  The goal of this study is to reconstruct the evolution and the dust formation
processes during the final AGB phases of a sample of carbon-rich, post-AGB
Galactic stars, with particular attention to the determination of the past
mass-loss history. We study the IR excess of sources classified as single stars
by means of dust formation modelling where dust grains form and grow in a
static wind and expand from the surface of the star. The method is applied to
various evolutionary stages of the final AGB phase of stars with different
masses and metallicities. The detailed analysis of the SED of the sources
investigated, which included the derivation of the luminosities and the dust
properties, is used to infer information on mass loss, efficiency of dust
formation, and wind dynamics. We confirm previous results that most of the
investigated sources descend from low-mass(M<1.5Msun) progenitors that reached
the C-star stage. Metal-poor carbon stars are characterised by higher IR
excesses with respect to their more metal-rich counterparts of similar
luminosity due to a higher surface carbon-to-oxygen excess. This work confirms
previous conclusions that more luminous stars descending from higher-mass
progenitors are generally more opaque due to shorter evolutionary timescales
that place the dust shell closer to the central object. We also find that the
mass-loss rate at the tip of the AGB phase of metal-rich low-mass carbon stars
is approximately 1-1.5x10^-5Msun/yr, whereas in the metal-poor domain
M~4-5x10^-5Msun/yr is required. These results indicate the need for an upwards
revision of the theoretical mass-loss rates of low-mass carbon stars in the
available literature, which in turn require a revised determination of carbon
dust yields by AGB stars.
