Multi-wavelength observations of protoplanetary disks in the sub-millimeter continuum have measured spectral indices values which are significantly lower than what is found in the diffuse interstellar medium. Under the assumption that mm-wave emission of disks is mostly optically thin, these data have been generally interpreted as evidence for the presence of mm/cm-sized pebbles in the disk outer regions. In this work we investigate the effect of possible local optically thick regions on the mm-wave emission of protoplanetary disks without mm/cm-sized grains. A significant local increase of the optical depth in the disk can be caused by the concentration of solid particles, as predicted to result from a variety of proposed physical mechanisms. We calculate the filling factors and implied overdensities these optically thick regions would need to significantly affect the millimeter fluxes
