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Transient behaviour and stability points of the Poiseuille flow of a KBKZ-fluid

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Abstract

The Poiseuille flow of a KBKZ-fluid, being a nonlinear viscoelastic model for a polymeric fluid, is studied. The flow starts from rest and especially the transient phase of the flow is considered. It is shown that under certain conditions the steady flow equation has three different equilibrium points. The stability of these points is investigated. It is proved that two points are stable, whereas the remaining one is unstable, leading to several peculiar phenomena such as discontinuities in the velocity gradient near the wall of the pipe (‘spurt’) and hysteresis. Our theoretical results are confirmed by numerical calculationsof the velocity gradient.

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Authors and Affiliations

  1. Department of mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    A. C. T. Aarts & A. A. F. Van De Ven

Authors
  1. A. C. T. Aarts
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  2. A. A. F. Van De Ven
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Aarts, A.C.T., Van De Ven, A.A.F. Transient behaviour and stability points of the Poiseuille flow of a KBKZ-fluid. J Eng Math 29, 371–392 (1995). https://doi.org/10.1007/BF00042762

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  • DOI: https://doi.org/10.1007/BF00042762

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