The imbibition dynamics of poly(n-butyl methacrylate) (PnBMA) in nanoporous alumina is studied by in situ dielectric spectroscopy at temperatures in the range 30-50 K above the glass temperature. A model provides the imbibition length from the measured dielectric strength of the segmental process. The relaxation times of the segmental process during imbibition are isochronal, except at early stages where a speed-up is observed. Furthermore, as polymer segments flow inside the pores, the distribution of relaxation times remains constant (Havriliak-Negami shape parameters similar to the bulk). Imbibition at longer length scales associates with the effetive viscosity of the chains and provides a stringent test of the Lucas-Washburn equation applicable to Newtonian liquids. The equation fails to describe the imbibition process because the prefactor to the t(1/2) (t; time) dependence does not adequately describe the process. Imbibition of polymer blends composed of long and short chains reveals the enrichment of the pores by the shorter chains by their faster imbibition with possible application in fractionation.