In this paper we study the long-term dynamical evolution of multiple-population clusters, focusing on the evolution of the spatial distributions of the first- (FG) and second-generation (SG) stars.In previous studies we have suggested that SG stars formed from the ejecta of FG AGB stars are expected initially to be concentrated in the cluster inner regions. Here, by means of N-body simulations, we explore the time scales and the dynamics of the spatial mixing of the FG and the SG populations and their dependence on the SG initial concentration.Our simulations show that, as the evolution proceeds, the radial profile of the SG/FG number ratio, NSG/NFG, is characterized by three regions: 1) a flat inner part; 2) a declining part in which FG stars are increasingly dominant; and 3) an outer region where the NSG/NFG profile flattens again (the NSG/NFG profile may rise slightly again in the outermost cluster regions). The radial variation of NSG/NFG implies that the fraction of SG stars determined by observations covering a limited range of radial distances is not, in general, equal to the SG global fraction, (NSG/NFG)glob. The distance at which NSG/NFG equals (NSG/NFG)glob is approximately between 1 and 2 cluster half-mass radii. The results of our simulations suggest that in many Galactic globular clusters the SG should still be more spatially concentrated than the FG.[abridged]
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