Rheology pp 171-194 | Cite as

Uniform Elongational Flow of Molten Polymers

  • C. J. S. Petrie
  • J. M. Dealy


In this review we shall concentrate on uniaxial elongational flows which are uniform (i.e. spatially homogeneous) and may be time-dependent. We trace briefly the development of the subject from the study by Trouton (1906) through a series of errors and their correction to the beginnings of the modern period around 1950. The “early modern period”, which is characterised by the development of techniques for measuring the elongational viscosity of soft solid and highly viscous molten polymers and by the derivation of theoretical expressions for elongational viscosity, may conveniently be divided from the “late modern period” by the review of Dealy (1971). In this latter period we find that experimental techniques have been refined and their limits pushed further and further, revealing new facets of behaviour for the theorists to explain. There has also been a growing interest in unsteady flows of well-defined character both by experimenters and by theorists.


Maxwell Model Normal Stress Difference Elongational Viscosity Uniaxial Extension Elongational Flow 
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. D. Acierno, G. Titomanlio and G. Marrucci (1972), Internal viscosity effects on transient elongational behaviour of dilute ‘polymer solutions (elastic dumbbell model), Trans. Soc. Rheol., 16, 651–667.CrossRefGoogle Scholar
  2. D. Acierno, F. P. La Mantia, G. Marrucci and G. Titomanlio (1976a), A nonlinear viscoelastic model with structure-dependent relaxation times. I. Basic formulation, J. Non-Newtonian Fluid Mech., 1, 125–146.CrossRefGoogle Scholar
  3. D. Acierno, F. P. La Mantia, G. Marrucci, G. Rizzo and G. Titomanlio (1976b), A nonlinear viscoelastic model with structure-dependent relaxation times. II. Comparison with LDPE transient stress results, J. Non-Newtonian Fluid Mech., 1, 147–157.CrossRefGoogle Scholar
  4. D. Acierno, F. P. La Mantia and G. Marrucci (1977a), A nonlinear viscoelastic model with structure-dependent relaxation times. III. Comparison with LD polyethylene creep and recovery data, J. Non-Newtonian Fluid Mech., 2, 271–280.CrossRefGoogle Scholar
  5. D. Acierno, F. P. La Mantia, B. de Cindio and L. Nicodemo (1977b), Transient shear and elongational data for polyisobutylene melts, Trans. Soc. Rheol., 21, 261–271.CrossRefGoogle Scholar
  6. P. K. Agrawal, W.-K. Lee, J. M. Lorntson, C. I. Richardson, K. F. Wissbrun and A. B. Metzner (1977), Rheological behaviour of molten “polymers in shearing and in extensional flows, Trans. Soc. Rheol., 21, 355–379.CrossRefGoogle Scholar
  7. G. Astarita and L. Nicodemo (1970), Extensional flow behaviour of polymer solutions, Chem. Eng. J., 1, 57–66.CrossRefGoogle Scholar
  8. R. L. Ballman (1965), Extensional flow of polystyrene melt, Rheol. Acta, 4, 137–140.CrossRefGoogle Scholar
  9. R. B. Bird and T. W. Spriggs (1965), Elongational viscosity of viscoelastic fluids, Phys. Fluids, 8, 1390–1392.CrossRefGoogle Scholar
  10. R. B. Bird, M. W. Johnson Jr. and J. F. Stevenson (1970), Molecular theories of elongational viscosity, Proc. 5th Int. Congr. Rheol., 4, 159–168.Google Scholar
  11. F. Bueche (1955), Visco elasticity of polymethylmethacrylates, J. Appl. Phys., 26, 738–749.CrossRefGoogle Scholar
  12. J. M. Burgers (1935), in First Report on Viscosity and Plasticity, Ch. II, Academy of Sciences, Amsterdam, 73–109.Google Scholar
  13. P. J. Carreau (1972), Rheological equations from molecular network theories, Trans. Soc. Rheol., 16, 99–127.CrossRefGoogle Scholar
  14. H. Chang and A. S. Lodge (1972), Comparison of rubberlike-liquid theory with stress-growth data for elongation of a low-density branched polyethylene melt, Rheol. Acta, 11, 127–129.CrossRefGoogle Scholar
  15. I.-J. Chen, G. E. Hagler, L. E. Abbott, D. C. Bogue and J. L. White (1972), Interpretation of tensile and melt spinning experiments on LDPE and HDPE, Trans. Soc. Rheol., 16, 473–494.CrossRefGoogle Scholar
  16. F. N. Cogswell (1968), The rheology of polymer melts under tension, Plast. Polym., 36, 109–111.Google Scholar
  17. F. N. Cogswell (1969), Tensile deformations in molten polymers, Rheol. Acta, 8, 187–194.CrossRefGoogle Scholar
  18. F. N. Cogswell (1978), Converging flow and stretching flow: a compilation, J. Non-Newtonian Fluid Mech., 4, 23–38.CrossRefGoogle Scholar
  19. B. D. Coleman and W. Noll (1962), Steady extension of incompressible simple fluids, Phys. Fluids, 5, 840–843.CrossRefGoogle Scholar
  20. J. M. Dealy (1971), Extensional flow of non-Newtonian fluids — a review, Polym. Eng. Sci., 11, 433–445.CrossRefGoogle Scholar
  21. J. M. Dealy (1978), Extensional rheometers for molten polymers: a review, J. Non-Newtonian Fluid Mech., 4, 9–21.CrossRefGoogle Scholar
  22. M. M. Denn (1977), Extensional flows: experiment and theory, in The Mechanics of Viscoelastic Fluids ed. R. S. Rivlin, AMD-Volume 22, ASME, New York, 101–125.Google Scholar
  23. M. M. Denn (1980), Continuous drawing of liquids to form fibers, Ann. Revs. Fluid Mech., 12 (in press).Google Scholar
  24. M. M. Denn and G. Marrucai (1971), Stretching of viscoelastic liquids, AIChE J., 17, 101–103.CrossRefGoogle Scholar
  25. C. D. Denson (1980), Polymer processing, Proc. VIIIth Int. Congr. Rheol., Naples.Google Scholar
  26. M. Doi and S. F. Edwards (1979), Dynamics of concentrated polymer systems. Part 4. Rheological properties, J. Chem. Soc. Faraday Trans. II, 75, 38–54.Google Scholar
  27. S. English (1924), The effect of composition on the viscosity of glass, Part II, J. Soc. Glass Technol. Trans., 8, 205–248.Google Scholar
  28. J. D. Goddard (1979), Review of Elongational Flows (Pétrie, 1979a), J. Fluid Mech., 95, 787–790.CrossRefGoogle Scholar
  29. W. Goldberg, B. Bernstein and G. Lianis (1969), The exponential extension rate history, comparison of theory with experiment, Int. J. Nonlinear Mech., 4, 277–300.CrossRefGoogle Scholar
  30. R. Greco, G. Titomanlio and G. Marrucci (1975), Transient elongational viscosity of dumbbell suspensions at high rates of stretching, Rheol. Acta, 14, 127–134.CrossRefGoogle Scholar
  31. Y. Ide and J. L. White (1978), Experimental study of elongational flow and failure of polymer melts, J. Appl. Polym. Sci., 22, 1061–1079.CrossRefGoogle Scholar
  32. E. Jenckel (1937), The effect of cooling on the properties of glasses anaplastics, Zeitschr. Elektrochem., 43, 796–806.Google Scholar
  33. E. Jenckel and K. Uberreiter (1938), On polystyrene glasses of various chain lengths, Zeitschr. Phys. Chem. A, 182, 361–383.Google Scholar
  34. V. A. Kargin and T. I. Sogolova (1949a), Development of a method of study of the true processes of flow in polymers, Zh. Fiz. Khim., 23, 540–550.Google Scholar
  35. V. A. Kargin and T. I. Sogolova (1949b), Investigation of the process of viscous flow of polyisobutyIene, Zh. Fiz. Khim., 23, 551–562.Google Scholar
  36. H. M. Laun and H. Miinstedt (1976), Comparison of the elongational behaviour of a polyethylene melt at constant stress and constant strain rate, Rheol. Acta, 15, 517–524.CrossRefGoogle Scholar
  37. H. M. Laun and H. Miinstedt (1978), Elongational behaviour of a LDPE melt. I. Strain rate and stress dependence of viscosity and recoverable strain in the steady state. Comparison with shear data. Influence of interfacial tension, Rheol. Acta, 17, 415–425.CrossRefGoogle Scholar
  38. A. I. Leonov and G. V. Vinogradov (1965), On the rheological relationships in the motion of an elastic-viscous medium in the field of a constant longitudinal velocity gradient, Dokl. Phys. Chem., 162, 442–445 (translation of Dokl. Akad. Nauk. SSSR, 162, 869–872).Google Scholar
  39. H. R. Lillie (1931), Viscosity of glass between the strain point and the melting temperature, J. Amer. Ceram. Soc., 14, 502–511.CrossRefGoogle Scholar
  40. A. S. Lodge (1964), Elastic liquids, Academic Press.Google Scholar
  41. A. S. Lodge and J. Meissner (1973), Comparison of network theory predictions with stress/time data in shear and elongation for a low-density polyethylene melt, Rheol. Acta, 12, 41–47.CrossRefGoogle Scholar
  42. A. S. Lodge, J. B. McLeod and J. A. Nohel (1978), A nonlinear singularly perturbed Volterra integro differential equation occurring in polymer rheology, Proc. Roy. Soc. Edinburgh, 80A, 99–137.CrossRefGoogle Scholar
  43. C. W. Macosko and J. M. Lorntson (1973), The rheology of two blow moulding polyethylenes, SPE Tech. Papers, 19, 461–467.Google Scholar
  44. H. Markovitz and B. D. Coleman (1964), Incompressible second order fluids, Adv. Appl. Mech., 8, 69–101.CrossRefGoogle Scholar
  45. G. Marrucci (1970), Prediction of polystyrene melt tensile behaviour, Ind. Eng. Chem. Fundam., 10, 514.CrossRefGoogle Scholar
  46. G. Marrucci and J. J. Hermans (1979), Non-linear visco elasticity of concentrated polymeric liquids (submitted for publication).Google Scholar
  47. W. R. Marshall Jr. and R. L. Pigford (1947), The application of differential equations to chemical engineering problems, University of Delaware Press.Google Scholar
  48. J. Meissner (1969), A rheometer for investigation of deformation-mechanical properties of plastic melts under defined extensional straining, Rheol. Acta, 8, 78–88.CrossRefGoogle Scholar
  49. J. Meissner (1971), Elongational properties of polyethylene melts, Rheol. Acta, 10, 230–242.CrossRefGoogle Scholar
  50. J. Meissner (1972), Development of a universal extensional rheometer for the uniaxial extension of polymer melts, Trans. Soc. Rheol., 16, 405–420.CrossRefGoogle Scholar
  51. J. Meissner, T. Raible and S. E. Stephenson (1979), The rotary clamp and its relevance in extensional rheometry, Society of Rheology, 50th Annual Meeting, paper 34–1, Abstracts booklet, p. 69.Google Scholar
  52. S. Middleman (1969), Transient response for an elastomer to large shearing and stretching deformations, Trans. Soc. Rheol., 13, 123–139.CrossRefGoogle Scholar
  53. W. Minoshima, J. L. White and J. E. Spruiell (1979), Experimental investigation of the influence of molecular weight distribution on the rheological properties of polypropylene melts, University of Tennessee, Polymer Science and Engineering Report, No. 126.Google Scholar
  54. K. Missaghi and C. J. S. Petrie (1980), Stretching the Jeffreys liquid: stressing, creep and recovery, Proc. VIIIth Int. Congr. Rheol., Naples.Google Scholar
  55. H. Mlinstedt (1975), Viscoelasticity of polystyrene melts in tensile creep experiments, Rheol. Acta, 14, 1077–1088.CrossRefGoogle Scholar
  56. H. Mlinstedt (1979), New universal extensional rheometer for polymer melts. Measurements on a polystyrene sample, J. Rheol., 23, 421–436.CrossRefGoogle Scholar
  57. H. Münstedt and H. M. Laun (1979), Elongational behaviour of an LDPE melt. II. Transient behaviour in constant stretching rate and tensile creep experiments. Comparison with shear data. Temperature dependence of the elongational properties, Rheol. Acta, 18, 492–504.CrossRefGoogle Scholar
  58. H. Nitschmann and J. Schrade (1948), On the fibre-forming ability of non-Newtonian liquids, Helv. Chim. Acta, 31, 297–319.CrossRefGoogle Scholar
  59. S. T. J. Peng (1972), Extensional flow of bulk polymers, JPL Quart. Rev., 2, 40–45. (See also S. T. J. Peng and R. F. Landel (1973), Rheol. Acta, 13, 548–556.)Google Scholar
  60. C. J. S. Petrie (1976), Some problems in unsteady flow for co-rotational rheological models, VIIth Int. Congr. Rheol., 446–447.Google Scholar
  61. C. J. S. Petrie (1977), On stretching Maxwell models, J. Non-Newtonian Fluid Mech., 2, 221–253.CrossRefGoogle Scholar
  62. C. J. S. Petrie (1979a), Elongational Flows, Pitman Publishing, London.Google Scholar
  63. C. J. S. Petrie (1979b), Measures of deformation and convected derivatives, J. Non-Newtonian Fluid Mech., 5, 147–176.CrossRefGoogle Scholar
  64. C. J. S. Petrie (1979c), A review of theoretical predictions for uniaxial elongation, Society of Rheology, 50th Annual Meeting, paper 30–6, Abstracts booklet, p. 61.Google Scholar
  65. N. Phan-Thien (1978), A nonlinear network viscoelastic model, J. Rheol., 22, 259–283.CrossRefGoogle Scholar
  66. N. Phan-Thien and R. I. Tanner (1977), A new constitutive equation derived from network theory, J. Non-Newtonian Fluid Mech., 2, 353–365.CrossRefGoogle Scholar
  67. A. C. Pipkin and R. I. Tanner (1977), Steady non-vis come trie flows of viscoelastic liquids, Ann. Revs. Fluid Mech., 9, 13–32.CrossRefGoogle Scholar
  68. B. V. Radushkevich, V. D. Fikhman and G. V. Vinogradov (1968), Uniaxial uniform-speed elongation of high-elasticity liquids (of low-molecular polyisobutylene as an example), Dokl. Phys. Chem., 180, 358–361. (Translation of Dokl. Akad. Nauk SSSR, 180, 404–407.)Google Scholar
  69. T. Raible, A. Demarmels and J. Meissner (1979), Stress and recovery maxima in LDFE melt elongation, Polymer Bulletin, 1, 397–402.CrossRefGoogle Scholar
  70. M. Reiner (1946), The coefficient of viscous traction. Amer. J. Math., 68, 672–680.CrossRefGoogle Scholar
  71. M. Reiner and A. Freudenthal (1938), Failure of a material showing creep. (A dynamical theory of strength), Proc. 5th Int. Congr. Appl. Mech., 228–233.Google Scholar
  72. R. S. Rivlin (1948), Large elastic deformations of isotropic materials. II. Some uniqueness theorems for pure, homogeneous deformation, Phil. Trans. Roy. Soc., A240, 491–508.Google Scholar
  73. G. Ronca (1977), Cooperative diffusion in a temporary network, Rheol. Acta, 16, 581–597.CrossRefGoogle Scholar
  74. R. Roscoe (1965), The steady elongation of elasto-viscous liquids, Brit. J. Appl. Phys., 16, 1567–1571.CrossRefGoogle Scholar
  75. M. T. Shaw (1976), Extensional viscosity of melts using a programmable tensile testing machine, VIIth Int. Congr. Rheol., 304–305.Google Scholar
  76. J. F. Stevenson and R. B. Bird (1971), Elongational viscosity of nonlinear elastic dumbbell suspensions, Trans. Soc. Rheol., 15, 135–145.CrossRefGoogle Scholar
  77. J. F. Stevenson (1972), Elongational flow of polymer melts, AIChE J., 18, 540–547.CrossRefGoogle Scholar
  78. V. H. Stott (1925), The viscosity of glass, J. Soc. Glass Technol. Trans., 9, 207–225.Google Scholar
  79. R. I. Tanner (1969), Comparative studies of some simple viscoelastic theories, Trans. Soc. Rheol., 12, 155–182.CrossRefGoogle Scholar
  80. R. I. Tanner and R. L. Ballman (1969), Prediction of polystyrene melt tensile behaviour, Ind. Eng. Chem. Fundam., 8, 588–589.CrossRefGoogle Scholar
  81. R. I. Tanner (1970), Prediction of polystyrene melt tensile behaviour, Ind. Eng. Chem. Fundam., 9, 688.CrossRefGoogle Scholar
  82. F. T. Trouton (1906), On the coefficient of viscous traction and its relation to that of viscosity, Proc. Roy. Soc, A77, 426–440.Google Scholar
  83. G. V. Vinogradov, A. I. Leonov and A. N. Prokunin (1969), On uniaxial extension of an elasto-viscous cylinder, Rheol. Acta, 8, 482–490.CrossRefGoogle Scholar
  84. G. V. Vinogradov, B. V. Radushkevich and V. D. Fikhman (1970a), Extension of elastic liquids: polyisobutylene, J. Polym. Sci., A2, 8, 1–17.Google Scholar
  85. G. V. Vinogradov, V. D. Fikhman, B. V. Radushkevich and A. Ya Malkin (1970b), Viscoelastic and relaxation properties of a polystyrene melt in axial extension, J. Polym. Sci., A2, 8, 657–678.Google Scholar
  86. G. V. Vinogradov, V. D. Fikhman and B. V. Radushkevich (1972), Uniaxial extension of polystyrene at true constant stress, Rheol. Acta, 11, 286–291.CrossRefGoogle Scholar
  87. M. H. Wagner (1976), Analysis of time-dependent non-linear stress growth data for shear and elongational flow of a low-density branched polyethylene melt, Rheol. Acta, 15, 136–142.CrossRefGoogle Scholar
  88. M. H. Wagner (1978), A constitutive analysis of uniaxial elongational flow data of a low-density polyethylene melt, J. Non-Newtonian Fluid Mech., 4, 39–55.CrossRefGoogle Scholar
  89. M. H. Wagner, T. Raible and J. Meissner (1979), Tensile stress overshoot in uniaxial extension of a LDPE melt, Rheol. Acta, 18, 427–428.CrossRefGoogle Scholar
  90. J. L. White (1964), Dynamics of viscoelastic fluids, melt fracture, and the rheology of fiber spinning, J. Appl. Polym. Sci., 8, 2339–2357.CrossRefGoogle Scholar
  91. J. L. White (1976), Dynamics and structure development during melt spinning of fibers, J. Soc. Rheol. Japan, 4, 137–148.Google Scholar
  92. J. L. White (1978), Experimental study of elongational flow of polymer melts, Appl. Polym. Symp., 33, 31–47.Google Scholar
  93. J. L. White (1979), Personal communication.Google Scholar
  94. M. Yamamoto (1957), The viscoelastic properties of network structure. II. Structural viscosity, J. Phys. Soc. Japan, 12, 1148–1158.CrossRefGoogle Scholar
  95. L. J. Zapas and T. Craft (1965), Correlation of large longitudinal deformations with different strain histories, J. Res. Nat. Bur. Stand., 69A, 541–546.Google Scholar
  96. A. Ziabicki (1976), Fundamentals of fibre formation. The science of fibre spinning and drawing, Wiley-Interscience, London.Google Scholar
  97. A. Ziabicki (1980), Fibers, Proc. VIIIth Int. Congr. Rheol., Naples.Google Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • C. J. S. Petrie
    • 1
  • J. M. Dealy
    • 2
  1. 1.Department of Engineering MathematicsUniversity of Newcastle upon TyneEngland
  2. 2.Department of Chemical EngineeringMcGill UniversityMontrealCanada

Personalised recommendations