Pulsed field gradient nuclear magnetic resonance (PFG-NMR) and NMR imaging were used to study temporal and spatial domains of an electrokinetically-driven mobile phase through open and packed segments of capillaries. Characteristics like velocity distribution and an asymptotic dispersion are contrasted to viscous flow behavior. We show that electroosmotic flow in microchannel geometries can offer a significant performance advantage over the pressure-driven flows at comparable Peclét numbers, indicating that velocity extremes in the pore space of open tubes and packed beds are drastically reduced. An inherent problem of capillary electrochromatography that we finally address is the existence of wall effects when in the general case the surface zeta-potentials of the capillary inner wall and the adsorbent particles are different. Using dynamic NMR microscopy we were able resolve this systematic velocity inequality of the flow pattern which strongly influences axial dispersion and may be responsible for long time-tails of velocity distribution in the mobile phase.