### 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 surrounding the sign of the first Rivlin-Ericksen constant is completely irrelevant to the discussion. It is shown qualitatively 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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Pages (from-to) | 305-313 |

Number of pages | 9 |

Journal | Journal of Applied Mechanics, Transactions ASME |

Volume | 71 |

Issue number | 3 |

DOIs | |

Publication status | Published - May 1 2004 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

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**On the nearly viscometric torsional motion of viscoelastic liquids between shrouded rotating disks.** / Siginer, Dennis A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the nearly viscometric torsional motion of viscoelastic liquids between shrouded rotating disks

AU - Siginer, Dennis A.

PY - 2004/5/1

Y1 - 2004/5/1

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 surrounding the sign of the first Rivlin-Ericksen constant is completely irrelevant to the discussion. It is shown qualitatively 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 surrounding the sign of the first Rivlin-Ericksen constant is completely irrelevant to the discussion. It is shown qualitatively 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.

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U2 - 10.1115/1.1651538

DO - 10.1115/1.1651538

M3 - Article

VL - 71

SP - 305

EP - 313

JO - Journal of Applied Mechanics, Transactions ASME

JF - Journal of Applied Mechanics, Transactions ASME

SN - 0021-8936

IS - 3

ER -