Viscosity and Normal Stress Differences

  • John M. Dealy
  • Jian Wang
Part of the Engineering Materials and Processes book series (EMP)


Viscosity is the property most used with molten plastics. It relates the shear stress to the shear rate in steady simple shear flow, which is the deformation generated between two parallel plates, one of which undergoes linear displacement. For viscoelastic fluids, two other quantities are needed for a complete description of the stress field, and these are the first and second normal stress differences. The viscosity and the two normal stress differences are functions of shear rate that are called the viscometric functions, and flows governed by these are called viscometric flow s. In addition to simple shear, other viscometric flows include flow in straight channels and rotational flows between concentric cylinders, between a cone and plate and between two disks. Flow in an extruder is dominated by the viscometric functions, mainly the viscosity. This chapter describes the dependence of viscosity on shear rate, temperature, molecular weight and its distribution, tacticity, comonomer content, and long-chain branching.


Shear Rate Molecular Weight Distribution Complex Viscosity Shift Factor Normal Stress Difference 
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  1. 1.
    Bird RB, Armstrong RC, Hassager O (1987) Dynamics of Polymeric Liquids, vol 1. Wiley, New YorkGoogle Scholar
  2. 2.
    Meissner J (1971) Deformationsverhalten der Kunststoffe im flüssigen und im festen Zustand. Kunststoffe 61:576–582Google Scholar
  3. 3.
    Stratton RA (1966) The dependence of non-Newtonian viscosity on molecular weight for “Monodisperse” polystyrene. J Colloid Interface Sci 22:517–530CrossRefGoogle Scholar
  4. 4.
    Cross MM (1965) Rheology of non-Newtonian fluids: a new flow equation for pseudoplastic systems. J Coll Sci 20:417–437CrossRefGoogle Scholar
  5. 5.
    Carreau PJ (1972) Rheological equations from molecular network theories. Trans Soc Rheol1 6:99–127Google Scholar
  6. 6.
    Hieber CA, Chiang HH (1992) Shear-rate-dependence modeling of polymer melt viscosity. Polym Eng Sci 14:931–938CrossRefGoogle Scholar
  7. 7.
    Yasuda KY, Armstrong RC, Cohen RE (1981) Shear flow properties of concentrated solutions of linear and star-branched polystyrenes. Rheol Acta 20:163–178CrossRefGoogle Scholar
  8. 8.
    Elberli B, Shaw MT (1978) Time constants from shear viscosity data. J Rheol 22:561–570CrossRefGoogle Scholar
  9. 9.
    Plumley TA, Lai S, Betso SR, Knight GW (1994) Rheological modeling of Insite technology polymers. SPE ANTEC Tech Papers 40:1221–1224Google Scholar
  10. 10.
    Wang J (2010) Double cross model—A novel way to model viscosity curves, Society of Rheology. 82nd annual meeting, Santa Fe, NMGoogle Scholar
  11. 11.
    Cox WP, Merz EH (1958) Correlation of dynamic and steady flow viscosities. J Polym Sci 28:619–621CrossRefGoogle Scholar
  12. 12.
    Utracki LA, Gendron R (1984) Pressure oscillation during extrusion of polyethylenes. J Rheol 28:601–623CrossRefGoogle Scholar
  13. 13.
    Venkatraman S, Okano M, Nixon AA (1990) A comparison of torsional and capillary rheometry for polymer melts: the Cox-Merz rule revisited. Polym Eng Sci 30:308–313CrossRefGoogle Scholar
  14. 14.
    Park HE, Dealy JM (2006) Effect of pressure and supercritical CO2 on the viscosity of Polyethylene. Macromolecules 39:5438–5452CrossRefGoogle Scholar
  15. 15.
    Park HE, Dealy JM, Münstedt H (2006) Influence of long-chain branching on time-pressure and time-temperature shift factors for polystyrene and polyethylene. Rheol Acta 46:153–159CrossRefGoogle Scholar
  16. 16.
    Berry GC, Fox TG (1968) The viscosity of polymers and their concentrated solutions. Adv Polym Sci 5:261–357CrossRefGoogle Scholar
  17. 17.
    Bartels CR, Crist B, Fetters LJ, Graessley WW (1986) Self-diffusion in branched polymer melts. Macromol 19:785–793CrossRefGoogle Scholar
  18. 18.
    Struglinski MJ, Graessley WW (1985) Effects of polydispersity on the linear viscoelastic properties of entangled polymers 1: experimental observations for binary mixtures of linear polybutadiene. Macromol 18:2630–2643CrossRefGoogle Scholar
  19. 19.
    Kumar R, Khanna YP (1989) SPE Tech. Papers 35, 1675Google Scholar
  20. 20.
    Shroff AR, Mavridis H (1995) New measures of polydispersity from rheological data on polymer melts. J Appl Polym Sci 57:1605–1626CrossRefGoogle Scholar
  21. 21.
    Fuchs K, Chr Friedrich, Weese J (1996) Viscoelastic properties of narrow-distribution poly(methylmethacrylates). Macromol 29:5893–5901CrossRefGoogle Scholar
  22. 22.
    Huang CL, Chen YC, Hsiao TJ, Tsai JC, Wang C (2011) Effect of tacticity on viscoelastic properties of poplystyrene. Macromol 44:6155–6161CrossRefGoogle Scholar
  23. 23.
    Wood-Adams P, Dealy JM, deGroot AW, Redwine OD (2000) Rheological properties of metallocene polyethylenes. Macromol 33:7489–7499CrossRefGoogle Scholar
  24. 24.
    Wood-Adams P, Costeux S (2001) Thermorheological behavior of polyethylene: effects of microstructure and long chain branching. Macromol 34:6281–6290CrossRefGoogle Scholar
  25. 25.
    Garcia-Franco CA, Harrington BA, Lohse DJ (2006) Effect of short-chain branching on the rheology of polyolefins. Macromol 39:2710–2717CrossRefGoogle Scholar
  26. 26.
    Dealy JM, Larson RG (2006) Structure and rheology of molten polymers. Hanser Publishers, MunichGoogle Scholar
  27. 27.
    Pearson DS, Helfand E (1984) Viscoelastic properties of star-shaped polymers. Macromol 17:888–895CrossRefGoogle Scholar
  28. 28.
    Kraus G, Gruver JT (1965) Rheological properties of multichain polybutadienes. J Polym Sci A 3:105–122Google Scholar
  29. 29.
    Graessley WW, Roovers J (1979) Melt Rheology of four-arm and six-arm star polystyrenes. Macromol 12:959–965CrossRefGoogle Scholar
  30. 30.
    Gell CB, Graessley WW, Efstratiadis V, Pitsikalis M, Kadjichristidis N (1997) Viscoelasticity and self-diffusion in melts of entangled asymmetric star polymers. J Polym Sci, Part B: Polym Phys 35:1943–1954CrossRefGoogle Scholar
  31. 31.
    Stevens JC (1994) INSITE™ catalyst structure/activity relationships for olefin polymerization. Stud Surf Sci Catal 89:277–284; Constrained geometry and other single site metallocene polyolefin catalysts: A revolution in olefin polymerization. Ibid. (1996) 101:11–20Google Scholar
  32. 32.
    Lai SY, Wilson JR, Knight JR, Stevens JC (1993) Elastic substantially linear olefin polymers. US Patent 5(380):810Google Scholar
  33. 33.
    Soares JBP, Hamielec AE (1996) Bivariate chain length and long chain branching distribution for copolymerization of olefins and polyolefin chains containing terminal double-bonds. Macromol Theory Simul 5:547–572CrossRefGoogle Scholar
  34. 34.
    Soares JBP, Hamielec AE (1997) The chemical composition component of the distribution of chain length and long chain branching for copolymerization of olefins and polyolefin chains containing terminal double bonds. Macromol Theory Simul 6:591–596CrossRefGoogle Scholar
  35. 35.
    Read DJ, McLeish TCB (2001) Molecular rheology and statistics of long chain branched metallocene-catalyzed polyolefins. Macromol 34:1928–1945Google Scholar
  36. 36.
    Costeux S, Wood-Adams P, Beigzadeh D (2002) Molecular structure of metallocene-catalyzed polyethylene: rheologically relevant representation of branching architecture in single catalyst and blended systems. Macromol 35:2514–2528CrossRefGoogle Scholar
  37. 37.
    Soares JBP (2004) Polyolefins with long chain branches made with single-site coordination catalysts: a review of mathematical modeling techniques for polymer microstructure. Macromol Mater Eng 289:70–87CrossRefGoogle Scholar
  38. 38.
    Wood-Adams PM, Dealy JM (2000) Using rheological data to determine the branching level in metallocene polyethylenes. Macromol 33:7481–7488CrossRefGoogle Scholar
  39. 39.
    Robertson CG, García-Franco CA, Srinivas S (2004) Extent of branching from linear viscoelasticity of long-chain branched polymers. J Polym Sci, Part B: Polym Phys 42:1671–1684CrossRefGoogle Scholar
  40. 40.
    Auhl D, Stange J, Münstedt H, Krause B, Voigt D, Lederer A, Lappan U, Lunkwitz K (2004) Long-chain branched polypropylenes by electron beam irradiation and their rheological properties. Macromol 37:9465–9472CrossRefGoogle Scholar
  41. 41.
    Gabriel C, Münstedt H (2003) Strain hardening of various polyolefins in uniaxial elongational flow. J Rheol 47:619–630CrossRefGoogle Scholar
  42. 42.
    Gabriel C, Kokko E, Löfgren B, Seppälä J, Münstedt H (2003) Analytical and rheological characterization of long-chain branched metallocene-catalyzed ethylene homopolymers. Polymer 43:6383–6390CrossRefGoogle Scholar
  43. 43.
    Wang J, Mangnus M, Yau W, deGroot W, Karjala T, Demirors M (2008) Structure-property relationships of LDPE. SPE ANTEC Tech Papers, pp 878–881Google Scholar
  44. 44.
    Gabriel C, Lilge D (2006) Molecular mass dependence of the zero shear-rate viscosity of LDPE melts: evidence of an exponential behavior. Rheol Acta 45:995–1002CrossRefGoogle Scholar
  45. 45.
    Schweizer T, van Meerveld J, Öttinger HC (2004) Nonlinear shear rheology of polystyrene melt with narrow molecular weight distribution—experiment and theory. J Rheol 48:1345–1363CrossRefGoogle Scholar
  46. 46.
    Lee CS, Magda JJ, DeVries KL, Mays JW (1992) Measurements of the second normal stress difference for star polymers with highly entangled branches. Macromol 25:4744–4750CrossRefGoogle Scholar
  47. 47.
    Lodge AS (1996) On-line measurement of elasticity and viscosity in flowing polymeric liquids. Rheol Acta 35:110–116CrossRefGoogle Scholar
  48. 48.
    Xu J, Costeux S, Dealy JM, De Decker MN (2007) Use of a sliding plate rheometer to measure the first normal stress difference at high shear rates. Rheol Acta 46:815–824CrossRefGoogle Scholar
  49. 49.
    Laun HM (1986) Prediction of elastic strains of polymers melts in shear and elongation. J Rheol 30:459–501CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.MontrealCanada
  2. 2.FreeportUSA

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