Optimizing electroosmotic pumping rates in a rectangular channel with vertical gratings

Abstract

The Helmholtz-Smoluchowski (H-S) velocity is known to be an accurate and useful formula for estimating the electro-osmotic (EO) flow rates in a simple micro-channel with a thin electric-double layer. However, in case the channel cross section is not so simple, the usefulness of H-S velocity could be sharply limited. A case of fundamental interest representing this situation is a rectangular channel (comprising parallel plates) with built-in vertical gratings, in which the surfaces inside the channel may develop different normalized zeta potentials α (on the gratings) and β (on the side walls). In this study, analytical solutions are pursued under the Debye-Hückel approximation to obtain EO pumping rates in a rectangular channel with vertical gratings. In particular, we identify the conditions under which the H-S formula can be properly applied and investigate how the EO flow rates may deviate from those predicted by the H-S velocity with varying physical parameters. Moreover, a diagram of the optimal EO pumping rates on the α-β plane is introduced that accounts for the general features of the analysis, which is consistent with a mathematical model and may serve as a convenient guide for engineering design and applications.