Electrokinetic transport of charged samples through rectangular channels with small zeta potentials

In this article, we analyze the electrokinetic transport of charged samples through rectangular channels having a small zeta potential at their walls. Using the method of moments formulation, the diffusion-advection equation has been solved numerically to evaluate the mean velocity and the dispersion of analyte bands in these systems. In addition, a semianalytical theory has been presented for estimating the solutal spreading rate by decoupling the effects of vertical and horizontal velocity gradients in the channel. We demonstrate that this theory can estimate the band broadening of charged samples in rectangular conduits of all aspect ratios within an accuracy of 5% with significantly less computational effort than that required in the numerical simulations. Moreover, our analysis shows that while die side walls in a rectangular conduit modify the solute velocity only to a moderate extent, they can increase the hydrodynamic dispersion of sample slugs by as much as an order of magnitude 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 transverse electromigration of the solute molecules and the aspect ratio of the channel.