Application to solar prominence threads. Growth rates as functions of the shear flow velocity for the following set of parameters: ρ_i,0 + ρ_n,0 = 10^-9 kg m^-3, ρ_i,ex + ρ_n,ex = 2 × 10^-10 kg m^-3, B₀ = B_ex = 10^-3 T, a = 100 km, T₀ = 7000 K and T_ex = 35 000 K; in the left panel the wavenumber is k_z = 2π/λ = 2π × 10^-5 m^-1 and in the right panel it is k_z = 2π × 10^-6 m^-1. The red dashed lines correspond to a fully ionized plasma (χ = 0), the blue crosses to a partially ionized case (χ = 4), and the black diamonds to a weakly ionized case (χ = 100). The solid lines represent the solutions given by the analytical approximation in Eq. (30). The shaded zone denotes the region of flow velocity values that have been frequently measured in solar prominences.