Different snapshots of our fiducial model. Shown are the different distribution functions as defined by Eqs. (43) at 10 000 yr, 100 000 yr, 500 000 yr, and at 1 Myr. The solid line denotes the particle sizes with Stokes number unity, The dashed line is an analytical estimation of the drift barrier. The dotted line encompasses a region outside of the ice line that is free of small particles.