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The role of the Gordon–Schowalter derivative term in the constitutive models—improved flexibility of the modified XPP model

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Abstract

Constitutive models that complete the set of equations describing the flow of polymer melts should respect objective thermodynamics and stability conditions ensuring their validity in the whole range of possible deformation flow. However, in practice, a very good description of flow situations can be achieved with the models not complying with the physical assumptions in all respects. Analogously to the term characterizing yield stress in empirical viscoplastic models, the term represented by the Gordon–Schowalter (GS) derivative in the differential constitutive models contributes to better fitting the experimental data, especially shear thinning. Efficiency of the recently presented modified eXtended Pom-Pom model (just one non-linear parameter per mode) implementing the GS derivative term (one additional non-affine motion parameter per mode) is improved (documented on LDPE, HDPE, and polyvinyl butyral (PVB) materials), and a comparison with the exponential Phan-Tien–Tanner (PTT) and PTT-XPP models (a priori containing the GS derivative term) are presented.

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References

  1. Larson RG (1988) Constitutive equations for polymer melts and solutions. Butterworth, Stoneham

    Google Scholar 

  2. Doi M, Edwards S (1986) The theory of polymer dynamics. Oxford Science publications, Oxford University Press, Oxford

    Google Scholar 

  3. Dealy JM, Larson RG (2006) Structure and rheology of molten polymers. Carl Hanser Verlang, Munich

    Book  Google Scholar 

  4. Johnson MW, Segalman D (1977) Model for visoelastic fluid behaviour which allows non-affine deformation. J Non-Newtonian Fluid Mech 2:255–270

    Article  Google Scholar 

  5. Phan-Thien N, Tanner RI (1977) A new constitutive equation derived from network theory. J Non-Newtonian Fluid Mech 2:353–365

    Article  Google Scholar 

  6. Stephanou PS, Baig C, Mavrantzas VG (2009) A generalized differential constitutive equation for polymer melts based on principles of nonequilibrium thermodynamics. J Rheol 53:309–337

    Article  CAS  Google Scholar 

  7. Pivokonsky R, Zatloukal M, Filip P (2006) On the predictive/fitting capabilities of the advanced differential constitutive equations for branched LDPE melts. J Non-Newtonian Fluid Mech 135:58–67

    Article  CAS  Google Scholar 

  8. Pivokonsky R, Zatloukal M, Filip P (2008) On the predictive/fitting capabilities of the advanced differential constitutive equations for linear polyethylene melts. J Non-Newtonian Fluid Mech 150:56–64

    Article  CAS  Google Scholar 

  9. Vlassopoulos D, Hatzikiriakos SG (1995) A generalized Giesekus constitutive model with retardation time and its association to the spurt effect. J Non-Newtonian Fluid Mech 57:136–136

    Article  Google Scholar 

  10. Arsac A, Carrot C, Guillet J, Revenu P (1994) Problems originating from the use of the Gordon-Schowalter derivative in the Johnson-Segalman and related models in various shear flow situations. J Non-Newtonian Fluid Mech 55:21–36

    Article  CAS  Google Scholar 

  11. Ferri D, Lomellini P (1999) Melt rheology of randomly branched polystyrenes. J Rheol 43:1355–1377

    Article  CAS  Google Scholar 

  12. Venkatraman S, Okano M, Nixon A (1990) A comparison of torsional and capillary rheometry for polymer melts—the Cox-Merz rule revisited. Polym Eng Sci 30:308–313

    Article  CAS  Google Scholar 

  13. Utracki LA, Gendron R (1984) Pressure oscillation during extrusion of polyethylenes. J Rheol 28:601–623

    Article  CAS  Google Scholar 

  14. Pivokonsky R, Filip P (2014) Predictive/fitting capabilities of differential constitutive models for polymer melts—reduction of nonlinear parameters in the eXtended Pom-Pom model. Colloid Polym Sci 292:2753–2763

    Article  CAS  Google Scholar 

  15. Shin DM, Lee JS, Kim JM, Jung HW, Hyun JC (2007) Transient and steady-state solutions of 2D viscoelastic nonisothermal simulation model of film casting process via finite element method. J Rheol 51:393–407

    Article  CAS  Google Scholar 

  16. Glomsaker T, Hincrichsen EL, Irgens F, Thorsteinsen P (2000) Numerical simulation of extrusion of S-PVC formulations in a capillary rheometer. Rheol Acta 39:80–96

    Article  CAS  Google Scholar 

  17. Kajiwara T, Ninomyia S, Kuwano Y, Funatsu K (1993) Numerical simulation of converging flow of polymer melts through a tapered slit die. J Non-Newtonian Fluid Mech 48:111–124

    Article  CAS  Google Scholar 

  18. Echendu SOS, Tamaddon-Jahromi HR, Webster MF (2014) Viscoelastic computations for reverse roll coating with dynamic wetting lines and the Phan-Thien-Tanner models. Rheol Acta 53:315–331

    Article  CAS  Google Scholar 

  19. Kim JH, Lyu MY (2014) Predictions of flow behaviors and entrance pressure drop characteristics of rubber compound in a capillary die using various rheological models. Polym Eng Sci 54:2441–2448

    Article  CAS  Google Scholar 

  20. Verbeeten WMH, Peters GWM, Baaijens FPT (2001) Differential constitutive equations for polymer melts: the extended Pom-Pom model. J Rheol 45:823–843

    Article  CAS  Google Scholar 

  21. Tanner RI, Nasseri S (2003) Simple constitutive models for linear and branched polymers. J Non-Newtonian Fluid Mech 116:1–17

    Article  CAS  Google Scholar 

  22. Tanner RI (2006) On the congruence of some network and pom-pom models. Korea Aust Rheol J 18:9–14

    Google Scholar 

  23. Pivokonsky R, Zatloukal M, Filip P, Tzoganakis C (2009) Rheological characterization and modeling of linear and branched metallocene polypropylenes prepared by reactive processing. J Non-Newtonian Fluid Mech 156:1–6

    Article  CAS  Google Scholar 

  24. Zatloukal M (2003) Differential viscoelastic constitutive equations for polymer melts in steady shear and elongational flows. J Non-Newtonian Fluid Mech 113:209–227

    Article  CAS  Google Scholar 

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Acknowledgments

The authors wish to acknowledge the RVO: 67985874.

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Correspondence to Radek Pivokonsky.

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Pivokonsky, R., Filip, P. & Zelenkova, J. The role of the Gordon–Schowalter derivative term in the constitutive models—improved flexibility of the modified XPP model. Colloid Polym Sci 293, 1227–1236 (2015). https://doi.org/10.1007/s00396-015-3498-7

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  • DOI: https://doi.org/10.1007/s00396-015-3498-7

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