Mass Transfer and Flow in Electrically Charged Micro- and Nanochannels

In this work, the fluid flow and mass transfer due to the presence of an electric field in a rectangular channel is examined. We consider a mixture of water or another neutral solvent and a salt compound, such as sodium chloride, for which the ionic species are entirely dissociated. Results are produced for the case in which the channel height is much greater than the electric double layer (EDL) (microchannel) and for the case in which the channel height is of the order of the width of the EDL (nanochannel). Both symmetric and nonsymmetric velocity, potential, and mole fraction distributions are considered, unlike previous work on this problem. At small electrolyte concentrations, the Debeye-Huckel picture of the electric double layer is recovered; at larger concentrations, the Gouy-Chapman picture of the electric double emerges naturally. The numerical results presented here agree with analytical solutions of a singular perturbation analysis, which is valid as the channel height increases. In the symmetric case for the electroosmotic flow so induced, the velocity field and the potential are similar. In the asymmetric case corresponding to different wall potentials, the velocity and potential can be vastly different. The fluid is assumed to behave as a continuum, and the volume flow rate is observed to vary linearly with channel height for electrically driven flow, in contrast to pressure-driven flow, which varies as height cubed. This means that very large pressure drops are required to drive flows in small channels. However, useful volume flow rates may be obtained at a very low driving voltage.