Long term evolution of the dust-to-gas ratio max(ϵ) (black), combined with the horizontal (red) and vertical (blue). The grey dashed lines represent the growth rate scaling with , as found from the toy model (Eq. (11)). The growth rate decreases with dust-to-gas ratio, and we are unable to measure growth rates below ϵ₀ = 0.05. The small oscillations seen in vertical velocity dispersion for the low metallicity runs are the result of vertical waves, which are due to a slight imbalance in the initial condition in elongated domains. The figure is based on the simulations run1.01, run2.01, run3.01, and run4.01 (in order of decreasing metallicity).