### Abstract

Flow of a viscoelastic liquid in a cylindrical cavity, driven by rotating finite disks is investigated. The cylindrical sidewall is fixed and the covers rotate with different angular velocities either in the same or in opposite directions. A regular perturbation in terms of the angular velocity of the caps is used. The flow field is resolved into a primary azimuthal stratified viscometric field and a weaker secondary meridional field. Results are presented for a range of cylinder aspect and cap rotation ratios and viscoelastic parameters. Interesting instabilities of the fluid of second grade are discussed. The controversy concerning the sign of the first Rivlin-Ericksen constant is completely irrelevant to the discussion. It is shown that loss of stability occurs repeatedly and bifurcating flows exist for critical values of an elasticity parameter at fixed aspect and cap rotation ratio. Branching flows also occur at a fixed value of the elasticity parameter for critical values of the cap rotation ratio, when the aspect ratio is fixed.

Original language | English |
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Title of host publication | Developments in Non-Newtonian Flows |

Publisher | ASME |

Pages | 17-30 |

Number of pages | 14 |

Volume | 206 |

Publication status | Published - 1994 |

Event | Proceedings of the 1994 International Mechanical Engineering Congress and Exposition - Chicago, IL, USA Duration: Nov 6 1994 → Nov 11 1994 |

### Other

Other | Proceedings of the 1994 International Mechanical Engineering Congress and Exposition |
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City | Chicago, IL, USA |

Period | 11/6/94 → 11/11/94 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Developments in Non-Newtonian Flows*(Vol. 206, pp. 17-30). ASME.

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*Developments in Non-Newtonian Flows.*vol. 206, ASME, pp. 17-30, Proceedings of the 1994 International Mechanical Engineering Congress and Exposition, Chicago, IL, USA, 11/6/94.

**On the instability of the fluids of second grade in nearly viscometric motions.** / Siginer, Dennis A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - On the instability of the fluids of second grade in nearly viscometric motions

AU - Siginer, Dennis A.

PY - 1994

Y1 - 1994

N2 - Flow of a viscoelastic liquid in a cylindrical cavity, driven by rotating finite disks is investigated. The cylindrical sidewall is fixed and the covers rotate with different angular velocities either in the same or in opposite directions. A regular perturbation in terms of the angular velocity of the caps is used. The flow field is resolved into a primary azimuthal stratified viscometric field and a weaker secondary meridional field. Results are presented for a range of cylinder aspect and cap rotation ratios and viscoelastic parameters. Interesting instabilities of the fluid of second grade are discussed. The controversy concerning the sign of the first Rivlin-Ericksen constant is completely irrelevant to the discussion. It is shown that loss of stability occurs repeatedly and bifurcating flows exist for critical values of an elasticity parameter at fixed aspect and cap rotation ratio. Branching flows also occur at a fixed value of the elasticity parameter for critical values of the cap rotation ratio, when the aspect ratio is fixed.

AB - Flow of a viscoelastic liquid in a cylindrical cavity, driven by rotating finite disks is investigated. The cylindrical sidewall is fixed and the covers rotate with different angular velocities either in the same or in opposite directions. A regular perturbation in terms of the angular velocity of the caps is used. The flow field is resolved into a primary azimuthal stratified viscometric field and a weaker secondary meridional field. Results are presented for a range of cylinder aspect and cap rotation ratios and viscoelastic parameters. Interesting instabilities of the fluid of second grade are discussed. The controversy concerning the sign of the first Rivlin-Ericksen constant is completely irrelevant to the discussion. It is shown that loss of stability occurs repeatedly and bifurcating flows exist for critical values of an elasticity parameter at fixed aspect and cap rotation ratio. Branching flows also occur at a fixed value of the elasticity parameter for critical values of the cap rotation ratio, when the aspect ratio is fixed.

UR - http://www.scopus.com/inward/record.url?scp=0028740823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028740823&partnerID=8YFLogxK

M3 - Conference contribution

VL - 206

SP - 17

EP - 30

BT - Developments in Non-Newtonian Flows

PB - ASME

ER -