Because of the large neutron excess of $^{22}$Ne, this isotope rapidly sediments in the interior of the white dwarfs. This process releases an additional amount of energy, thus delaying the cooling times of the white dwarf. This influences the ages of different stellar populations derived using white dwarf cosmochronology. Furthermore, the overabundance of $^{22}$Ne in the inner regions of the star, modifies the Brunt-Vaisala frequency, thus altering the pulsational properties of these stars. In this work, we discuss the impact of $^{22}$Ne sedimentation in white dwarfs resulting from Solar metallicity progenitors ($Z=0.02$). We performed evolutionary calculations of white dwarfs of masses $0.528$, $0.576$, $0.657$ and $0.833$ M$_{sun}$, derived from full evolutionary computations of their progenitor stars, starting at the Zero Age Main Sequence all the way through central hydrogen and helium burning, thermally-pulsing AGB and post-AGB phases. Our computations show that at low luminosities ($log(L/L_{sun})la -4.25$), $^{22}$Ne sedimentation delays the cooling of white dwarfs with Solar metallicity progenitors by about 1~Gyr. Additionally, we studied the consequences of $^{22}$Ne sedimentation on the pulsational properties of ZZ~Ceti white dwarfs. We find that $^{22}$Ne sedimentation induces differences in the periods of these stars larger than the present observational uncertainties, particularly in more massive white dwarfs.
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