Optimizing electroosmotic pumping rates in a rectangular channel with vertical gratings

摘要

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 alpha (on the gratings) and beta (on the side walls). In this study, analytical solutions are pursued under the Debye-Huckel 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 alpha-beta 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. Published by AIP Publishing.