Context : The nearby young stellar association \epsilon Cha 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 . Aims : We wish to complement existing optical and near-infrared data of the \epsilon Cha association , which provide the stellar properties of its members , with mid-infrared data that probe the presence , geometry , and mineralogical composition of protoplanetary disks around individual stars . Methods : We combine the available literature data with our Spitzer IRS spectroscopy and VLT/VISIR imaging data . We use proper motions to refine the membership of \epsilon Cha . Masses and ages of individual stars are estimated by fitting model atmospheres to the optical and near-infrared photometry , followed by placement in the HR-diagram . The Spitzer IRS spectra are analyzed using the two-layer temperature distribution spectral decomposition method . Results : Two stars previously identified as members , CXOU J120152.8 and 2MASS J12074597 , have proper motions that are very different from those of the other stars . But other observations suggest that the two stars are still young and thus might still be related to \epsilon Cha . HD 104237C is the lowest mass member of \epsilon Cha with an estimated mass of \sim 13–15 Jupiter masses . 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 \mu m radiation of the warm inner disk can still reach us . We find that 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 \mu m on the IRS spectrum of USNO-B120144.7 . We find strong signatures of grain growth and crystallization in all \epsilon Cha members with 10 \mu m 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 , \eta Cha associations , and in the cores-to-disks 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 \sim 10 ^ { -9 } M _ { \odot } yr ^ { -1 } , possibly indicating that those disks are sufficiently turbulent to prevent grains of several microns in size to sink into the disk interior . Conclusions :