hansen, T.

Harrington, J.A.

J.A. Harrington, "A review of IR transmitting, hollow waveguides," Fib. Integr. Opt. 19, 211 (2000).
[CrossRef]

Hart, S.D.

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, Y. Fink "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650 (2002).
[CrossRef] [PubMed]

Henry, G.

M.A. van Eijkelenborg, A. Argyros, G. Barton, I.M. Bassett, M. Fellew, G. Henry, N.A. Issa, M.C.J. Large, S. Manos, W. Padden, L. Poladian, J. Zagari, "Recent progress in microstructured polymer optical fibre fabrication and characterisation," Opt. Fiber Techn. 9, 199-209 (2003).
[CrossRef]

Howell, P.D.

L.J. Cummings, P.D. Howell, "On the evolution of non-axisymmetric viscous fibres with surface tension, inertia and gravity," J. Fluid mech. 389, 361-389 (1999).
[CrossRef]

Huang, Y.

Issa, N.A.

M.A. van Eijkelenborg, A. Argyros, G. Barton, I.M. Bassett, M. Fellew, G. Henry, N.A. Issa, M.C.J. Large, S. Manos, W. Padden, L. Poladian, J. Zagari, "Recent progress in microstructured polymer optical fibre fabrication and characterisation," Opt. Fiber Techn. 9, 199-209 (2003).
[CrossRef]

Ito, K.

Jakobsen, C.

Jensen, J.

Joannopoulos, J.D.

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, Y. Fink "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650 (2002).
[CrossRef] [PubMed]

Katagiri, T.

Keunings, R.

B.D. Freeman, M.M. Denn, R. Keunings, G.E. Molau and J. Ramos, "Profile development in drawn hollow tubes," J. Polym. Eng. 6, 171-186 (1986).
[CrossRef]

Kikuchi, K.

M. Saito and K. Kikuchi, "Infrared optical fiber sensors," Opt. Rev. 4, 527-538 (1997).
[CrossRef]

Koch, K.W.

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

Large, M.C.J.

Lee, R.

Lwin, R.

Lyttikainen, K.

J. Canning, E. Buckley, K. Lyttikainen, and T. Ryan, "Wavelength dependent leakage in a Fresnel-based air-silica structured optical fibre," Optics Communications 207, 35 (2002).
[CrossRef]

Lyytikainen, K.

Manos, S.

M.A. van Eijkelenborg, A. Argyros, G. Barton, I.M. Bassett, M. Fellew, G. Henry, N.A. Issa, M.C.J. Large, S. Manos, W. Padden, L. Poladian, J. Zagari, "Recent progress in microstructured polymer optical fibre fabrication and characterisation," Opt. Fiber Techn. 9, 199-209 (2003).
[CrossRef]

Matovich, M.R.

M.R. Matovich and J.R.A. Pearson, "Spinning a molten threadline - Steady-state isothermal viscous flows," Ind. Eng. Chem. Fundam. 8, 512-520 (1969).
[CrossRef]

Matsuura, Y.

Mescher, A.M.

H.M. Reeve, A.M. Mescher and A.F. Emery, "Investigation of steady-state drawing force and heat transfer in polymer optical fiber manufacturing," J. Heat Transfer 126, 236-243 (2004).
[CrossRef]

Miyagi, M.

Molau, G.E.

B.D. Freeman, M.M. Denn, R. Keunings, G.E. Molau and J. Ramos, "Profile development in drawn hollow tubes," J. Polym. Eng. 6, 171-186 (1986).
[CrossRef]

Monro, T.M.

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, 201-227 (2002).
[CrossRef]

Mortensen, N.

Muller, D.

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

Padden, W.

M.A. van Eijkelenborg, A. Argyros, G. Barton, I.M. Bassett, M. Fellew, G. Henry, N.A. Issa, M.C.J. Large, S. Manos, W. Padden, L. Poladian, J. Zagari, "Recent progress in microstructured polymer optical fibre fabrication and characterisation," Opt. Fiber Techn. 9, 199-209 (2003).
[CrossRef]

Pearson, J.R.A.

Y.T. Shah and J.R.A. Pearson, "On the stability of nonisothermal fiber spinning," Ind. Eng. Chem. Fundam. 11, 145-149 (1972).
[CrossRef]

M.R. Matovich and J.R.A. Pearson, "Spinning a molten threadline - Steady-state isothermal viscous flows," Ind. Eng. Chem. Fundam. 8, 512-520 (1969).
[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, 201-227 (2002).
[CrossRef]

Poladian, L.

Ramos, J.

B.D. Freeman, M.M. Denn, R. Keunings, G.E. Molau and J. Ramos, "Profile development in drawn hollow tubes," J. Polym. Eng. 6, 171-186 (1986).
[CrossRef]

Reeve, H.M.

H.M. Reeve, A.M. Mescher and A.F. Emery, "Investigation of steady-state drawing force and heat transfer in polymer optical fiber manufacturing," J. Heat Transfer 126, 236-243 (2004).
[CrossRef]

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, 201-227 (2002).
[CrossRef]

Russell, P.

P. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Ryan, T.

J. Canning, E. Buckley, K. Lyttikainen, and T. Ryan, "Wavelength dependent leakage in a Fresnel-based air-silica structured optical fibre," Optics Communications 207, 35 (2002).
[CrossRef]

Saito, M.

M. Saito and K. Kikuchi, "Infrared optical fiber sensors," Opt. Rev. 4, 527-538 (1997).
[CrossRef]

Shah, Y.T.

Y.T. Shah and J.R.A. Pearson, "On the stability of nonisothermal fiber spinning," Ind. Eng. Chem. Fundam. 11, 145-149 (1972).
[CrossRef]

Shi, Y.W.

Simonsen, H.

Skorobogatiy, M.

Smith, C.M.

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

Sorensen, T.

Steven,

Tanner, R.I.

Temelkuran, B.

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, Y. Fink "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650 (2002).
[CrossRef] [PubMed]

Terrel, M.

van Eijkelenborg, M.A.

M.A. van Eijkelenborg, A. Argyros, G. Barton, I.M. Bassett, M. Fellew, G. Henry, N.A. Issa, M.C.J. Large, S. Manos, W. Padden, L. Poladian, J. Zagari, "Recent progress in microstructured polymer optical fibre fabrication and characterisation," Opt. Fiber Techn. 9, 199-209 (2003).
[CrossRef]

Venkataraman, N.

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

Vienne, G.

West, J.A.

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

Wu, S.

S. Wu, "Surface and interfacial tensions of polymer melts. II. Poly(methylmethacrylate), poly(nbutylmethacrylate), and polystyrene," J. Phys. Chem. 74, 632-638 (1970).
[CrossRef]

Xu, Y.

Xue, S.C.

Yariv, A.

Zagari, J.

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Figures (8)

Fig. 1.
Fig. 1.

a) Left - 30cm long all-polymer preform with 10 consecutive PMMA/PS layers deposited on the inside of a PMMA cladding tube. Right - PMMA/PS preform cross section. b) Left - 30cm long all-polymer preform with 15 consecutive PVDF/PC layers deposited on the inside of a PC cladding tube. Right - PVDF/PC preform cross section c) Left - end part of a rolled 19 layer PVDF/PC preform. Middle - cross section of a drawn PVDF/PC fiber with a 1:20 drawdown ratio. Right - cross section of a drawn PMMA/PS fiber with a 1:20 drawdown ratio.

Fig. 2.
Fig. 2.

a) Radiation loss of the bandgap guided TE 01 core modes for the high index-contrast (2.0/1.5) air filled fibers with different hole collapse ratios C r , while the same outside radii Roft . Hole collapse leads to the shift of a bandgap center into the longer wavelength, as well as to a considerable increase in the modal radiation losses. b) Radiation losses of the bandgap guided TE 01 and HE 11 core modes for the low index-contrast (1.6/1.4) water filled fibers with different hole collapse ratios.

Fig. 3.
Fig. 3.

Schematic of a hollow multilayer preform during drawing. Different colors correspond to different materials in a multilayer.

Fig. 4.
Fig. 4.

Temperature distribution in the furnace.

Fig. 5.
Fig. 5.

(a) Hole collapse parameter Cr as a function of the draw ratio D r for different temperatures. Solid lines correspond to multilayer preform. Dotted lines correspond to a simple tube with the same thickness as the multilayer preform. Dashed lines represent the curves of a constant outside diameter. (b) Ratio h o /h i between the inner and outer layer thicknesses as a function of the draw ratio for different temperatures.

Fig. 6.
Fig. 6.

Effect of mismatch in the viscosities of materials in a multilayer on hole collapse (solid lines), and layer non-uniformity (dotted lines). Maximum furnace temperature is T=190°C, draw ratio D r =30000. (a) Effects of η 0. (b) Effects of (T 0-T 0, PMMA )/T 0, PMMA .

Fig. 7.
Fig. 7.

The hole collapse and thickness non-uniformity as a function of the hole overpressure and feeding speed. Maximal furnace temperature is T=190°C and draw ratio D r =5000. (a) Effects of hole overpressure P i . (b) Effects of feeding speed V f .

Fig. 8.
Fig. 8.

a) Comparison between Newtonian and generalized Newtonian model. Solid lines correspond to generalized Newtonian model and dotted lines to Newtonian model. b) Viscosity distribution in the furnace for different draw ratios at T=180°C. Solid lines correspond to generalized Newtonian model and dotted line to Newtonian model.

Equations (33)

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( r f ) 2 = ( r p D ) 2 ( 1 C r 2 ) ( R i p D ) 2 ( R o p ) 2 ( r p ) 2 ( R o p ) 2 ( R i p ) 2 .
1 r ( r v r ) r + v z z = 0
ρ ( v r v r r + v z v r z ) = p r + 1 r ( r τ rr ) r τ θ θ r + τ rz z
ρ ( v r v z r + v z v z z ) = p z + 1 r ( r τ rz ) r τ zz z + ρ g
σ i j = p δ i j + τ i j
v r = R j v z at r = R j
σ ̿ · n i = ( γ κ i P i ) n i
σ ̿ · t i = 0
κ i = 1 R i ( 1 + R i 2 ) 1 2 R i " ( 1 + R i 2 ) 3 2
n i T = ( n r , n θ , n z ) = ( 1 1 + R i 2 , 0 , R i 1 + R i 2 ) ,
t i T = ( n z , 0 , n r )
σ ̿ · n o = γ κ o n o
σ ̿ · t o = 0
φ ¯ ( z ) = 1 π ( R o 2 R i 2 ) R i R o 2 π r φ ( r , z ) d r
σ rr = γ R i P i
σ rz = ( γ R i + P i ) R i at r = R i
σ zz = ( γ R i P i ) R i 2
σ rr = γ R o
σ rz = γ R o R o at r = R o
σ zz = γ R o R o 2
p ¯ = τ ¯ rr + τ ¯ θ θ 2 + γ ( R o + R i ) R i 2 P i R o 2 R i 2
ρ ¯ Q v z = [ Q v z ( τ ¯ z z τ ¯ r r + τ ¯ θ θ 2 ) + γ ( R o + R i ) ] + ρ ¯ g Q v z
τ ̿ = η ( r , z ) ( v + v T )
v r = r v z 2 + A r
τ ̿ = ( η ( v z + 2 A r 2 ) 0 0 0 η ( v z 2 A r 2 ) 0 0 0 2 η v z )
τ ¯ z z τ ¯ r r + τ ¯ θ θ 2 = 3 η ¯ v z
ρ ¯ Q v z = [ 3 η ¯ Q v z v z + γ ( R o + R i ) ] + ρ ¯ g Q v z
A = P i γ ( 1 R i + 1 R o ) 4 R i R o η ( r ) r 3 d r
( R j 2 v z ) = 2 A
η ¯ v z v z = C
v z ( z ) = exp ( ln V f + 0 z d z η ¯ ( z ) 0 L d z η ¯ ( z ) ln V d V f )
η ( T ) = η 0 exp [ α ( 1 T 1 T 0 ) ]
η ( T , I I D ) = η 0 f [ 1 + ( K 1 f 2 I I D ) a ] 1 n a

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