Linear instability of planar shear banded flow

Area of Science:

• Rheology and fluid dynamics
• Nonlinear continuum mechanics

Background:

• Shear banding is a common phenomenon in complex fluids, leading to the formation of distinct low- and high-strain regions.
• Understanding the stability of these bands is crucial for predicting fluid behavior under shear.
• The nonlocal Johnson-Segalman model provides a theoretical framework for studying shear banding.

Purpose of the Study:

• To investigate the linear stability of planar shear banded flow within the nonlocal Johnson-Segalman model.
• To analyze the growth of perturbations and determine the conditions for interface instability.
• To characterize the nature of the instability using unstable eigenfunctions.

Main Methods:

• Linear stability analysis of the nonlocal Johnson-Segalman model.
• Perturbation analysis with wave vectors in the plane of the banding interface.
• Numerical computation of unstable eigenfunctions.

Main Results:

• The planar shear banded flow interface is found to be linearly unstable.
• Perturbations grow over a range of wave vectors, confirming the instability.
• The study provides insights into the characteristics of the unstable eigenfunctions.

Conclusions:

• The interface in planar shear banded flow is inherently unstable under the nonlocal Johnson-Segalman model.
• The findings suggest that shear banding structures are dynamic and can evolve over time.
• Further investigation into model H stability provides context for phase-separated domains in shear flow.