Midplane pebble-to-gas density ratio (Z = ρ_p∕ρ_g) as a functionof α_Dz and F_p/g (at r = 5 au and τ_s,p = 0.125). Top panels: cases where the back-reaction onto the gas motion is neglected (i.e., v_g = v_g,ν). Bottom panels: cases where the back-reaction to the gas motion is included, following Eq. (16). The color contours are obtained by directly solving Eq. (86). Left and right two panels: cases where α_acc = 10⁻³ and α_acc = 10⁻² with/without a KH instability (Ri = 0.5), respectively. The red-colored regions indicate where a steady-state solution is not found (i.e., ρ_p ∕ρ_g > 100 and it keeps increasing; the “no-drift (ND)” region). The white (Eq. (91)) and black (Eq. (95) with Ri = 0.5) dashed lines are analytically derived critical F_p/g,crit above which no steady-state are found (the “no-drift (ND)” region). Analytical predictions (dashed lines) well predict critical boundaries of the ND region. Including a KH instability reduces the ND region as the minimum scale height of pebbles is regulated by a KH instability. Due to the back-reaction to the gas motion that slows down the radial velocity of the gas, the midplane concentration of pebbles as well as the ND region (red-colored region) are shifted toward slightly larger F_p/g values.