Semi-analytical solutions for electroosmotic flows with interfacial slip in microchannels of complex cross-sectional shapes

In this article, we investigate the implications of electroosmosis with interfacial slip on electrohydrodynamic transport in microchannels having complex (yet symmetric) cross-sectional shapes, by employing a generic semi-analytical approach. We also devise an approximate technique of flow rate prediction under these conditions, using a combined consideration of electroosmotic slip (under thin electrical double layer limits) and Navier slip conditions (originating out of confinement-induced hydrophobic interactions) at the fluid-solid interface. We further assess the effectiveness of the approximate solutions in perspective of the exact solutions, as a parametric function of the relative thickness of the electrical double layer with respect to the channel hydraulic diameter. We illustrate the underlying consequences through examples of elliptic, polygonal, point star-shaped, and annular microchannel cross sections.