Considering a Non-Constant Anisotropicity Parameter in the Giesekus Model

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.