Although the micro-channels of typical lab-on-a-chip micro-fluidic devices are connected to reservoirs, existing analyses of the flow physics within the micro-channels frequently ignore the end effects induced by these reservoirs. Accordingly, this study presents an analytical and numerical investigation into electro-osmotic flow (EOF) which takes into account the end effects associated with the inlets and outlets of the micro-channels. The results indicate that the EOF contractions and expansions which occur in the inlet and outlet regions, respectively, induce streamwise pressure gradients, which result in non-flat EOF velocity profiles within the micro-channel. Furthermore, it is proven theoretically that this pressure gradient eventually vanishes once the micro-channel becomes sufficiently long that the end effects no longer exert an influence on the flow. An empirical relation between the entrance length and Reynolds number is established via parametric studies.
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