Electrokinetic transport in nanochannels. 1. Theory.

Electrokinetic transport in fluidic channels facilitates control and separation of ionic species. In nanometer-scale electrokinetic systems, the electric double layer thickness is comparable to characteristic channel dimensions, and this results in nonuniform velocity profiles and strong electric fields transverse to the flow. In such channels, streamwise and transverse electromigration fluxes contribute to the separation and dispersion of analyte ions. In this paper, we report on analytical and numerical models for nanochannel electrophoretic transport and separation of neutral and charged analytes. We present continuum-based theoretical studies in nanoscale channels with characteristic depths on the order of the Debye length. Our model yields analytical expressions for electroosmotic flow, species transport velocity, streamwise-transverse concentration field distribution, and ratio of apparent electrophoretic mobility for a nanochannel to (standard) ion mobility. The model demonstrates that the effective mobility governing electrophoretic transport of charged species in nanochannels depends not only on electrolyte mobility values but also on zeta potential, ion valence, and background electrolyte concentration. We also present a method we term electrokinetic separation by ion valence (EKSIV) whereby both ion valence and ion mobility may be determined independently from a comparison of micro- and nanoscale transport measurements. In the second of this two-paper series, we present experimental validation of our models.