  Convergence of particle systems to the Vlasov-Navier-Stokes equations is a
difficult topic with only fragmentary results. Under a suitable modification of
the classical Stokes drag force interaction, here a partial result in this
direction is proven. A particle system is introduced, its interaction with the
fluid is modelled and tightness is proved, in a suitable topology, for the
family of laws of the pair composed by solution of Navier-Stokes equations and
empirical measure of the particles. Moreover, it is proved that every limit law
is supported on weak solutions of the Vlasov-Navier- Stokes system. Open
problems, like weak-strong uniqueness for this system and its relevance for the
convergence of the particle system, are outlined.
