Rheologica Acta

, Volume 50, Issue 7–8, pp 675–689 | Cite as

The effect of boundary curvature on the stress response of linear and branched polyethylenes in a contraction–expansion flow

  • David Geraint Hassell
  • T. D. Lord
  • L. Scelsi
  • D. H. Klein
  • D. Auhl
  • O. G. Harlen
  • T. C. B. McLeish
  • M. R. Mackley
Original Contribution


The effect of flow-boundary curvature on the principal stress difference (PSD) profiles observed through a contraction–expansion (CE) slit flow is evaluated for three different polyethylenes exhibiting increasing levels of branching. Studies were performed using both experimental optical techniques and computational simulations, in the latter case to evaluate the ability of constitutive models to predict these complex flows. The materials were characterised using linear and extensional rheology, which were fitted to the multi-mode ROLIE-POLY and POM-POM models depending upon material branching. Three CE-slit geometries were used; with sharp corners, and with rounding equal to one quarter and one half of the slit length. These created a mixed, but primarily simple shear flow, with different levels of extension and shear depending upon the level of curvature. The PSD developed from an initial Newtonian profile to increasing levels of asymmetry between the inlet and the outlet flow as the level of material branching increased. The rounding was found to lead to the delocalisation of PSD within the flow and removal of the stress singularity from the corner of the CE-slit. It also led to a decrease in the pressure drop across the geometry and an “opening out” of features such as downstream stress fangs to create downstream “crab-claws”. Matching between experiments and simulations for the time evolution of flow from start up for each material in the various geometries illustrated good agreement for both models.


Stress difference Contraction flow Flow visualisation Birefringence 



We would like to thank S Butler and J Embery for useful input and discussions and Dow Chemical for materials. All authors would like to acknowledge funding under the EPSRC Microscale Polymer Processing 2 research project, EPSRC Contract No. GR/T11807/01.


  1. Abedijaberi A, Soulages J, Kröger M, Khomami B (2009) Flow of branched polymer melts in a lubricated cross-slot channel: a combined computational and experimental study. Rheol Acta 48(1):97–108CrossRefGoogle Scholar
  2. Agassant JF, Baaijens F, Bastian H, Bernnat A, Bogaerds ACB, Coupez T, Debbaut B, Gavrus AL, Goublomme A, van Gurp M, Koopmans RJ, Laun HM, Lee K, Nouatin OH, Mackley MR, Peters GWM, Rekers G, Verbeeten WHM, Vergnes B, Wagmer MH, Wassner E, Zoetelief WF (2002) The matching of experimental polymer processing flows to viscoelastic numerical simulation. Int Polym Process XVII(1):3–10Google Scholar
  3. Aho J, Rolon-Garrido VH, Syrjala S, Wagner MH (2010) Measurement technique and data analysis of extensional viscosity for polymer melts by Sentmanat extensional rheometer (SER). Rheo Acta 49(4):359–370CrossRefGoogle Scholar
  4. Blackwell RJ, Harlen OG, McLeish TCB (2000) Molecular drag-strain coupling in branched polymer melts. J Rheol 44:121–136CrossRefGoogle Scholar
  5. Clemeur N, Rutgers RPG, Debbaut B (2004a) Numerical simulation of abrupt contraction flows using the double convected Pom-Pom model. J Non-Newton Fluid Mech 117:193–209CrossRefGoogle Scholar
  6. Clemeur N, Rutgers RPG, Debbaut B (2004b) Numerical evaluation of three dimensional effects in planar flow birefringence. J Non-Newton Fluid Mech 123:105–120CrossRefGoogle Scholar
  7. Collis MW, Mackley MR (2005) The melt processing of monodisperse and polydisperse polystyrene melts within a slit entry and exit flow. J Non-Newton Fluid Mech 128(1):29–41CrossRefGoogle Scholar
  8. Collis MW, Lele AK, Mackley MR, Graham RS, Groves DJ, Likhtman AE, Nicholson TM, Harlen OG, McLeish TCB, Hutchings L, Fernyhough CM and Young RN (2005) Constriction flows of monodisperse linear entangled polymers: multiscale modelling and flow visualization. J Rheol 49(2):501CrossRefGoogle Scholar
  9. Combeaud C, Demay Y, Vergnes B (2004) Experimental study of the volume defects in polystyrene extrusion. J Non-Newton Fluid Mech 121(2–3):175CrossRefGoogle Scholar
  10. Coventry KD (2006) Cross-slot rheology of polymers. PhD Thesis, Department of Chemical Engineering, University of CambridgeGoogle Scholar
  11. Coventry, KD, Mackley, MR (2008) Cross-slot extensional flow of polymer melts using a multi-pass rheometer. J Rheol 52(2):401CrossRefGoogle Scholar
  12. Crosby, BJ, Mangnus, M, de Groot, W, Daniels, R, McLeish, TCB (2002) Characterisation of long chain branching: dilution rheology of industrial polyethylenes. J Rheol 46:401CrossRefGoogle Scholar
  13. den Doelder, CF, Koopmans R, Dees M, Mangnus M (2005). Pressure oscillations and periodic extrudate distortions of long-chain branched polyolefins. J Rheol 49(1):113–126CrossRefGoogle Scholar
  14. Embery J, Tassier M, Hine PJ, Lord TD (2010) An investigation into the constriction flow of a particle reinforced polystyrene melt using a combination of flow visualisation and finite element simulations. J Rheol 54(5):1097–1118CrossRefGoogle Scholar
  15. Ganvir V, Gautham BP, Pol H, Bhamia MS, Scelsi L, Thaokar R, Lele A, Mackley MR (2011) Extrudate swell of linear and branched polyethylene’s: ALE simulations and comparison with experiments. J Non-Newton Fluid Mech 166(1–2):12–24CrossRefGoogle Scholar
  16. Gough T, Spares R, Kelly AL, Brook SM, Coates PD (2008) Three-dimensional characterisation of full field stress and velocity fields for polyethylene melt through abrupt contraction. Plast Rubber Compos 37(2–4):158–165CrossRefGoogle Scholar
  17. Graham RS, Likhtman AE, Milner ST, McLeish TCB (2003) Microscopic theory of linear entangled polymer chains under rapid deformation including chain stretch and convective constraint release. J Rheol 47:1171–1200CrossRefGoogle Scholar
  18. Harlen OG, Rallison JM, Szabo P (1995) A split Lagrangian–Eulerian method for simulating transient viscoelastic flows. J Non-Newton Fluid Mech 60:81CrossRefGoogle Scholar
  19. Hassell DG, Mackley MR (2011) The multipass rheometer; a review. J Non-Newton Fluid Mech 166:421–456CrossRefGoogle Scholar
  20. Hassell DG, Auhl D, McLeish TCB, Mackley MR (2008) The effect of viscoelasticity on stress fields within polyethylene melt flow for a cross-slot and contraction–expansion slit geometry. Rheol Acta 47:821–834CrossRefGoogle Scholar
  21. Hassell DG, Embery J, McLeish TCB, Mackley MR (2009) An experimental evaluation of the formation of an instability in mono and polydisperse polystyrenes. J Non-Newton Fluid Mech 157:1–14CrossRefGoogle Scholar
  22. Hertel D, Valette R, Münstedt H (2008) Three-dimensional entrance flow of a low-density polyethylene (LDPE) and a linear low-density polyethylene (LLDPE) into a slit die. J Non-Newton Fluid Mech 153(2–3):82–94CrossRefGoogle Scholar
  23. Inkson NJ, McLeish TCB, Harlen OG, Groves DG (1999) Predicting low density polyethylene melt rheology in elongational and shear flows with “Pom-Pom” constitutive equations. J Rheol 43:873–896CrossRefGoogle Scholar
  24. Lee K, Mackley MR, Mcleish TCB, Nicholson TM, Harlen O (2001) Experimental observation and numerical simulation of transient stress fangs within flowing molten polyethylene. J Rheol 45(6):1261–1277CrossRefGoogle Scholar
  25. Likhtman AE, Graham RS (2003) Simple constitutive equation for linear polymer melts derived from molecular theory: the ROLIEPOLY equation. J Non-Newton Fluid Mech 114(1):1–12CrossRefGoogle Scholar
  26. Lodge AS (1955) Variation of flow birefringence with stress. Nature 176:838CrossRefGoogle Scholar
  27. Lord TD, Scelsi L, Hassell DG, Mackley MR, Embery J, Auhl D, Harlen OG, Tenchev R, Jimack PK, Walkley MA (2010) The matching of 3D Rolie-Poly viscoelastic numerical simulations with experimental polymer melt flow within a slit and a cross-slot geometry. J Rheol 54(2):355–373CrossRefGoogle Scholar
  28. Mackley MR, Marshall RTJ, Smeulders JBAF (1995) The multipass rheometer. J Rheol 39(6):1293–1309CrossRefGoogle Scholar
  29. Macosko CW (1994) Rheology, principles, measurements and applications. Wiley, New YorkGoogle Scholar
  30. McLeish, TCB (2002) Tube theory of entangled polymers. Adv Phys 51:1379–1527CrossRefGoogle Scholar
  31. McLeish TCB, Larson RC (1998) Molecular constitutive equations for a class of branched polymers: the Pom-Pom polymer. J Rheol 42(1):81–110CrossRefGoogle Scholar
  32. Martyn MT, Groves DJ, Coates PD (2000) In process measurement of apparent extensional viscosity of low density polyethylene melts using flow visualization. Plast Rubber Compos 29:14–22Google Scholar
  33. Mitsoulis E, Schwetz M, Münstedt H (2003) Entry flow of LDPE melts in a planar contraction. J Non-Newton Fluid Mech 111(1):41–61CrossRefGoogle Scholar
  34. Peters GWM, Schoonen JFM, Baaijens FPT, Meijer HEH (1999) On the performance of enhanced constitutive models for polymer melts in a cross-slot flow. J Non-Newton Fluid Mech 82:387–427CrossRefGoogle Scholar
  35. Russo G, Phillips TN (2010) Numerical prediction of extrudate swell of branched polymer melts. Rheol Acta 49(6):657–676CrossRefGoogle Scholar
  36. Sentmanat ML (2003) Dual windup extensional rheometer. US Patent No 6,578,413Google Scholar
  37. Silva L, Valette R, Laure P, Coupez T (2011) A new three-dimensional mixed finite element for direct numerical simulation of compressible viscoelastic flows with moving free surfaces. Int J Mater Form. doi: 10.1007/s12289-011-1030-2
  38. Sirakov I, Ainser A, Haouche M, Guillet J (2005) Three-dimensional numerical simulation of viscoelastic contraction flows using the Pom-Pom differential constitutive model. J Non-Newton Fluid Mech 126(2):163–173CrossRefGoogle Scholar
  39. Valette R, Mackley MR, Hernandez Fernandez del Castillo G (2006) Matching time dependent pressure driven flows with a Rolie Poly numerical simulation. J Non-Newton Fluid Mech 136(2–3):118–125CrossRefGoogle Scholar
  40. Wales JLS (1976) The application of flow birefringence to rheological studies of polymer melts. PhD Thesis, Delft University of Technology, DelftGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • David Geraint Hassell
    • 1
  • T. D. Lord
    • 1
  • L. Scelsi
    • 1
  • D. H. Klein
    • 2
  • D. Auhl
    • 2
  • O. G. Harlen
    • 3
  • T. C. B. McLeish
    • 2
  • M. R. Mackley
    • 1
  1. 1.Department of Chemical EngineeringUniversity of CambridgeCambridgeUK
  2. 2.IRC in Polymer Science and Technology, Department of Physics and AstronomyUniversity of LeedsLeedsUK
  3. 3.Department of MathematicsUniversity of LeedsLeedsUK

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