We study EOF through microchannels, made of glass or glass-PDMS, by displacing an electrolyte solution at given concentration with the same electrolyte at a different concentration via an external electric field. When a constant voltage is applied over the channel, the electric current through the channel varies during the displacement process. We propose a simple analytical model that describes the time dependence of the current regardless of the concentration ratio chosen. With this model, which is applicable beyond the Debye-Hückel limit, we are able to quantify the EOF velocity and to determine the surface charge on the microchannel walls from the measured current behavior, as well as the zeta potential at given local electrolyte concentration.