  (abridge) The nearby young stellar association Epsilon Cha association has an
estimated age of 3-5 Myr, making it an ideal laboratory to study the disk
dissipation process and provide empirical constraints on the timescale of
planet formation. We combine the available literature data with our Spitzer IRS
spectroscopy and VLT/VISIR imaging data. The very low mass stars USNO-B120144.7
and 2MASS J12005517 show globally depleted spectral energy distributions
pointing at strong dust settling. 2MASS J12014343 may have a disk with a very
specific inclination where the central star is effectively screened by the cold
outer parts of a flared disk but the 10 micron radiation of the warm inner disk
can still reach us. We find the disks in sparse stellar associations are
dissipated more slowly than those in denser (cluster) environments. We detect
C_{2}H_{2} rovibrational band around 13.7 micron on the IRS spectrum of
USNO-B120144.7. We find strong signatures of grain growth and crystallization
in all Epsilon Cha members with 10 micron features detected in their IRS
spectra. We combine the dust properties derived in the Epsilon Cha sample with
those found using identical or similar methods in the MBM 12, Coronet cluster,
Eta Cha associations, and in the cores to disks (c2d) legacy program. We find
that disks around low-mass young stars show a negative radial gradient in the
mass-averaged grain size and mass fraction of crystalline silicates. A positive
correlation exists between the mass-averaged grain sizes of amorphous silicates
and the accretion rates if the latter is above ~10^{-9} Msun/yr, possibly
indicating that those disks are sufficiently turbulent to prevent grains of
several microns in size to sink into the disk interior.
