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

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 assumptionthat each particle is surrounded by a thin rough layer of reduced permeability. We prove that, as thenumber of particles tends to infinity (and their size tends to 0), the microscopic dynamics converges to amacroscopic hydrodynamic model in which congestion effects are encoded directly into the macroscopicinteraction forces, depending on a local critical density transported by the flow. In particular, we extendthe work of Lefebvre-Lepot and Maury where non-inertial particles, submitted to only a lubricationforce were considered, and present the convergence proof when inertial effects and roughness are takeninto account.