Evolution of the pebble flux (top) and the pebble-to-gas flux ratio (bottom) at 10 AU according to different analytical models and according to the simulation from Appelgren et al. (2023). Analytical models are described in Eq. (E.1) for a constant ξ = 0.01,0.03 or 0.06, Eqs. (36) and (32) for a constant St_χ, and St, respectively, and Eq. (E.2) for the pebble flux derived by Lambrechts & Johansen (2014). We assumed Z₀ = 0.008 and to match the simulation, and the rest of the parameter values are listed in Table 1. The simulation shows that, for the given disk parameters, the pebbles deplete on a shorter timescale than the gas due to the radial drift. This behavior is exhibited in the analytical models with a constant St_χ, and constant St.