Special Features of Nonlinear Behavior of a Polymer Solution on Large Periodic Deformations

Study of the behavior of polymer solution flows in the region of nonlinear viscoelasticity allows one to more accurately evaluate the adequacy of rheological models and to describe the rheological properties of a material in more detail. The nonlinear viscoelastic properties manifesting themselves in the process of studying the behavior of a polymer material on significant deformations were investigated with the aid of time dependences of shear stresses calculated at different amplitudes. The present work considers the applicability of the modified Vinogradov–Pokrovskii rheological model to describing the oscillating shearing of polymer fluids with a large amplitude. It has been established that on increase of the deformation amplitude, the shear stresses cease to be a true harmonic, and one observes the appearance of a "step" on their left front, which speaks of the substantial nonlinearity in the behavior of the sample. The obtained theoretical dependences are compared with experimental data for a 5% solution of polyethylene oxide in dimethyl sulfoxide. The comparison was made as by plotting the time dependences of normalized stresses, so by analyzing Lissajous figures. Despite the simplicity, the modifi ed Vinogradov–Pokrovskii rheological model adequately describes the behavior of polymer materials on significant periodic deformations.

This is a preview of subscription content, log in to check access.


  1. 1.

    V. N. Pokrovskii, Mesoscopic Theory of Polymer Dynamics, 2nd edn., Springer, Berlin (2010).

    Google Scholar 

  2. 2.

    A. Ya. Malkin and A. I. Isaev, Rheology: Concept, Methods, Applications [in Russian], Professiya, St. Petersburg (2007).

  3. 3.

    H. Giesekus, A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility, J. Non-Newtonian Fluid Mech., 11, 69–109 (1982).

    Article  Google Scholar 

  4. 4.

    A. I. Leonov, Analysis of simple constitutive equations for viscoelastic liquids, J. Non-Newtonian Fluid Mech., 42, 323–350 (1992).

    Article  Google Scholar 

  5. 5.

    N. J. Inkson, T. C. B. McLeish, O. G. Harlen, and D. J. Groves, Predicting low density polyethylene melt rheology in elongational and shear flows with "Pom−Pom" constitutive equations, J. Rheol., 43, 873−896 (1999).

    Article  Google Scholar 

  6. 6.

    Yu. A. Altukhov, I. É. Golovicheva, and G. V. Pyshnograi, Molecular approach in the dynamics of linear polymers: Theory and numerical experiment, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 1, 3–13 (2000).

  7. 7.

    R. Pivokonsky and P. Filip, 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 (2014).

    Article  Google Scholar 

  8. 8.

    A. Ya. Malkin and V. G. Kulichikhin, Application of the method of high-amplitude harmonic effects for the analysis of the properties of polymer materials in nonlinear region of mechanical behavior, Vysokomol. Soedin., Ser. A, 56, No. 1, 99–112 (2014).

  9. 9.

    H. Ewoldt Randy, A. E. Hosoi, and Gareth H. McKinley, New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear, J. Rheol., 52, Issue 6, 1427−1758 (2008).

  10. 10.

    J. Zelenkova, R. Pivokonsky, and P. Filip, Two ways to examine differential constitutive equations: Initiated on steady or initiated on unsteady (LAOS) shear characteristics, Polymers, 9 (6), 205 (2017).

    Google Scholar 

  11. 11.

    K. B. Koshelev, G. V. Pyshnograi, and M. Yu. Tolstykh, Modeling three-dimensional flow of polymer melt in a convergent channel with rectangular cross section, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 3, 3−11 (2015).

  12. 12.

    D. A. Merzlikina, G. V. Pyshnograi, R. Pivokonskii, and P. Filip, Rheological model for describing viscometric flows of melts of branched polymers, J. Eng. Phys. Thermophys., 89, No. 3, 652−659 (2016).

    Article  Google Scholar 

  13. 13.

    A. S. Gusev, M. A. Makarova, and G. V. Pyshnograi, Mesoscopic equation of state of polymer systems and description of the dynamic characteristics based on it, J. Eng. Phys. Thermophys., 78, No. 5, 892−898 (2005).

    Article  Google Scholar 

  14. 14.

    G. V. Pyshnograi, A. S. Gusev, and V. N. Pokrovskii, Constitutive equations for weakly entangled linear polymers, J. Non-Newtonian Fluid Mech., 164, Nos. 1−3, 17−28 (2009).

  15. 15.

    A. R. Payne, The dynamic properties of carbon black-loaded natural rubber vulcanizates. Part I, J. Appl. Polym. Sci., 6, 57–63 (1962).

  16. 16.

    W. P. Fletcher and A. N. Gent, Non-linearity in the dynamic properties of vulcanized rubber compounds, Trans. Inst. Rubber Ind., 29, 266−280 (1953).

    Google Scholar 

  17. 17.

    J. Harris, Response of time-dependent materials to oscillatory motion, Nature, 207, 744 (1965).

    Article  Google Scholar 

  18. 18.

    W. Philippoff, Vibrational measurements with large amplitudes, Trans. Soc. Rheol., 10, 317 (1966).

    Article  Google Scholar 

  19. 19.

    I. F. MacDonald, B. D. Marsh, and E. Ashare, Rheological behavior for large amplitude oscillatory shear motion, Chem. Eng. Sci., 24, 1615−1625 (1969).

    Article  Google Scholar 

  20. 20.

    S. Onogi, T. Masuda, and T. Matsumoto, Nonlinear behavior of viscoelastic materials. I: Disperse systems of polystyrene solution and carbon black, Trans. Soc. Rheol., 14, 275−294 (1970).

  21. 21.

    J. S. Dodge and I. M. Krieger, Oscillatory shear of nonlinear fluids. I: Preliminary investigation, Trans. Soc. Rheol., 15, 589−601 (1971).

  22. 22.

    T. Matsumoto, Y. Segawa, Y. Warashina, and S. Onogi, Nonlinear behavior of viscoelastic materials. II: The method of analysis and temperature dependence of nonlinear viscoelastic functions, Trans. Soc. Rheol., 17, 47−62 (1973).

  23. 23.

    H. Komatsu, T. Mitsui, and S. Onogi, Nonlinear viscoelastic properties of semisolid emulsions, Trans. Soc. Rheol., 17, 351−364 (1973).

    Article  Google Scholar 

  24. 24.

    T. T. Tee and J. M. Dealy, Nonlinear viscoelasticity of polymer melts, J. Rheol., 19, 595−615 (1975).

    Google Scholar 

  25. 25.

    K. Walters and T. E. R. Jones, Further studies on the usefulness of the Weissenberg rheogoniometer, in: S. Onogi (Ed.), Proc. 5th Int. Congress Rheol., 337−350 (1970).

  26. 26.

    K. S. Cho, K. Hyun, K. H. Ahn, and S. J. Lee, A geometrical interpretation of large amplitude oscillatory shear response, J. Rheol., 49, 747−758 (2005).

    Article  Google Scholar 

  27. 27.

    O. C. Klein, P. Venema, L. Sagis, and E. Van der Linden, Rheological discrimination and characterization of carrageenans and starches by Fourier transform-rheology in the non-linear viscous regime, J. Non-Newtonian Fluid Mech., 151, 145−150 (2008).

    Article  Google Scholar 

  28. 28.

    A. V. Pogorelov, Analytical Geometry [in Russian], 3rd edn., Nauka, Moscow (1968).

    Google Scholar 

Download references

Author information



Corresponding authors

Correspondence to N. A. Cherpakova or H. N. A. Al Joda.

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 93, No. 3, pp. 637–645, May–June, 2020.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Pyshnograi, G.V., Cherpakova, N.A. & Al Joda, H.N.A. Special Features of Nonlinear Behavior of a Polymer Solution on Large Periodic Deformations. J Eng Phys Thermophy 93, 617–625 (2020). https://doi.org/10.1007/s10891-020-02159-8

Download citation


  • rheology
  • rheological model
  • nonlinear viscoelasticity
  • oscillations
  • shear
  • polymer solutions