Steady inhomogeneous shear flows as mechanical phase transitions

Area of Science:

• Non-equilibrium statistical mechanics
• Fluid dynamics
• Materials science

Background:

• Inhomogeneous flows and shear banding lack comprehensive theoretical understanding.
• Existing frameworks do not adequately address systems far from thermal equilibrium.
• A need exists for a mechanical equilibrium approach.

Purpose of the Study:

• To develop a theoretical framework for understanding inhomogeneous flows and shear banding.
• To apply a mechanical equilibrium concept to non-equilibrium systems.
• To illustrate the framework with applications in complex fluids and solid-melt systems.

Main Methods:

• Revisiting models of fluids in stationary states obeying mechanical equilibrium.
• Utilizing a nonlocal constitutive relation.
• Applying the concept of a "mechanical phase transition" and mapping to a dynamical system via an integrating factor.

Main Results:

• A novel mechanical framework for inhomogeneous systems away from thermal equilibrium.
• Successful application to shear banding in complex fluids.
• Demonstration of solid-melt coexistence using the proposed framework.

Conclusions:

• The developed mechanical framework offers a new route to describe inhomogeneous systems.
• This approach provides insights into shear banding and phase coexistence phenomena.
• The study contributes to a deeper understanding of non-equilibrium fluid mechanics.