Pré-Publication, Document De Travail Année : 2026

Microscopic derivation of a one-dimensional lubrication model including rough repulsive layers

Résumé

We derive a hydrodynamic model for the motion of inertial particles with a spherical hard core, inter- acting 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.

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hal-05500125 , version 1 (09-02-2026)

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  • HAL Id : hal-05500125 , version 1

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Aline Lefebvre-Lepot, Muhammed Ali Mehmood, Charlotte Perrin, Ewelina Zatorska. Microscopic derivation of a one-dimensional lubrication model including rough repulsive layers. 2026. ⟨hal-05500125⟩
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