Growth rate in units of the reciprocal orbital time (1 /t_orbit = Ω_K/ 2π) of the dust-driven viscous instability, as a function of dust particle size (expressed as Stokes number St), according to the simplified analysis of Sect. 3. Dashed lines: case 1 (i.e. φ_g = 0), solid lines: case 2 (i.e. φ_g = −φ_d). The different lines show modes of different dimensionless wavelength λ in the dimensionless coordinate x, where λ = 2π/k. A dimensionless wavelength λ = 1 means a wavelength as large as r₀. The parameters of the model shown here are φ_d = −1.0, α₁ = 10^-4, M_∗ = 1 M_⊙, L_∗ = 10 L_⊙, r₀ = 60 au, T = 43,K, Sc = 1 (i.e. c_s = 0.39 km s^-1 and t_orbit = 465 yr).