The time-dependent extrudate-swell problem of an Oldroyd-B fluid with slip along the wall

Eric Brasseur, Marios M. Fyrillas, Georgios C. Georgiou, Marcel J. Crochet

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43 Citations (Scopus)


We demonstrate that viscoelasticity combined with nonlinear slip acts as a storage of elastic energy generating oscillations of the pressure drop similar to those observed experimentally in extrusion instabilities. We consider the time-dependent axisymmetric incompressible Poiseuille and extrudate-swell flows of an Oldroyd-B fluid. We assume that slip occurs along the wall of the die following a slip equation which relates the shear stress to the velocity at the wall and exhibits a maximum and a minimum. We first study the stability of the one-dimensional axisymmetric Poiseuille flow by means of a one-dimensional linear stability analysis and time-dependent calculations. The numerically predicted instability regimes agree well with the linear stability ones. The calculations reveal that periodic solutions are obtained when an unstable steady-state is perturbed and that the amplitude and the period of the oscillations are increasing functions of the Weissenberg number. We then continue to numerically solve the time-dependent two-dimensional axisymmetric Poiseuille and extrudate-swell flows using the elastic-viscous split stress method for the integration of the constitutive equation. Again, oscillations are observed in the unstable regime; consequently, the surface of the extrudate is wavy. However, the amplitude and the period of the pressure drop oscillations are considerably smaller than in the one-dimensional flow. The most important phenomenon revealed by our two-dimensional calculations is that the flow in the die is periodic in the axial direction.

Original languageEnglish
Pages (from-to)549-566
Number of pages18
JournalJournal of Rheology
Issue number3
Publication statusPublished - 1998

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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