This Paper presents simulation of Electroosmotic phenomenon in a capillary using an extended hybrid finite-volume-element method. Most of the last electroosmotic phenomenon studies in microchannels do not take into consideration the effect of reservoirs and pressure drops occurred at the inlet and outlet of the microchannel. This neglect may lead to a few drawbacks. For example, the incorrect pressure drops can significantly alter the flow patterns and mass flow rates in microchannels. As a remedy the use of reservoirs at the two ends of a microchannel has been recently practiced as a novel strategy to overcome this drawback. However, this remedy needs careful attention because the resulting solutions need to be independent of the reservoirs’ sizes. In this paper, we introduce a novel geometry and new boundary conditions, which resolves the difficulties encountered with inserting the reservoirs at the two ends of a microchannel. The results of applying the new geometry and implementing the new boundary conditions are satisfactory. Therefore, using the outcomes of this paper, the real simulation of electroosmotic field is possible.

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