Mass and charge transport in micro and nano-fluidic channels

We consider laminar flow of incompressible electrolytes in long, straight channels driven by pressure and electro-osmosis. We use a Hilbert space eigenfunction expansion to address the general problem of an arbitrary cross section and obtain general results in linear-response theory for the mass and charge transport coefficients which satisfy Onsager relations. In the limit of non-overlapping Debye layers the transport coefficients are simply expressed in terms of parameters of the electrolyte as well as the hydraulic radius R=2A/P with A and P being the cross-sectional area and perimeter, respectively. In articular, we consider the limits of thin non-overlapping as well as strongly overlapping Debye layers, respectively, and calculate the corrections to the hydraulic resistance due to electro-hydrodynamic interactions.