Comparison of steady-state results for the fiducial parameters between the simple model (dashed lines) and the complete model (solid lines), which includes collective effects and the effects of the variation of the mean molecular weight μ. The upper two panels correspond to the single-seed evaporation model; the lower two panels correspond to the many-seeds evaporation model. In the latter case, we made the conservative choice of not including the free silicates in the back-reaction onto the gas. a) Surface densities of ice (Σ_ice), vapor (Σ_Z) and silicates (Σ_sil) for the single-seed model. The grey line indicates the mean molecular weight of the gas in units of proton mass m_H. b) Midplane pebbles-to-gas ratio ρ_peb/ρ_gas. c) Same as a), but the silicates are now divided into “free silicates” (Σ_sil) and “locked silicates” (Σ_dirt). For clarity, we only show the clean Σ_ice profile for comparison. d) Same as b), with an additional line denoting the “free silicates”-to-gas ratio ρ_sil/ρ_gas.