Microscopic derivation of a one-dimensional lubrication model with roughness
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917207549673472 |
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| author | Lefebvre-Lepot, Aline Mehmood, Muhammed Ali Perrin, Charlotte Zatorska, Ewelina |
| author_facet | Lefebvre-Lepot, Aline Mehmood, Muhammed Ali Perrin, Charlotte Zatorska, Ewelina |
| contents | We derive a hydrodynamic model for the motion of inertial particles with a spherical hard core, interacting through lubrication forces and pairwise repulsive forces. The repulsion arises from the assumption that each particle is surrounded by a thin rough layer of reduced permeability. We prove that, as the number of particles tends to infinity (and their size tends to 0), the microscopic dynamics converges to a macroscopic hydrodynamic model in which congestion effects are encoded directly into the macroscopic interaction forces, depending on a local critical density transported by the flow. In particular, we extend the work of Lefebvre-Lepot and Maury where non-inertial particles, submitted to only a lubrication force were considered, and present the convergence proof when inertial effects and roughness are taken into account. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11999 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Microscopic derivation of a one-dimensional lubrication model with roughness Lefebvre-Lepot, Aline Mehmood, Muhammed Ali Perrin, Charlotte Zatorska, Ewelina Analysis of PDEs 35Q92, 74Q05, 74Q15, 35B40, 76M50 We derive a hydrodynamic model for the motion of inertial particles with a spherical hard core, interacting through lubrication forces and pairwise repulsive forces. The repulsion arises from the assumption that each particle is surrounded by a thin rough layer of reduced permeability. We prove that, as the number of particles tends to infinity (and their size tends to 0), the microscopic dynamics converges to a macroscopic hydrodynamic model in which congestion effects are encoded directly into the macroscopic interaction forces, depending on a local critical density transported by the flow. In particular, we extend the work of Lefebvre-Lepot and Maury where non-inertial particles, submitted to only a lubrication force were considered, and present the convergence proof when inertial effects and roughness are taken into account. |
| title | Microscopic derivation of a one-dimensional lubrication model with roughness |
| topic | Analysis of PDEs 35Q92, 74Q05, 74Q15, 35B40, 76M50 |
| url | https://arxiv.org/abs/2601.11999 |