Two-dimensional perturbations in a scalar model for shear banding
1Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands. j.l.a.dubbeldam@ewi.tudelft.nl
The European Physical Journal. E, Soft Matter
|August 1, 2009
Summary
This study analyzes a simplified shear banding model without normal stresses, revealing a stable state. This contrasts with models including normal stresses, suggesting their role in instabilities.
Area of Science:
- Rheology
- Continuum Mechanics
- Material Science
Background:
- Shear banding is a critical phenomenon in non-Newtonian fluids and solids.
- Understanding the stability of shear banding is crucial for predicting material behavior.
- Existing models like the Johnson-Segalman model incorporate normal stress effects, leading to complex stability analyses.
Purpose of the Study:
- To investigate the stability of shear banding in a simplified model.
- To elucidate the role of normal stresses in shear banding instabilities.
- To provide a contrasting perspective to existing models.
Main Methods:
- Analytical study of a toy model for shear banding.
- Utilized a piecewise linear approximation of the flow curve (shear stress vs. shear rate).
- Examined linear stability against general two-dimensional perturbations.
Main Results:
- The simplified model exhibits multiple stationary states.
- One stationary state was found to be linearly stable.
- Normal stress-free models show different stability characteristics compared to models with normal stresses.
Conclusions:
- Normal stress effects are likely responsible for the linear instabilities observed in the Johnson-Segalman model.
- Simplified models can offer valuable insights into complex phenomena like shear banding.
- Further research into the precise mechanisms of normal stress influence is warranted.
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