  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.
