A theoretical framework for the description of the phenomenon of electro-osmosis is developed. The main emphasis of the work is to develop relations that describe the time and spatial resolution of the velocity of the liquid in contact with a charged surface when a train of electric field pulses are applied parallel to the surface. The work is motivated by the recent development of NMR detected electrophoresis to a powerful tool in the field of colloid chemistry. In this approach one employs pulsed electric fields, and the process of electro-osmosis is a complication. In developing this framework, we make use of results from electro-osmosis outside a single charged plane and in a slot, when the electric held is applied as a step-function. Results for both planar and cylindrical geometries are presented. In both cases we present results without and with effects due to counterflow taken into account. Finally, we compare the results of our theoretical description with some recently published velocity profiles obtained from NMR imaging techniques.