  The nuclear-matter liquid-gas phase transition induces instabilities against
finite-size density fluctuations. This has implications for both
heavy-ion-collision and compact-star physics. In this paper, we study the
clusterization properties of nuclear matter in a scenario of spinodal
decomposition, comparing three different approaches: the quantal RPA, its
semi-classical limit (Vlasov method), and a hydrodynamical framework. The
predictions related to clusterization are qualitatively in good agreement
varying the approach and the nuclear interaction. Nevertheless, it is shown
that i) the quantum effects reduce the instability zone, and disfavor
short-wavelength fluctuations; ii) large differences appear bewteen the two
semi-classical approaches, which correspond respectively to a collisionless
(Vlasov) and local equilibrium description (hydrodynamics); iii) the
isospin-distillation effect is stronger in the local equilibrium framework; iv)
important variations between the predicted time-scales of cluster formation
appear near the borders of the instability region.
