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Considering a Non-Constant Anisotropicity Parameter in the Giesekus Model.

Fatemeh Karami1, Pavlos S Stephanou2

  • 1Department of Mechanical Engineering, Lorestan University, Khorramabad 68151-44316, Iran.

Polymers
|September 27, 2025
PubMed
Summary

The Giesekus model was modified to allow a variable anisotropicity parameter, improving predictions for the second normal stress coefficient in shear flow. This rheological model modification aligns better with experimental data, particularly in start-up flows.

Keywords:
Curtiss–Bird modelGiesekus modelfriction tensorlink tension coefficientmobility tensorpolymer meltsrheological model

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Area of Science:

  • Rheology
  • Polymer Physics
  • Fluid Mechanics

Background:

  • The Giesekus model is a widely used constitutive model in rheology.
  • The anisotropicity parameter in the Giesekus model was traditionally treated as a constant.
  • Recent findings suggest that the anisotropicity parameter may vary.

Purpose of the Study:

  • To investigate the implications of a variable anisotropicity coefficient in the Giesekus model.
  • To develop a modified Giesekus model with a non-constant anisotropicity parameter.
  • To compare the predictions of the modified model with experimental data.

Main Methods:

  • Modification of the Giesekus constitutive equation to incorporate a variable anisotropicity parameter.
  • Analysis of the model's predictions for the second normal stress coefficient in simple shear flow.
  • Comparison with existing experimental data in the literature.

Main Results:

  • The modified Giesekus model with a variable anisotropicity coefficient shows significant differences in predicting the second normal stress coefficient.
  • A key finding is the shift of the linear viscoelastic envelope of the second normal stress coefficient to higher values.
  • This shift is particularly notable in start-up simple shear flow scenarios.

Conclusions:

  • Allowing the anisotropicity parameter to vary in the Giesekus model leads to improved predictions for rheological behavior.
  • The modified model provides results more consistent with experimental observations, especially for transient shear flows.
  • This work presents a novel rheological model with potential applications in polymer processing and fluid dynamics.