Dust is formed out of stellar material and is constantly affected by different mechanisms occurring in the ISM. Dust grains behave differently under these mechanisms depending on their sizes, and therefore the dust grain size distribution also evolves as part of the dust evolution itself. Following how the grain size distribution evolves is a difficult computing task that is just recently being overtaking. Smoothed particle hydrodynamic (SPH) simulations of a single galaxy as well as cosmological simulations are producing the first predictions of the evolution of the dust grain size distribution. We compare for the first time the evolution of the dust grain size distribution predicted by the SPH simulations with the results provided by the observations. We analyse how the radial distribution of the small to large grain mass ratio (D(S)/D(L)) changes over the whole discs in three galaxies: M 101, NGC 628 and M 33. We find good agreement between the observed radial distribution of D(S)/D(L) and what is obtained from the SPH simulations of a single galaxy. The central parts of NGC 628, at high metallicity and with a high molecular gas fraction, are mainly affected not only by accretion but also by coagulation of dust grains. The centre of M 33, having lower metallicity and lower molecular gas fraction, presents an increase of D(S)/D(L), showing that shattering is very effective in creating a large fraction of small grains. Observational results provided by our galaxies confirm the general relations predicted by the cosmological simulations based on the two grain size approximation. However, we present evidence that the simulations could be overestimating the amount of large grains in high massive galaxies.
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