In the current work, the mixing of a diffusive passive-scalar, e.g., thermal energy or species concentration, driven by electro-osmotic fluid motion being induced by an applied potential across a micro-channel is studied numerically. Secondary time-dependent periodic or random electric fields, orthogonal to the main stream, are applied to generate cross-sectional mixing. This investigation focuses on the mixing dynamics and its dependence on the frequency (period) of the driving mechanism. For periodic flows, the probability density function (PDF) of the scaled passive scalar (i.e., concentration), settles into a self-similar curve showing spatially repeating patterns. In contrast, for random flows there is a lack of self-similarity in the PDF for the interval of time considered in this investigation. The present study confirms an exponential decay of the variance of the concentration for the periodic and random flows.