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

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    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 languageEnglish
    Title of host publicationDevelopments in Non-Newtonian Flows
    PublisherASME
    Pages17-30
    Number of pages14
    Volume206
    Publication statusPublished - 1994
    EventProceedings of the 1994 International Mechanical Engineering Congress and Exposition - Chicago, IL, USA
    Duration: Nov 6 1994Nov 11 1994

    Other

    OtherProceedings of the 1994 International Mechanical Engineering Congress and Exposition
    CityChicago, IL, USA
    Period11/6/9411/11/94

    Fingerprint

    Angular velocity
    Fluids
    Elasticity
    Aspect ratio
    Flow fields
    Liquids

    All Science Journal Classification (ASJC) codes

    • Engineering(all)

    Cite this

    Siginer, D. A. (1994). On the instability of the fluids of second grade in nearly viscometric motions. In Developments in Non-Newtonian Flows (Vol. 206, pp. 17-30). ASME.
    Siginer, Dennis A. / On the instability of the fluids of second grade in nearly viscometric motions. Developments in Non-Newtonian Flows. Vol. 206 ASME, 1994. pp. 17-30
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    Siginer, DA 1994, On the instability of the fluids of second grade in nearly viscometric motions. in 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.

    Developments in Non-Newtonian Flows. Vol. 206 ASME, 1994. p. 17-30.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

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    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.

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    Siginer DA. On the instability of the fluids of second grade in nearly viscometric motions. In Developments in Non-Newtonian Flows. Vol. 206. ASME. 1994. p. 17-30