The inertialess limit of particle sedimentation modeled by the Vlasov-Stokes equations

We study the Vlasov-Stokes equations which macroscopically model the sedimentation of a cloud of particles in a fluid, where particle inertia are taken into account but fluid inertia are assumed to be negligible. We consider the limit when the inertia of the particles tends to zero, and obtain convergence of the dynamics to the solution of an associated inertialess system of equations. This system coincides with the model that can be derived as the homogenization limit of the microscopic inertialess dynamics.