  In supernovae (SNe), where the light curves show evidence of strong and early
interaction between the ejecta and the circumstellar matter (CSM), the
formation of new dust is estimated to take place in a dense shell of gas
between the forward (FS) and the reverse shock (RS). For the first time, in
this study, the mechanism of dust formation in this dense shell is modeled. A
set of 9 cases, considering variations of the ejecta mass, and the
pre-explosion mass-loss rates is considered, accounting for the diverse nature
of interactions reported in such SNe. For a single main sequence mass, the
variation of ejecta mass was manifested as a variation of the H-shell mass of
the star, lost due to pre-explosion mass-loss. We find that the dust masses in
the dense shell range between 10$^{-3}$ M$_{\odot}$ and 0.8 M$_{\odot}$,
composed of O-rich and C-rich grains, whose relative proportions are determined
by the nature of interaction. Dust formation in the post-shock gas is
characterized by a gradual production rate, mostly ranging from 10$^{-6}$ to
10$^{-3}$ M$_{\odot}$ day$^{-1}$, which may continue for a decade,
post-explosion. A higher mass-loss rate leads to a larger mass of dust, while a
smaller ejecta mass (smaller left-over H-shell) increases the efficiency of
dust production in such SNe. Dust formed behind the RS, as in our calculations,
is not subject to destruction by either the FS or RS and is thus likely to
survive in larger proportion than dust formed in the ejecta.
