Steady inhomogeneous shear flows as mechanical phase transitions
arXiv:2411.11823 · doi:10.1103/PhysRevE.111.015430
Abstract
Inhomogeneous flows and shear banding are of interest for a range of applications but have been eluding a comprehensive theoretical understanding, mostly due to the lack of a framework comparable to equilibrium statistical mechanics. Here we revisit models of fluids that reach a stationary state obeying mechanical equilibrium. Starting from a non-local constitutive relation, we apply the idea of a "mechanical phase transition" and map the constitutive relation onto a dynamical system through an integrating factor. We illustrate this framework for two applications: shear banding in strongly thinning complex fluids and the coexistence of a solid with its sheared melt. Our results contribute to the growing body of work following a mechanical route to describe inhomogeneous systems away from thermal equilibrium.
References in corpus (20)
- Shear Banding of Complex Fluids
- A random critical point separates brittle and ductile yielding transitions in amorphous materials
- Shear localization in a model glass
- Generalized Thermodynamics of Phase Equilibria in Scalar Active Matter
- Shear banding and flow-concentration coupling in colloidal glasses
- Cluster phases and bubbly phase separation in active fluids: Reversal of the Ostwald process
- Generalized thermodynamics of Motility-Induced Phase Separation: Phase equilibria, Laplace pressure, and change of ensembles
- Flow phase diagrams for concentration-coupled shear banding
- Quantitative measurement of density in a shear band of metallic glass monitored along its propagation direction
- Spontaneous formation of permanent shear bands in a mesoscopic model of flowing disordered matter
- Shear bands as manifestation of a criticality in yielding amorphous solids
- Shear banding in soft glassy materials
- Colloidal Hard Spheres: Triumphs, Challenges and Mysteries
- Inhomogeneous shear flows in soft jammed materials with tunable attractive forces
- Mechanical Theory of Nonequilibrium Coexistence and Motility-Induced Phase Separation
- Shear banding of colloidal glasses - a dynamic first order transition?
- Phase Coexistence of Complex Fluids in Shear Flow
- Coexistence of active Brownian discs: Van der Waals theory and analytical results
- Classical Nucleation Theory for the Crystallization Kinetics in Sheared Liquids
- Coexistence of uniform and oscillatory states resulting from nonreciprocity and conservation laws