Gravitational settling is widely accepted as being a fundamental physical process acting upon superficial layers of white dwarfs and resulting in an important alteration of their atmospheric composition. Several investigators have been interested by the problem of gravitational settling in white dwarfs (Fontaine and Michaud 1979; Vauclair, Vauclair, and Greenstein 1979; Alcock and Illarianov 1980; Muchmore 1984; Paquette et al. 1986). As pointed out in Paquette et al. 1986, they all reached the same qualitative conclusion: the gravitational settling time scales of metals in cool white dwarfs are small compared to their evolutionary time scales. These stars should therefore have their photospheres depleted of metals if there is no extrinsic source such as accretion for example. This is consistent with the observational fact that most of the cool white dwarfs spectra just show hydrogen and helium lines while the absence of metallic lines indicates a strong depletion of metals. Although the qualitative agreement between theory and observations is satisfactory, only time-dependent calculations can lead to a thorough understanding of the heavy element abundance patterns in cool white dwarfs. In particular, the predicted abundance of an element within the framework of the accretion-diffusion model does depend explicitly on the results of such calculations. We have already presented some preliminary results of numerical simulation of accretion episodes of heavy elements into white dwarfs (Dupuis et al. 1987). As part of an ongoing detailed investigation of these processes, we focus here exclusively on the mechanism of gravitational settling in white dwarfs in order to clear some confusion which has appeared in the literature.