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tokens: More specifically, we can summarize our findings as follows: 1. Because the drag force experienced by small dust grains is very strong, a specific implicit numerical scheme was implemented in the code RoSSBi to accurately follow the dynamics of the disk. This method is very accurate for any value of the Stokes number of the pressureless dust fluid, and we use it to study the evolution a vortex model with dust characterized by Stokes numbers in the range . 2. Dust is systematically accumulated inside the vortex for every value of the Stokes number. The exponential growth rate of the dust density at the vortex center follows the analytical model we developed in our previous study. The timescale depends on the grain size, but the density enhancement reached at the end, when the gas is perturbed by the drag force, is similar regardless of the Stokes number, and produces dust-to-gas ratios of order unity. We highlight the existence of a generic capture process, characterized by a timescale that scales with the Stokes number, which allows us to compare disks with different dust sizes at an equivalent state of evolution, but corresponding to intrinsically different physical timescales. 3. The vortex instability is triggered at the end of the capture, regardless of the grain size. The growth rates of the excited modes also depend weakly on the Stokes number. This effect is highly correlated with the similarity of the dust capture, and the concept of equivalent states of evolution, producing almost the same perturbation of the gas vorticity profile. 4. A new phase of dusty vortex evolution is discovered for Stokes numbers on the order of 10 −3 and below, where a succession of vortex instabilities followed by dust capture events occurs. This period lasts several hundred of disk orbits and produces strong mixing and a fast reorganization of the dust during the relaxation of the vortex. The dust-to-gas ratio increases progressively to high values, up to 8 at the vortex center. The very dense core that forms and survives even after eventual vortex dissipation could be a preferential place for planetesimal formation. 5. When the timescale of the drag effect is too long compared to the resistance and relaxation of the vortex, the formation of a dust ring becomes unlikely. In our case, the runs with St = 10 −3 were still in the unstable phase by the end of the simulations. Even when it forms, for St 10 −2 , the dust ring produced by well-coupled grains has fewer eddies than with larger Stokes numbers. Even if the dust-to-gas ratios are comparable, they suffer diffusion, and their role in planetesimal formation is less promising than the unstable phase. There are a number of caveats to our model that need to be pointed out. First, the fact that the simulations are still only two-dimensional, which could have a relevance both for the development of two-fluid turbulence during and after the vortex instability phase (see the discussion in Surville et al. 2016