Electroosmotic transport through rectangular channels with small zeta potentials

In this article, we analyze the electroosmotic transport of neutral samples through rectangular channels having a small zeta potential at their walls. Exact analytical expressions have been derived for quantifying the solute velocity in such conduits and the Taylor-Aris dispersivity in large-aspect-ratio rectangular geometries. In addition, a semianalytical theory has been presented for estimating the solutal spreading rate in rectangular profiles of all aspect ratios by decoupling the effects of vertical and horizontal velocity gradients in the system. Finally, the predictions made by this theory have been compared with the results from numerical simulations in which all assumptions were relaxed. Our analysis shows that while the sidewalls in a rectangular conduit modify the fluid velocity only to a moderate extent, they can increase the hydrodynamic dispersion of sample slugs as much as by a factor of 8 under strong Debye-layer overlap conditions. In the opposite limit of thin Debye layers, however, the increase in dispersion due to the side regions is only by a factor of 2 and remains nearly unaffected by the aspect ratio of the channel, in agreement with the prediction by E.K. Zholkovskij, J.H. Masliyah, J. Czarnecki, Anal. Chem. 75 (2003) 901].