Enhanced electroosmotic flow and ion selectivity in a channel patterned with periodically arranged polyelectrolyte-filled grooves

An enhanced electroosmotic flow through a surface-modulated microchannel is considered. The microchannel is modulated by periodically arranged rectangular grooves filled with polyelectrolyte materials. The flat surface of the walls is maintained at a constant charge density. A nonlinear model based on the Poisson-Nernst-Planck equations coupled with the Darcy-Brinkman-Forchheimer equation in the polyelectrolyte region and Navier-Stokes equations in the clear fluid region is adopted. Going beyond the widely employed Debye-Huckel linearization, we adopt numerical methods to elucidate the effect of pertinent parameters on electroosmosis in the patterned channel. The patterned microchannel results in an enhancement in the average EOF by creating an intrinsic velocity slip at the polyelectrolyte-liquid interface. An analytical solution of the EOF for a limiting case in which the groove width is much higher than the channel height is obtained based on the Debye-Huckel approximation. This analytical solution is in good agreement with the present numerical model when a low charge density and a thin Debye layer are considered. We have also established an analogy between the EOF in a polyelectrolyte-filled grooved-channel with the EOF in which the grooves are replaced by the charged slipping planes.