  Background: Most of the stars in the Universe will end their evolution by
losing their envelope during the thermally pulsing asymptotic giant branch
(TP-AGB) phase, enriching the interstellar medium of galaxies with heavy
elements, partially condensed into dust grains formed in their extended
circumstellar envelopes. Among these stars, carbon-rich TP-AGB stars (C-stars)
are particularly relevant for the chemical enrichment of galaxies. We here
investigated the role of the metallicity in the dust formation process from a
theoretical viewpoint. Methods: We coupled an up-to-date description of dust
growth and dust-driven wind, which included the time-averaged effect of shocks,
with FRUITY stellar evolutionary tracks. We compared our predictions with
observations of C-stars in our Galaxy, in the Magellanic Clouds (LMC and SMC)
and in the Galactic Halo, characterised by metallicity between solar and 1/10
of solar. Results: Our models explained the variation of the gas and dust
content around C-stars derived from the IRS Spitzer spectra. The wind speed of
the C-stars at varying metallicity was well reproduced by our description. We
predicted the wind speed at metallicity down to 1/10 of solar in a wide range
of mass-loss rates.
