Mass and charge transport in arbitrarily shaped microchannels

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 problem of arbitrarily shaped cross sections and obtain general results in linear-response theory for the mass and charge transport coefficients which satisfy Onsager relations~[1,2]. In the limit of non-overlapping Debye layers the transport coefficients are simply expressed in terms of parameters of the electrolyte as well as half the hydraulic diameter ${\cal R}=2 {\cal A}/{\cal P}$ with $\cal A$ and $\cal P$ being the cross- sectional area and perimeter, respectively. In particular, 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.\newline \newline [1] N. A. Mortensen, F. Okkels, and H. Bruus, Phys. Rev. E \textbf{71}, 057301 (2005) \newline [2] N. A. Mortensen, L. H. Olesen, and H. Bruus, New J. Phys. \textbf{8}, 37 (2006)