Intrinsic characteristic times in the drift-diffusion problem

The redistribution of impurities in a sample in the shape of a slab filled with an isotropic liquid submitted to an external field is considered. The case in which the impurities are ions dissolved in the liquid, and the external field is an electric field is also investigated. It is shown that the intrinsic time connected with the presence of the electric field is proportional to the drift time. The constant of proportionality is of the order of the ratio between the thermal agitation energy and the electrostatic energy. A closed solution for the time evolution of the density of particles is obtained. The importance of the effect on real situations is investigated. The possible application of these results to nematic samples submitted to an external electric field is discussed.