Modelling Dust Evolution in Galaxies with a Multiphase, Inhomogeneous
  ISM
  We develop a model of dust evolution in a multiphase, inhomogeneous ISM
including dust growth and destruction processes. The physical conditions for
grain evolution are taken from hydrodynamical simulations of giant molecular
clouds in a Milky Way-like spiral galaxy. We improve the treatment of dust
growth by accretion in the ISM to investigate the role of the
temperature-dependent sticking coefficient and ion-grain interactions. From
detailed observational data on the gas-phase Si abundances [Si/H]_{gas}
measured in the local Galaxy, we derive a relation between the average
[Si/H]_{gas} and the local gas density n(H) which we use as a critical
constraint for the models. This relation requires a sticking coefficient that
decreases with the gas temperature. The synthetic relation constructed from the
spatial dust distribution reproduces the slope of -0.5 of the observed relation
in cold clouds. This slope is steeper than that for the warm medium and is
explained by the dust growth. We find that it occurs for all adopted values of
the minimum grain size a_{min} from 1 to 5nm. For the classical cut-off of
a_{min}=5 nm, the ion-grain interactions result in longer growth timescales and
higher [Si/H]_{gas} than the observed values. For a_{min} below 3 nm, the
ion-grain interactions enhance the growth rates, steepen the slope of
[Si/H]_{gas}-n(H) relation and provide a better match to observations. The
rates of dust re-formation in the ISM by far exceed the rates of dust
production by stellar sources as expected from simple evolution models. After
the cycle of matter in and out of dust reaches a steady state, the dust growth
balances the destruction operating on similar timescales of 350 Myr.
