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arXiv · 2411.11823

Steady inhomogeneous shear flows as mechanical phase transitions

Thomas Speck
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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.

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Thomas Speck. 2024-11-18. Steady inhomogeneous shear flows as mechanical phase transitions. https://doi.org/10.1103/physreve.111.015430

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