Rheologica Acta

, Volume 57, Issue 4, pp 317–325 | Cite as

Flow and breakup in extension of low-density polyethylene

  • Henrik Koblitz Rasmussen
  • Andrea Fasano
Original Contribution


The breakup during the extension of a low-density polyethylene Lupolen 1840D, as observed experimentally by Burghelea et al. (J Non-Newt Fluid Mech 166:1198–1209 2011), was investigated. This was observed during the extension of an circular cylinder with radius R0 = 4 mm and length L0 = 5mm. The sample was attached to two flat end plates, separated exponentially in time to extend the samples. A numerical method based on a Lagrangian kinematics description in a continuum mechanical framework was used to calculate the extension of an initially cylindrically shaped sample with and without small long-waved and centrally located suppression in the surface. The flow properties of the branched polymer melt were defined by a multi mode version of the molecular stress function constitutive equation. A multi mode version based on a Maxwell relaxation spectrum was applied, and the involved parameters were fitted based on previous measured extensional viscosities including the startup, relaxed and reversed flow of the Lupolen 1840D melt. For an ideal cylindrically shaped geometry, at some of the extensional rates, there was a match with the calculated break of strain values, but most were just below the error bars as reported experimentally by Burghelea et al. (J Non-Newt Fluid Mech 166:1198–1209 2011). At low extensional rates, the measurements were considerably above the calculated ones. A very small relative suppression in the surface (0.1%) was required to achieve an agreement with all measurements on average. The largest sensitivity to the surface suppression was at low extensional rates.


Finite-element analysis Integral constitutive equation Stability Extensional flow 


  1. Bach A, Rasmussen HK, Longin P-Y, Hassager O (2002) Growth of non-axisymmetric disturbances of the free surface in the filament stretching rheometer: experiments and simulation. J Non-Newtonian Fluid Mech 108:163–186CrossRefGoogle Scholar
  2. Barroso VC, Andrade RJ, Maia JM (2010) An experimental study on the criteria for failure of polymer melts in uniaxial extension: the test case of a polyisobutylene melt in different deformation regimes. J Rheol 54:605–618CrossRefGoogle Scholar
  3. Becker J, Grün G, Seemann R, Mantz H, Jacobs K, Mecke KR, Blossey R (2003) Complex dewetting scenarios captured by thin-film models. Nat Mater 2:59–62CrossRefGoogle Scholar
  4. Bernstein B, Kearsley EA, Zapas LJ (1963) Study of stress relaxation with finite strain. Trans Soc Rheol 7:391–410CrossRefGoogle Scholar
  5. Burghelea T, Starý Z, Münstedt H (2011) On the “viscosity overshoot” during the uniaxial extension of a low density polyethylene. J Non-Newtonian Fluid Mech 166:1198–1209CrossRefGoogle Scholar
  6. Chang H, Lodge AS (1971) A possible mechanism for stabilizing elongational flow in certain polymeric liquids at constant temperature and composition. Rheol Acta 10:448–449CrossRefGoogle Scholar
  7. Cohen A (1991) A Padé approximant to the inverse Langevin function. Rheol Acta 30:270–273CrossRefGoogle Scholar
  8. Currie PK (1982) Constitutive equations for polymer melts predicted by the Doi-Edwards and Curtiss-Bird kinetic theory models. J Non-Newtonian Fluid Mech 11(1–2):53–68CrossRefGoogle Scholar
  9. Denn MM (2001) Extrusion instabilities and wall slip. Annu Rev Fluid Mech 33:265–287CrossRefGoogle Scholar
  10. Doi M, Edwards SF (1978) Dynamics of concentrated polymer systems, III, the constitutive equation. J Chem Soc Farad Trans II(74):1818–1832CrossRefGoogle Scholar
  11. Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon Press, OxfordGoogle Scholar
  12. Fasano A, Rasmussen HK (2017) A third order accurate Lagrangian finite element scheme for the computation of generalized molecular stress function fluids. J Non-Newtonian Fluid Mech 246:10–20CrossRefGoogle Scholar
  13. Fetters LJ, Lohse DJ, Colby RH (2007) Chain dimensions and entanglement spacings. In: Mark JE (ed) Physical properties of polymers handbook. 2nd edn. Springer, New York, pp 447–455Google Scholar
  14. Hassager O, Kolte MI, Renardy M (1998) Failure and nonfailure of fluid filaments in extension. J Non-Newtonian Fluid Mech 76:137–151CrossRefGoogle Scholar
  15. Hoyle DM, Fielding SM (2016) Criteria for extensional necking instability in complex fluids and soft solids. Part I: imposed Hencky strain rate protocol. J Rheol 60(6):1347–1375CrossRefGoogle Scholar
  16. Hoyle DM, Huang Q, Auhl D, Hassell D, Rasmussen HK, Skov AL, Harlen OG, Hassager O, McLeish TCB (2013) Transient overshoot extensional rheology of long-chain branched polyethylenes: experimental and numerical comparisons between filament stretching and cross-slot flow. J Rheol 57(1):293–313CrossRefGoogle Scholar
  17. Huang Q, Rasmussen HK, Skov AL, Hassager O (2012) Stress relaxation and reversed flow of low-density polyethylene melts following uniaxial extension. J Rheol 56(6):1535–1554CrossRefGoogle Scholar
  18. Huang Q, Alvarez NJ, Shabbir A, Hassager O (2016) Multiple cracks propagate simultaneously in polymeric liquids in tension. Phys Rev Lett 117:087801CrossRefGoogle Scholar
  19. Ide Y, White JL (1978) Experimental study of elongational flow and failure of polymer melts. J Appl Polymer Sci 22:1061–1079CrossRefGoogle Scholar
  20. Joshi YM, Denn MM (2003) Rupture of entangled polymeric liquids in elongational flow. J Rheol 47:291–298CrossRefGoogle Scholar
  21. Joshi YM, Denn MM (2004) Rupture of entangled polymeric liquids in elongational flow with dissipation. J Rheol 48:591–598CrossRefGoogle Scholar
  22. Kaye A (1962) College of aeronautics, Cranheld, Note no 134Google Scholar
  23. Kolte MI, Rasmussen HK, Hassager O (1997) Transient filament stretching rheometer II: numerical simulation. Rheol Acta 36:285–302Google Scholar
  24. Krishnamoorti R, Graessley WW, Zirkel A, Richter D, Hadjichristidis N, Fetters LJ, Lohse DJ (2002) Melt-state polymer chain dimensions as a function of temperature. J Polym Sci Part B: Polym Phys 40:1768–1776CrossRefGoogle Scholar
  25. Malkin AY, Petrie CJS (1997) Some conditions for rupture of polymer liquids in extension. J Rheol 41:1–41CrossRefGoogle Scholar
  26. Marin JMR, Rasmussen HK (2009) Lagrangian finite-element method for the simulation of K-BKZ fluids with third order accuracy. J Non-Newtonian Fluid Mech 156:177–188CrossRefGoogle Scholar
  27. Marrucci G, Ianniruberto G (2004) Interchain pressure effect in extensional flows of entangled polymer melts. Macromolecules 37:3934–3942CrossRefGoogle Scholar
  28. Narimissa E, Wagner MH (2016) From linear viscoelasticity to elongational flow of polydisperse linear and branched polymer melts: the hierarchical multi-mode molecular stress function model. Polymer 104:204–214CrossRefGoogle Scholar
  29. Petrie CJS, Denn MM (1976) Instabilities in polymer processing. AIChE J 22:209–236CrossRefGoogle Scholar
  30. Rasmussen HK (2002) Lagrangian viscoelastic flow computations using a generalized molecular stress function model. J Non-Newtonian Fluid Mech 106:107–120CrossRefGoogle Scholar
  31. Rasmussen HK (2013) Catastrophic failure of polymer melts during extension. J Non-Newtonian Fluid Mech 198:136–140CrossRefGoogle Scholar
  32. Rasmussen HK (2015) Interchain tube pressure effect in the flow dynamics of bi-disperse polymer melts. Rheol Acta 54(1):9–18CrossRefGoogle Scholar
  33. Rasmussen HK, Bach A (2005) On the bursting of linear polymer melts in inflation processes. Rheol Acta 44:435–445CrossRefGoogle Scholar
  34. Rasmussen HK, Hassager O (2012) Reply to: ‘on the “viscosity overshoot” during the uniaxial extension of a low density polyethylene’. J Non-Newtonian Fluid Mech 171:106–106CrossRefGoogle Scholar
  35. Rasmussen HK, Huang Q (2014) Interchain tube pressure effect in extensional flows of oligomer diluted nearly monodisperse polystyrene melts. Rheol Acta 53(3):199–208CrossRefGoogle Scholar
  36. Rasmussen HK, Yu K (2008) On the burst of branched polymer melts during inflation. Rheol Acta 47:149–157CrossRefGoogle Scholar
  37. Rasmussen HK, Yu K (2011) Spontaneous breakup of extended monodisperse polymer melts. Phys Rev Lett 107:126001CrossRefGoogle Scholar
  38. Rasmussen HK, Nielsen JK, Bach A, Hassager O (2005) Viscosity overshoot in the start-up of uniaxial elongation of low density polyethylene melts. J Rheol 49(2):369–381CrossRefGoogle Scholar
  39. Shipman RWG, Denn MM, Keunings R (1991) Mechanics of the “falling plate” extensional rheometer. J Non-Newtonian Fluid Mech 40:281–288CrossRefGoogle Scholar
  40. Sridhar T, Tirtaatmadja V, Nguyen D, Gupta R (1991) Measurement of extensional viscosity of polymer solutions. J Non-Newtonian Fluid Mech 40:271–280CrossRefGoogle Scholar
  41. Stary Z, Papp M, Burghelea T (2015) Deformation regimes, failure and rupture of a low density polyethylene (LDPE) melt undergoing uniaxial extension. J Non-Newtonian Fluid Mech 219:35–49CrossRefGoogle Scholar
  42. Sujatha KS, Matallah H, Webster MF, Williams PR (2010) Numerical predictions of bubble growth in viscoelastic stretching filaments. Rheol Acta 49(11–12):1077–1092CrossRefGoogle Scholar
  43. Szabo P (1997) Transient filament stretching rheometer part I: force balance analysis. Rheol Acta 36:277–284Google Scholar
  44. Tome MF, Bertoco J, Oishi CM, Araujo MSB, Cruz D, Pinho FT, Vynnycky M (2016) A finite difference technique for solving a time strain separable K-BKZ constitutive equation for two-dimensional moving free surface flows. J Comput Phys 311:114–141CrossRefGoogle Scholar
  45. Vergnes B (2015) Extrusion defects and flow instabilities of molten polymers. Int Polym Process 30(1):3–28CrossRefGoogle Scholar
  46. Vinogradov GV (1975) Viscoelasticity and fracture phenomenon in uniaxial extension of high molecular linear polymers. Rheol Acta 14:942–954CrossRefGoogle Scholar
  47. Vinogradov GV, Malkin AY, Volosevitch VV, Shatalov VP, Yudin VP (1975) Flow, high-elastic (recoverable) deformation, and rupture of uncured high molecular weight linear polymers in uniaxial extension. J Polym Sci Polym Phys Edn 13:1721–1735CrossRefGoogle Scholar
  48. Wagner MH (1978) A constitutive analysis of uniaxial elongational flow data of a low-density polyethylene melt. J Non-Newton Fluid Mech 4:39–55CrossRefGoogle Scholar
  49. Wagner MH (2014) Scaling relations for elongational flow of polystyrene melts and concentrated solutions of polystyrene in oligomeric styrene. Rheol Acta 53(10-11):765–777CrossRefGoogle Scholar
  50. Wagner MH, Rolón-Garrido VH (2008) Verification of branch point withdrawal in elongational flow of pom-pom polystyrene melt. J Rheol 52(5):1049–1068CrossRefGoogle Scholar
  51. Wagner MH, Kheirandish S, Hassager O (2005) Quantitative prediction of transient and steady-state elongational viscosity of nearly monodisperse polystyrene melts. J Rheol 49:1317–1327CrossRefGoogle Scholar
  52. Webster MF, Matallah H, Sujatha KS, Banaai MJ (2008) Numerical modelling of step-strain for stretched filaments. J Non-Newtonian Fluid Mech 151(1–3):38–58CrossRefGoogle Scholar
  53. Ye X, Sridhar T (2005) Effects of the polydispersity on rheological properties of entangled polystyrene solutions. Macromolecules 38:3442–3449CrossRefGoogle Scholar
  54. Yu K, Rasmussen HK, Marin JMR, Hassager O (2012) Mechanism of spontaneous hole formation in thin polymeric films. Phys Rev B 85:024201CrossRefGoogle Scholar
  55. Ziabicki A, Takserman-Krozer R (1964) Mechanism of breakage of liquid threads. Kolloid-Zeitschrift und Zeitschrift für Polymere 198:60–65CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTechnical University of DenmarkKgs. LyngbyDenmark

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