Context. Using observations to deduce dust properties, grain size distribution, and physical conditions in molecular clouds is a highly degenerate problem. Aims. The coreshine phenomenon, a scattering process at 3.6 and 4.5 $mu$m that dominates absorption, has revealed its ability to explore the densest parts of clouds. We want to use this effect to constrain the dust parameters. The goal is to investigate to what extent grain growth (at constant dust mass) inside molecular clouds is able to explain the coreshine observations. We aim to find dust models that can explain a sample of Spitzer coreshine data. We also look at the consistency with near-infrared data we obtained for a few clouds. Methods. We selected four regions with a very high occurrence of coreshine cases: Taurus-Perseus, Cepheus, Chameleon and L183/L134. We built a grid of dust models and investigated the key parameters to reproduce the general trend of surface bright- nesses and intensity ratios of both coreshine and near-infrared observations with the help of a 3D Monte-Carlo radiative transfer code. The grid parameters allow to investigate the effect of coagulation upon spherical grains up to 5 $mu$m in size derived from the DustEm diffuse interstellar medium grains. Fluffiness (porosity or fractal degree), ices, and a handful of classical grain size distributions were also tested. We used the near- and mostly mid-infrared intensity ratios as strong discriminants between dust models. Results. The determination of the background field intensity at each wavelength is a key issue. In particular, an especially strong background field explains why we do not see coreshine in the Galactic plane at 3.6 and 4.5 $mu$m. For starless cores, where detected, the observed 4.5 $mu$m / 3.6 $mu$m coreshine intensity ratio is always lower than $sim$0.5 which is also what we find in the models for the Taurus-Perseus and L183 directions. Embedded sources can lead to higher fluxes (up to four times greater than the strongest starless core fluxes) and higher coreshine ratios (from 0.5 to 1.1 in our selected sample). Normal interstellar radiation field conditions are sufficient to find suitable grain models at all wavelengths for starless cores. The standard interstellar grains are not able to reproduce observations and, due to the multi-wavelength approach, only a few grain types meet the criteria set by the data. Porosity does not affect the flux ratios while the fractal dimension helps to explain coreshine ratios but does not seem able to reproduce near-infrared observations without a mix of other grain types. Conclusions. Combined near- and mid-infrared wavelengths confirm the potential to reveal the nature and size distribution of dust grains. Careful assessment of the environmental parameters (interstellar and background fields, embedded or nearby reddened sources) is required to validate this new diagnostic.
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