Residence time distribution for electrokinetic flow through a microchannel comprising a bundle of cylinders

The electrokinetic flow of an electrolyte solution through a microchannel that comprises a bundle of cylinders is investigated for the case of constant surface potential. The system under consideration is simulated by a unit cell model, and analytical expressions for the flow field and the corresponding residence time distribution under various conditions are derived. These results are readily applicable to the assessment of the performance of a microreactor such as that which comprises a bundle of optical fibers. Numerical simulations are conducted to investigate the influences of the key parameters, including the thickness of the double layer, the strength of the applied electric field, the magnitude of the applied pressure gradient, and the characteristic sizes of a microchannel, on the residence time distribution. We show that the following could result in a shorter residence time: thin double layer, strong applied electric field, large applied pressure gradient, and small number of cylinders. Based on the thickness of the double layer, criteria are proposed for whether the flow field can be treated as a laminar flow or as a plug flow, two basic limiting cases in reactor design.

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