Solid surface density as function of orbital distance (black), at different times (indicated by the labels representing the time in years). The solid black lines represent the dust surface density and the dotted lines the pebble surface density. The exponentially decaying gas surface density is represented in blue, for the same times as the solid surface density. We have here assumed a gas disc dissipation time scale of τ_dis = 3 Myr. Gas surface densities larger than the red dashed line (which represent Toomre Q = 1), would be gravitationally unstable (see also Sect. 2.6).