Electrokinetic flow in connected channels: a comparison of two circuit models

Abstract

We apply the recently developed ‘ion current model’ (ICM) to investigate mixed pressure-driven/electro-osmotic flow in electrokinetic series circuits. Under the ICM, the local geometric mean ion concentration varies throughout a microfluidic circuit as a consequence of ion conservation. ICM predictions are used to assess the accuracy of the earlier ‘total current model’ (TCM), which is instead based upon the simplifying assumption that the geometric mean ion concentration is uniform in all channels within a circuit. The model comparison is performed over an experimentally relevant range of physical parameters and channel dimensions. When the ratio of total current to flow rate is small, or when the inlet concentration is very low or very high, the ICM and TCM give similar predictions of the total pressure and potential differences across simple three-channel contraction–expansion networks. Otherwise, the errors introduced using the TCM may be very large. Our results demonstrate that the common assumption that the electrolyte concentration throughout a device is equal to the concentration of fluid supplied to the device is not always valid, even if there is little or no electric double layer overlap.