  Over the past decade a new generation of chemical models have included the
dust in the treatment of the ISM. This major accomplishment has been spurred by
the growing amounts of data on the highly obscured high-z Universe and the
intriguing local properties of the Solar Neighbourhood (SoNE). We present here
a new model able to simulate the formation and evolution of dust in the ISM.
The model follows the evolution of 16 elemental species, with particular
attention to those that are simultaneously present in form of gas and dust,
e.g. C, N, O, Mg, Si, S, Ca and Fe. In this study we focus on the SoNe and the
MW Disk as a whole which are considered as laboratories to test the physical
ingredients governing the dust evolution. Infall of primordial gas, birth and
death of stars, radial flows of matter between contiguous shells, presence of a
central bar, star-dust emission by SNae and AGB stars, dust destruction and
accretion are taken into account. The model reproduces the local depletion of
the elements in the gas, and simultaneously satisfies other constraints
obtained from the observations. The evolution of the element abundances in the
gas and dust has been well reproduced for plausible choices of the parameters.
The Mg/Si ratio, in particular, drives the formation of silicates. We show that
for most of the evolution of the MW, the main process for dust enrichment is
the accretion in the cold regions of the ISM. SNae dominate in the early phases
of the evolution. We have examined the main factors controlling the temporal
window in which SNae govern the dust budget both in low and high star forming
environments. The role played by AGB stars is discussed. We find that IMFs with
regular slope in the range of massive stars better reproduce the observed
depletions. The results obtained for the SoNe lead us to safely extend the
model.
