Steady inhomogeneous shear flows as mechanical phase transitions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910942696046592 |
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| author | Speck, Thomas |
| author_facet | Speck, Thomas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11823 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Steady inhomogeneous shear flows as mechanical phase transitions Speck, Thomas Statistical Mechanics 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. |
| title | Steady inhomogeneous shear flows as mechanical phase transitions |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2411.11823 |