We investigate the dynamics of unidirectional drying of silica dispersions. For small colloids (radii a<15 nm), the minute recession of the drying interface inside the growing solid leads to a slowing down of the evaporation rate, as recently proposed by Wallenstein and Russel [J. Phys. Condens. Matter 23, 194104 (2011)]. We first propose that Kelvin’s effect, i.e. the reduction of the partial pressure of water in the presence of highly curved nanomenisci at the drying air/dispersion interface, has to be taken into account, notably for such small colloids. Our model can fit qualitatively the literature measurements, but with a crossover between the linear regime and the slowing down regime that scales as a^2, as compared to the model of Wallenstein and Russel that predicts a linear scaling. We then also present careful measurements of the dynamics of solidification, that clearly demonstrate that both models (taking into account or not Kelvin’s effect) do not fit correctly the slowing down. This is consistent with a brief review of similar recent measurements. Nevertheless, the dynamics can be correctly estimated with a significantly lower effective permeability of the solid region. We suggest that this result may come from the polydispersity of the suspensions, and from the inhomogeneity of the flow within the fracturated solid region, as illustrated by infiltration experiments of a coloured dye.