  We provide a rigorous mathematical framework to establish the hydrodynamic
limit of the Vlasov model introduced by Noguchi and Takata in order to describe
phase transition of fluids by kinetic equations. We prove that, when the scale
parameter tends to 0, this model converges to a nonlocal Cahn-Hilliard equation
with degenerate mobility. For our analysis, we introduce apropriate forms of
the short and long range potentials which allow us to derive Helmhotlz free
energy estimates. Several compactness properties follow from the energy, the
energy dissipation and kinetic averaging lemmas. In particular we prove a new
weak compactness bound on the flux.
