Spurt in the Extrusion of Polymeric Melts: Discrete Models for Relaxation Oscillations

  • A. A. F. Van De Ven
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


In the extrusion of polymer melts, several types of flow instability can occur. One example of this is spurt. Spurt is manifested by periodic oscillations in the pressure and volumetric flow rate. These oscillations are of relaxation type. An extrusion through a cylindrical die is considered. A discrete model to describe spurt or relaxation oscillations is constructed. This model is based on observations from three-dimensional theory. When spurt occurs, the shear rates very near the wall of the die (i.e., in the spurt layer) are much higher than those in the kernel of the extruded polymeric melt. Therefore, the viscosity in the spurt layer is taken much smaller than in the kernel. In both regions a linear Newtonian fluid model is used. A no-slip boundary condition at the wall is maintained. The model developed here is compared to an analogous model, allowing for slip at the wall of the die. It is shown that corresponding results can be obtained from both models. Application of the model to a piston-driven extrusion flow shows the occurrence of spurt oscillations for a restricted range of prescribèd inlet flow rates. The found oscillations are qualitatively in correspondence with experimental results.


Shear Rate Discrete Model Spurt Flow High Shear Rate Volumetric Flow Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aarts, A.C.T., Analysis of the flow instabilities in the extrusion of polymeric melts, Ph.D. Thesis, Eindhoven University of Technology (1997).Google Scholar
  2. 2.
    . Aarts, A.C.T., and van de Ven, A.A.F., Instabilities in the extrusion of polymers due to spurt, Progress in Industrial Mathematics at ECM/94, H. Neunzert; ed., Wiley and Teubner, Chichester (1996), 216–23.CrossRefGoogle Scholar
  3. 3.
    Aarts, A.C.T., and van de Ven, A.A.F., The occurrence of periodic distortions in the extrusion of polymeric melts. Continuum Mechanics and Thermodynamics, 11 (1999), 113–139.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    den Doelder, C.F.J., Koopmans, R. J., and Molenaar, J., Quantitative modelling of HDPE spurt experiments using wall slip and generalised Newtonian flow. J. Non-Newtonian Fluid Mech, 79 (1998), 503–514.zbMATHCrossRefGoogle Scholar
  5. 5.
    den Doelder, C.F.J., Koopmans, R.J., Molenaar, J., and van de Ven, A.A.F., Comparison of wall slip and constitutive instability spurt models, J. Non-Newtonian Fluid Mechanics, 75 (1998), 25–41.zbMATHCrossRefGoogle Scholar
  6. 6.
    Greenberg, J.M., and Demay, Y., A simple model of the melt fracture instability, European J. Appl. Math., 5 (1994), 337–58.zbMATHCrossRefGoogle Scholar
  7. 7.
    Kissi, N.E., and Piau, J.M., The different capillary flow regimes of entangled polydimethylsiloxane polymers: Macroscopic slip at the wall, hysteresis and cork flow, J. Non-Newtonian Fluid Mech., 37 (1990), 55–94.CrossRefGoogle Scholar
  8. 8.
    Koopmans, R.J., and Molenaar, J., Polymer Melt Fracture, Marcel Dekker Inc., New York, to appear (1999).Google Scholar
  9. 9.
    Malkus, D.S., Nohel, J.A., and Plohr, B.J., Dynamics of shear flow of a non-Newtonian fluid, J. Computational Phy.,87 (1990), 464–87.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Molenaar, J., and Koopmans, R.J., Modeling polymer melt-flow instabilities, J. Rheology, 38 (1994), 99–109.CrossRefGoogle Scholar
  11. 11.
    Piau, J.M., and Kissi, N.E., Measurement and modelling of friction in polymeric melts during macroscopic slip at the wall, J. Non-Newtonian Fluid Mech., 54 (1994), 121–42.CrossRefGoogle Scholar
  12. 12.
    van de Ven, A.A.F., Comparing stick and slip models for spurt in the extrusion of polymeric melts. In: Progress in Industrial Mathematics, Eds. L. Arkeryd, J. Bergh, P. Brenner, R. Petterson; Proc. ECMI 98, Teubner, Stuttgart, 1999; pp.154–162.Google Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • A. A. F. Van De Ven
    • 1
  1. 1.Eindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations