Pebble-to-gas density ratios on the mid-plane with Discs A (upper panel) and B (lower panel). The yellow, light blue, and purple curves represent the snapshots of the density ratios with Ṁ_peb = 10⁻³, 10⁻⁴, and 10⁻⁵ M_E yr⁻¹, respectively, with the normal migration speed (i.e. the colour variations are the same with those of Fig. 2). The profiles represent the snapshots at t = 3.0 × 10⁵, 3.8 × 10⁵, and 4.0 × 10⁵ yr (from right to left) for Disc A and t = 3.2 × 10⁵, 3.8 × 10⁵, and 3.9 × 10⁵ yr for Disc B. The circles indicate the maximum value for each of the profiles. The dotted lines indicate the unperturbed pebble-to-gas density ratios on the mid-planes (Eq. (20)). The black lines represent where the ratio is unity.