  We propose an updated dust evolution model that focuses on the grain size
distribution in a galaxy. We treat the galaxy as a one-zone object and include
five main processes (stellar dust production, dust destruction in supernova
shocks, grain growth by accretion and coagulation, and grain disruption by
shattering). In this paper, we improve the predictions related to small
carbonaceous grains, which are responsible for the 2175 \AA\ bump in the
extinction curve and the polycyclic aromatic hydrocarbon (PAH) emission
features in the dust emission spectral energy distribution (SED), both of which
were underpredicted in our previous model. In the new model, we hypothesize
that small carbonaceous grains are not involved in interstellar processing.
This avoids small carbonaceous grains being lost by coagulation. We find that
this hypothetical model shows a much better match to the Milky Way (MW)
extinction curve and dust emission SED than the previous one. The following two
additional modifications further make the fit to the MW dust emission SED
better: (i) The chemical enrichment model is adjusted to give a nearly solar
metallicity in the present epoch, and the fraction of metals available for dust
growth is limited to half. (ii) Aromatization for small carbonaceous grains is
efficient, so that the aromatic fraction is unity at grain radii $\lesssim 20$
\AA. As a consequence of our modelling, we succeed in obtaining a dust
evolution model that explains the MW extinction curve and dust emission SED at
the same time.
