### Abstract

A model of Newtonian glass fiber drawing at fixed temperature in the unsteady range (the draw ratio E>20.22) is considered. In this range under steady boundary conditions, as is well known, the draw resonance instability sets in, resulting in self-sustained oscillations. These oscillations lead to a periodic variation of the cross-sectional radius of the fiber. In the present work we consider the case where the spinline radius varies periodically. Such a variation may result from flow oscillations in the fiber forming channels in the direct-melt process, or from the variation of the preform cross-sectional radius in drawing of optical fibers. When this variation takes place in the range E >20.22, the self-sustained periodic oscillations of the draw resonance are replaced by quasiperiodic and periodic (mode-locked) subharmonic or (under the appropriate conditions) chaotic oscillations (strange attractors). The routes to chaos found in the present work include (1) smooth period doubling bifurcation of (any) mode-locked periodic solution, (2) abrupt explosions of quasiperiodic solutions. The predicted chaotic variation of the spinline radius at the winding mandrel may result in a similar variation of the cross-sectional radius of the solidified fibers.

Original language | English |
---|---|

Pages (from-to) | 3201-3208 |

Number of pages | 8 |

Journal | Physics of Fluids |

Volume | 11 |

Issue number | 11 |

Publication status | Published - 1999 Nov 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes
- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*11*(11), 3201-3208.

**Newtonian glass fiber drawing : Chaotic variation of the cross-sectional radius.** / Yarin, Alexander; Gospodinov, P.; Gottlieb, O.; Graham, M. D.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 11, no. 11, pp. 3201-3208.

}

TY - JOUR

T1 - Newtonian glass fiber drawing

T2 - Chaotic variation of the cross-sectional radius

AU - Yarin, Alexander

AU - Gospodinov, P.

AU - Gottlieb, O.

AU - Graham, M. D.

PY - 1999/11/1

Y1 - 1999/11/1

N2 - A model of Newtonian glass fiber drawing at fixed temperature in the unsteady range (the draw ratio E>20.22) is considered. In this range under steady boundary conditions, as is well known, the draw resonance instability sets in, resulting in self-sustained oscillations. These oscillations lead to a periodic variation of the cross-sectional radius of the fiber. In the present work we consider the case where the spinline radius varies periodically. Such a variation may result from flow oscillations in the fiber forming channels in the direct-melt process, or from the variation of the preform cross-sectional radius in drawing of optical fibers. When this variation takes place in the range E >20.22, the self-sustained periodic oscillations of the draw resonance are replaced by quasiperiodic and periodic (mode-locked) subharmonic or (under the appropriate conditions) chaotic oscillations (strange attractors). The routes to chaos found in the present work include (1) smooth period doubling bifurcation of (any) mode-locked periodic solution, (2) abrupt explosions of quasiperiodic solutions. The predicted chaotic variation of the spinline radius at the winding mandrel may result in a similar variation of the cross-sectional radius of the solidified fibers.

AB - A model of Newtonian glass fiber drawing at fixed temperature in the unsteady range (the draw ratio E>20.22) is considered. In this range under steady boundary conditions, as is well known, the draw resonance instability sets in, resulting in self-sustained oscillations. These oscillations lead to a periodic variation of the cross-sectional radius of the fiber. In the present work we consider the case where the spinline radius varies periodically. Such a variation may result from flow oscillations in the fiber forming channels in the direct-melt process, or from the variation of the preform cross-sectional radius in drawing of optical fibers. When this variation takes place in the range E >20.22, the self-sustained periodic oscillations of the draw resonance are replaced by quasiperiodic and periodic (mode-locked) subharmonic or (under the appropriate conditions) chaotic oscillations (strange attractors). The routes to chaos found in the present work include (1) smooth period doubling bifurcation of (any) mode-locked periodic solution, (2) abrupt explosions of quasiperiodic solutions. The predicted chaotic variation of the spinline radius at the winding mandrel may result in a similar variation of the cross-sectional radius of the solidified fibers.

UR - http://www.scopus.com/inward/record.url?scp=0000586345&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000586345&partnerID=8YFLogxK

M3 - Article

VL - 11

SP - 3201

EP - 3208

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 11

ER -