Context. Current models of the size- and radial evolution of dust inprotoplanetary disks generally oversimplify either the radial evolution of thedisk (by focussing at one single radius or by using steady state disk models)or they assume particle growth to proceed monodispersely or withoutfragmentation. Further studies of protoplanetary disks - such as observations,disk chemistry and structure calculations or planet population synthesis models- depend on the distribution of dust as a function of grain size and radialposition in the disk. Aims. We attempt to improve upon current models to be able to investigate howthe initial conditions, the build-up phase, and the evolution of theprotoplanetary disk influence growth and transport of dust. Methods. We introduce a new version of the model of Brauer et al. (2008) inwhich we now include the time-dependent viscous evolution of the gas disk, andin which more advanced input physics and numerical integration methods areimplemented. Results. We show that grain properties, the gas pressure gradient, and theamount of turbulence are much more influencing the evolution of dust than theinitial conditions or the build-up phase of the protoplanetary disk. Wequantify which conditions or environments are favorable for growth beyond themeter size barrier. High gas surface densities or zonal flows may help toovercome the problem of radial drift, however already a small amount ofturbulence poses a much stronger obstacle for grain growth.
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