Unsteady solute dispersion by electrokinetic flow in a polyelectrolyte layer-grafted rectangular microchannel with wall absorption

The dispersion of a neutral solute band by electrokinetic flow in polyelectrolyte layer (PEL)-grafted rectangular/slit microchannels is theoretically studied. The flow is assumed to be both steady and fully developed and a first-order irreversible reaction is considered at the wall to account for probable surface adsorption of solutes. Considering low electric potentials, analytical solutions are obtained for electric potential, fluid velocity and solute concentration. Special solutions are also obtained for the case without wall adsorption. To track the dispersion properties of the solute band, the generalized dispersion model is adopted by considering the exchange, the convection and the dispersion coefficients. The solutions developed are validated by comparing the results with the predictions of finite-element-based numerical simulations. Even though the solutions can take any form of initial solute concentration into account, the results are presented by considering a solute band of rectangular shape. The results reveal that, while the short-term transport coefficients are strongly affected by the initial concentration profile, the long-term values are not dependent upon the initial conditions. In addition, it is shown that the mass transport coefficients are strong functions of the channel aspect ratio; hence, approximating a rectangular geometry by the space between two parallel plates may lead to considerable errors in the estimation of mass transport characteristics. This is particularly important for the dispersion coefficient for which the long-term values for a slit microchannel are quite different from those for a rectangular channel of very high aspect ratio. It is also illustrated that the exchange and convection coefficients increase on increasing the Damkohler number, whereas the opposite is true for the dispersion coefficient. The convection and dispersion coefficients are generally increasing functions of the PEL fixed charge density and the PEL thickness and decreasing functions of the PEL friction coefficient. Last but not least, a thicker electric double layer is found to provide a larger degree of solute dispersion, which is the opposite of that observed in a microchannel with bare walls.