Electro-osmotic dispersion in a circular tube with slip-stick striped wall

Abstract

The hydrodynamic dispersion of a neutral non-reacting solute due to steady electro-osmotic flow (EOF) in a circular channel with longitudinal step changes of zeta potential and hydrodynamic slippage is analysed in this study. The channel wall is periodically micro-patterned along the axial position with alternating slip-stick stripes of distinct zeta potentials. Existing studies on electrically driven hydrodynamic dispersion are based on flow subject to either the no-slip boundary condition on the capillary surface or simplification of the lubrication approximation. Taking wall slippage into account, a homogenization analysis is performed in this study to derive the hydrodynamic dispersion coefficient without being subject to the long-wave constraint of the lubrication approximation, but for a general case where the length of one periodic unit of wall pattern is comparable with the channel radius. The flow and the hydrodynamic dispersion coefficient are calculated numerically, using the packages MATLAB® and COMSOL®, as functions of controlling parameters including the period length of the wall pattern, the area fraction of the slipping region (EOF-suppressing) in a periodic unit, the ratio of the two zeta potentials, the intrinsic hydrodynamic slip length, the Debye parameter, and the Péclet number. The dispersion is found to show notable, non-monotonic in certain situations, dependence on these controlling parameters. It is noteworthy that the introduction of non-uniform slip will generate much richer behaviors of the hydrodynamic dispersion than the situation with no-slip or uniform-slip boundary conditions, as slippage interacts with zeta potentials in the EOF-suppressing region and EOF-supporting region.