Time evolution of the cumulative pebble flux. The solid lines show the cumulative pebble flux calculated with Eq. 17. The dashed lines are those obtained with Eq. 17 using the time evolving Σ_gas(t = t′) instead of Σ_gas(t = 0). The horizontal dotted lines show the initial total mass of solids in the protoplanetary disk. The different colors correspond to disks around different stellar masses.