Evolution of the dust surface density in time. A) No growth case. Particles always have a = 1 mm. The dashed lines show analytical results of Youdin & Shu (2002). B) Compact growth with perfect sticking. Dust particles start out as 0.1 μm monomers and grow on timescales given by Eq. (11), while staying compact at all times (φ = 1). The gas surface density is shown by the dotted line. The results are qualitatively different, with the no-growth case resulting in pile-ups (locally increasing Σ_d/ Σ_g) and the compact coagulation model showing an inside-out removal of dust (decreasing Σ_d/ Σ_g everywhere).