Abstract

A new class of multi-material fiber that incorporates micrometer-thickness concentric-cylindrical sheets of glass into polymer matrix has emerged. The ultimate lower limit of feature size and recent observation of interesting instability phenomenon in fiber system motivate us to examine fluid instabilities during the complicated thermal drawing fabrication processing. In this paper, from the perspective of a single instability mechanism, classical Plateau-Rayleigh instabilities in the form of radial fluctuation, we explore the stability of various microstructures (such as shells and filaments) in our composite fibers. The attained uniform structures are consistent with theoretical analysis. Furthermore, a viscous materials map is established from calculations and agrees well with various identified materials. These results not only shed insights into other forms of fluid instabilities, but also provide guidance to achieve more diverse nanostructures (such as filaments, wires, and particles) in the microstructured fibers.

© 2011 OSA

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    [CrossRef]
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2011 (1)

M. Yaman, T. Khudiyev, E. Ozgur, M. Kanik, O. Aktas, E. O. Ozgur, H. Deniz, E. Korkut, and M. Bayindir, “Arrays of indefinitely long uniform nanowires and nanotubes,” Nat. Mater. 10, 494–501 (2011).
[CrossRef] [PubMed]

2010 (3)

A. Mazhorova, J. F. Gu, A. Dupuis, M. Peccianti, O. Tsuneyuki, R. Morandotti, H. Minamide, M. Tang, Y. Wang, H. Ito, and M. Skorobogatiy, “Composite THz materials using aligned metallic and semiconductor microwires, experiments and interpretation,” Opt. Express 18, 24632–24647 (2010).
[CrossRef] [PubMed]

D. S. Deng, N. Orf, S. Danto, A. Abouraddy, J. Joannopoulos, and Y. Fink, “Processing and properties of centimeter-long, in-fiber, crystalline-selenium filaments,” Appl. Phys. Lett. 96, 23102 (2010).
[CrossRef]

S. Egusa, Z. Wang, N. Chocat, Z. M. Ruff, A. M. Stolyarov, D. Shemuly, F. Sorin, P. T. Rakich, J. D. Joannopoulos, and Y. Fink, “Multimaterial piezoelectric fibres,” Nat. Mater. 9, 643–648 (2010).
[CrossRef] [PubMed]

2008 (4)

I. M. Griffiths and P. D. Howell, “Mathematical modelling of non-axisymmetric capillary tube drawing,” J. Fluid Mech. 605, 181–206 (2008).
[CrossRef]

D. S. Deng, N. Orf, A. Abouraddy, A. Stolyarov, J. Joannopoulos, H. Stone, and Y. Fink, “In-fiber semiconductor filament arrays,” Nano. Lett. 8, 4265–4269 (2008).
[CrossRef]

J. Eggers and E. Villermaux, “Physics of liquid jets,” Rep. Prog. Phys. 71, 36601 (2008).
[CrossRef]

Y. Qin, S.M. Lee, A. Pan, U. Gosele, and M. Knez, “Rayleigh-instability-induced metal nanoparticle chains encapsulated in nanotubes produced by atomic layer deposition,” Nano. Lett. 8, 114–118 (2008).
[CrossRef]

2007 (3)

A. M. Ganan-Calvo, R. Gonzalez-Prieto, P. Riesco-Chueca, M. A. Herrada, and M. Flores-Mosquera, “Focusing capillary jets close to the continuum limit,” Nat. Phys. 3, 737–742 (2007).
[CrossRef]

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6, 336–347 (2007).
[CrossRef] [PubMed]

J. T. Chen, M. F. Zhang, and T. P. Russell, “Instabilities in nanoporous media,” Nano. Lett. 7, 183–187 (2007).
[CrossRef] [PubMed]

2006 (2)

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, 853–860 (2006).
[CrossRef]

S. Karim, M. E. Toimil-Molares, A. G. Balogh, W. Ensinger, T. W. Cornelius, E. U. Khan, and R. Neumann, “Morphological evolution of Au nanowires controlled by Rayleigh instability,” Nanotechnology 17, 5954–5959 (2006).
[CrossRef]

2005 (3)

T. M. Squires and S. R. Quake, “Microfluidics: fluid physics at the nanoliter scale,” Rev. Mod. Phys. 77, 977–1026 (2005).
[CrossRef]

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, 236–244 (2005).
[CrossRef] [PubMed]

E. Olsson and G. Kreiss, “A conservative level set method for two phase flow,” J. Comput. Phys. 210, 225–246 (2005).
[CrossRef]

2004 (4)

S. D. Hart and Y. Fink, “Interfacial energy and materials selection criteria in composite microstructured optical fiber fabrication,” Mat. Res. Soc. Symp. Proc. 797, W.7.5.1–W.7.5.7 (2004).

M. Bayindir, F. Sorin, A. F. Abouraddy, J. Viens, S. D. Hart, J. D. Joannopoulos, and Y. Fink, “Metal-insulator-semiconductor optoelectronic fibres,” Nature , 431, 826–829 (2004).
[CrossRef] [PubMed]

H. A. Stone, A.D. Stroock, and A. Ajdari, “Engineering flows in small devices: Microfluidics toward a lab-on-a-chip,” Annu. Rev. Fluid. Mech. 36, 381–411 (2004).
[CrossRef]

M. E. Toimil-Molares, A. G. Balogh, T. W. Cornelius, R. Neumann, and C. Trautmann, “Fragmentation of nanowires driven by Rayleigh instability,” Appl. Phys. Lett. 85, 5337–5339 (2004).
[CrossRef]

2003 (3)

E. Cerda and L. Mahadevan, “Geometry and physics of wrinkling,” Phys. Rev. Lett. 90, 074302 (2003).
[CrossRef] [PubMed]

J. A. Sethian and P. Smereka, “Level set methods for fluid interfaces,” Annu. Rev. Fluid Mech. 35, 341–372 (2003).
[CrossRef]

A. S. Tverjanovich, “Temperature dependence of the viscosity of chalcogenide glass-forming melts,” Glass Phys. Chem. 29, 532–536 (2003).
[CrossRef]

2002 (6)

G. P. Agrawal, Fiber-Optic Communication Systems , 3rd ed. (Wiley-Interscience, 2002).
[CrossRef]

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653 (2002).
[CrossRef] [PubMed]

R. Huang and Z. Suo, “Wrinkling of a compressed elastic film on a viscous layer,” J. Appl. Phys. 91, 1135–1142 (2002).
[CrossRef]

E. Cerda, K. Ravi-Chandar, and L. Mahadevan, “Thin films—wrinkling of an elastic sheet under tension,” Nature 419, 579–580 (2002).
[CrossRef] [PubMed]

P. de Gennes, F. Brochard-Wyart, and D. Quere, Capillarity and Wetting Phenomena (Springer, 2002).

2001 (3)

A. D. Fitt, K. Furusawa, T. M. Monro, and C. P. Please, “Modeling the fabrication of hollow fibers: Capillary drawing,” J. Lightwave. Technol. 19, 1924–1931 (2001).
[CrossRef]

S. Osher and R. P. Fedkiw, “Level set methods: An overview and some recent results,” J. Comput. Phys. 169, 463–502 (2001).
[CrossRef]

P. G. Debenedetti and F. H. Stillinger, “Supercooled liquids and the glass transition,” Nature 410, 259–267 (2001).
[CrossRef] [PubMed]

2000 (2)

G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, 2000).

M. Moseler and U. Landman, “Formation, stability, and breakup of nanojets,” Science 289, 1165–1169 (2000).
[CrossRef] [PubMed]

1999 (1)

R. Scardovelli and S. Zaleski, “Direct numerical simulation of free-surface and interfacial flow,” Annu. Rev. Fluid Mech. 31, 567–603 (1999).
[CrossRef]

1998 (1)

J. N. Winn, Y. Fink, S. H. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 15731575 (1998).
[CrossRef]

1997 (1)

J. Eggers, “Nonlinear dynamics and breakup of free-surface flows,” Rev. Mod. Phys. 69, 865–929 (1997).
[CrossRef]

1996 (1)

H. A. Stone and M. P. Brenner, “Note on the capillary thread instability for fluids of equal viscosities,” J. Fluid. Mech. 318, 373–374 (1996).
[CrossRef]

1994 (1)

X. D. Shi, M. P. Brenner, and S. R. Nagel, “A cascade of structure in a drop falling from a faucet,” Science 265, 219–222 (1994).
[CrossRef] [PubMed]

1992 (1)

J. B. Fournier and A. M. Cazabat, “Tears of wine,” Europhys. Lett. 20, 517–522 (1992).
[CrossRef]

1988 (1)

S. Osher and J. A. Sethian, “Front propagating with curvature-dependent speed - alogrithms based on Hamilton-Jacobi formulations,” J. Comput. Phys. 79, 12–49 (1988).
[CrossRef]

1983 (1)

V. F. Dobrescu and C. Radovici, “Temperature dependence of melt viscosity of polymers,” Polym. Bull. 10, 134–140 (1983).
[CrossRef]

1973 (1)

D. B. Keck, R. D. Maurer, and P. C. Schultz, “On the ultimate lower limit of attenuation in glass optical waveguides,” Appl. Phys. Lett. 22, 307–309 (1973).
[CrossRef]

1961 (1)

S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability , (Oxford University Press, 1961).

1957 (1)

M. F. Culpin, “The viscosity of liquid indium and liquid tin,” Proc. Phys. Soc. B70, 1069–1078 (1957).

1935 (1)

S. Tomotika, “On the instability of a cylinderical thread of a viscous liquid surrounded by another viscous fluid,” Proc. Roy. Soc. London. 150, 322–337 (1935).
[CrossRef]

1892 (1)

L. Rayleigh, “On the instability of a cylinder of viscous liquid under capillary force,” Philos. Mag. 34, 145–154 (1892).

1879 (1)

L. Rayleigh, “On the capillary phenomena of jets,” Proc. Roy. Soc. London 29, 71–97 (1879).
[CrossRef]

1873 (1)

J. Plateau, Statique Expérimentale et Theorique des Liquides Soumis aux Seules Force Molécularies , (Gauthier Villars, 1873), vol. 2.

Abouraddy, A.

D. S. Deng, N. Orf, S. Danto, A. Abouraddy, J. Joannopoulos, and Y. Fink, “Processing and properties of centimeter-long, in-fiber, crystalline-selenium filaments,” Appl. Phys. Lett. 96, 23102 (2010).
[CrossRef]

D. S. Deng, N. Orf, A. Abouraddy, A. Stolyarov, J. Joannopoulos, H. Stone, and Y. Fink, “In-fiber semiconductor filament arrays,” Nano. Lett. 8, 4265–4269 (2008).
[CrossRef]

Abouraddy, A. F.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6, 336–347 (2007).
[CrossRef] [PubMed]

M. Bayindir, F. Sorin, A. F. Abouraddy, J. Viens, S. D. Hart, J. D. Joannopoulos, and Y. Fink, “Metal-insulator-semiconductor optoelectronic fibres,” Nature , 431, 826–829 (2004).
[CrossRef] [PubMed]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems , 3rd ed. (Wiley-Interscience, 2002).
[CrossRef]

Ajdari, A.

H. A. Stone, A.D. Stroock, and A. Ajdari, “Engineering flows in small devices: Microfluidics toward a lab-on-a-chip,” Annu. Rev. Fluid. Mech. 36, 381–411 (2004).
[CrossRef]

Aktas, O.

M. Yaman, T. Khudiyev, E. Ozgur, M. Kanik, O. Aktas, E. O. Ozgur, H. Deniz, E. Korkut, and M. Bayindir, “Arrays of indefinitely long uniform nanowires and nanotubes,” Nat. Mater. 10, 494–501 (2011).
[CrossRef] [PubMed]

Balogh, A. G.

S. Karim, M. E. Toimil-Molares, A. G. Balogh, W. Ensinger, T. W. Cornelius, E. U. Khan, and R. Neumann, “Morphological evolution of Au nanowires controlled by Rayleigh instability,” Nanotechnology 17, 5954–5959 (2006).
[CrossRef]

M. E. Toimil-Molares, A. G. Balogh, T. W. Cornelius, R. Neumann, and C. Trautmann, “Fragmentation of nanowires driven by Rayleigh instability,” Appl. Phys. Lett. 85, 5337–5339 (2004).
[CrossRef]

Barton, G. W.

Batchelor, G. K.

G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, 2000).

Bayindir, M.

M. Yaman, T. Khudiyev, E. Ozgur, M. Kanik, O. Aktas, E. O. Ozgur, H. Deniz, E. Korkut, and M. Bayindir, “Arrays of indefinitely long uniform nanowires and nanotubes,” Nat. Mater. 10, 494–501 (2011).
[CrossRef] [PubMed]

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6, 336–347 (2007).
[CrossRef] [PubMed]

M. Bayindir, F. Sorin, A. F. Abouraddy, J. Viens, S. D. Hart, J. D. Joannopoulos, and Y. Fink, “Metal-insulator-semiconductor optoelectronic fibres,” Nature , 431, 826–829 (2004).
[CrossRef] [PubMed]

Benoit, G.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6, 336–347 (2007).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653 (2002).
[CrossRef] [PubMed]

Birks, T. A.

Brenner, M. P.

H. A. Stone and M. P. Brenner, “Note on the capillary thread instability for fluids of equal viscosities,” J. Fluid. Mech. 318, 373–374 (1996).
[CrossRef]

X. D. Shi, M. P. Brenner, and S. R. Nagel, “A cascade of structure in a drop falling from a faucet,” Science 265, 219–222 (1994).
[CrossRef] [PubMed]

Brochard-Wyart, F.

P. de Gennes, F. Brochard-Wyart, and D. Quere, Capillarity and Wetting Phenomena (Springer, 2002).

Cazabat, A. M.

J. B. Fournier and A. M. Cazabat, “Tears of wine,” Europhys. Lett. 20, 517–522 (1992).
[CrossRef]

Cerda, E.

E. Cerda and L. Mahadevan, “Geometry and physics of wrinkling,” Phys. Rev. Lett. 90, 074302 (2003).
[CrossRef] [PubMed]

E. Cerda, K. Ravi-Chandar, and L. Mahadevan, “Thin films—wrinkling of an elastic sheet under tension,” Nature 419, 579–580 (2002).
[CrossRef] [PubMed]

Chandrasekhar, S.

S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability , (Oxford University Press, 1961).

Chen, J. T.

J. T. Chen, M. F. Zhang, and T. P. Russell, “Instabilities in nanoporous media,” Nano. Lett. 7, 183–187 (2007).
[CrossRef] [PubMed]

Chocat, N.

S. Egusa, Z. Wang, N. Chocat, Z. M. Ruff, A. M. Stolyarov, D. Shemuly, F. Sorin, P. T. Rakich, J. D. Joannopoulos, and Y. Fink, “Multimaterial piezoelectric fibres,” Nat. Mater. 9, 643–648 (2010).
[CrossRef] [PubMed]

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S. Egusa, Z. Wang, N. Chocat, Z. M. Ruff, A. M. Stolyarov, D. Shemuly, F. Sorin, P. T. Rakich, J. D. Joannopoulos, and Y. Fink, “Multimaterial piezoelectric fibres,” Nat. Mater. 9, 643–648 (2010).
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Figures (9)

Fig. 1
Fig. 1

Optical-fiber thermal drawing. Preform is heated at elevated temperature to viscous fluid, and stretched into extended fibers by applied tension. This preform is specially designed with a thin cylindrical shell in polymer matrix.

Fig. 2
Fig. 2

SEM micrographs of cylindrical shells in fiber. (a) Photograph of fiber. (b) SEM of fiber cross-section. Magnified view of multilayer structures reveals the thickness of micrometer (c) and tens of nanometers (d), respectively. Bright and dark color for glass and polymer in SEM, respectively. (e) showing layer breakup into circles in the fiber cross-section, while (f) presenting the continuous filaments obtained from fiber after dissolving polymer matrix.

Fig. 3
Fig. 3

An instability time scale (τ) for unequal viscosity with a fixed shell viscosity (η shell). In the limit of η clad → 0, τ is determined by η shell and approaches to a constant. In the opposite limit of η clad → ∞, τ should be determined by η clad and is linearly proportional to η clad. Between these two limits of η clad, τ smoothly interpolates between the corresponding time scales.

Fig. 4
Fig. 4

Radial stability map. Linear theory calculations of the instability time scale (τ), which is dependent on the radius, thickness, and viscosity. Inset shows cross-sectional geometry of cylindrical shell. In our experiments, the dwelling time of thermal drawing is around τ dwelling ≈ 100 sec, and the fiber radius r ≈ 500 μm. Radially stable region is shaded yellow for τ > τ dwelling, while the unstable region corresponds to τ < τ dwelling.

Fig. 5
Fig. 5

Calculated shell–cladding viscous materials selection map during thermal drawing (τ dwelling = 100 sec). A red line for instability time for dwelling time τ = τ dwelling. The shaded region above the red line indicates potentially suitable viscous materials combination (τ > τ dwelling), those in which radial instabilities alone do not cause breakup. The region below the red line indicates radially unstable materials combinations (τ < τ dwelling), such as Se – PE materials combination, which are unstable for thermal drawing.

Fig. 6
Fig. 6

Relevant parameters in the neck-down region during thermal drawing. (a) Photograph of neck-down region from preform to fiber, (b)–(e) for the calculated radius, velocity, temperature and viscosity.

Fig. 7
Fig. 7

Snapshot of the flow field and interfaces during instability evolution. Color scale for pressure, arrows for fluid velocity.

Fig. 8
Fig. 8

Growth factor of instability as a function of perturbation wavelength. Fast- and slow- modes occur at wavelengths above their respective critical wavelengths λf , λs . Inset is a sketch of coaxial cylinder with radius R = 2r and equal viscosities.

Fig. 9
Fig. 9

Temperature-dependent viscosity for various chalcogenide glasses. Typical temperature during fiber drawing for glass Se, As2Se3, As2S3 is around 220, 260, 300 oC with the corresponding viscosities of 10, 105, 105 Pa · s, respectively.

Equations (18)

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{ ρ [ t u + ( u ) u ] = p + [ η u + ( u ) T 2 ] γ κ n δ , u = 0 ,
Re = ρ Uh η , Fr = U 2 gh , Ca = η U γ ,
Re 10 10 , Fr 10 2 , C a 10 4 .
τ = η r γ max λ Ψ ( λ , R / r ) ,
τ 2 r η c l a d γ max λ [ ( 1 x 2 ) Φ ( x , η c l a d / η s h e l l ) ] ,
Γ = 0 L d z v ( z ) τ ( z ) ,
τ ( z ) = 2 r η polymer ( z , T ) γ { max λ ( 1 x 2 ) Φ [ x , η polymer ( z , t ) / η clad ( z , t ) ] } .
R ( z ) R ( 0 ) = ( 1 + k z L ) 1 / p , k = [ R ( 0 ) R ( L ) ] p 1 , p = 2 .
v ( z ) v ( 0 ) = R 2 ( 0 ) R 2 ( z ) ,
r ( z ) r ( 0 ) = R ( z ) R ( 0 ) .
T = T max ( T max T min ) ( 2 z L 1 ) 2 .
Γ = 0.90.
φ t + u φ = 0.
κ = n = φ | φ | = ( φ r 2 φ z z + φ z 2 φ r r ) + ( φ r 2 + φ z 2 ) φ r / r φ r φ z ( φ r z + φ z r ) ( φ r 2 + φ z 2 ) 3 / 2 .
{ σ k 2 γ 1 r η [ 1 ( r k ) 2 ] Λ ( r , r ) } × { σ k 2 γ 2 R η [ 1 ( R k ) 2 ] Λ ( R , R ) } = k 4 γ 1 γ 2 r R η 2 [ 1 ( r k ) 2 ] [ 1 ( R k ) 2 ] Λ ( r , R ) 2 ,
Λ ( a , b ) = 0 s J 1 ( s a ) J 1 ( s b ) ( s 2 + k 2 ) 2 d s 1 2 k d d k [ I 1 ( a k ) K 1 ( b k ) ] .
σ ( λ ) = γ η r Ψ ( λ , R / r ) ,
log η = log η 0 + C e x p ( D / T ) 2.3 R T 1 ,

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