Electro-osmotic flow in polygonal ducts

The paper presents semi-analytical solutions to electro-osmotic (EO) flow through polygonal ducts under the Debye-Huckel approximation. Analytical series solutions assisted with numerical collocations are found to yield very fast convergence. The solutions have practical applications as the pores of EO membranes are mostly hexagonal, stacked densely in a beehive-like matrix. In addition, we develop simple asymptotic approximations that would be applicable to all EO tube flows of small as well as large dimensionless electrokinetic width. This facilitates investigation of analytical structures of general EO flows in all shapes of tubes, including the present geometries. In particular, for thick electrical double layers, the flow rate of EO is related to the corresponding viscous Poiseuille flow rate, while for thin electrical double layers, the flow rate is shown to be characterized by the cross-sectional area and the perimeter length of the tubes.