Electroosmosis with step changes in zeta potential in microchannels

This article presents an analytical solution for two‐dimensional fluid flow in a rectangular microchannel in the vicinity of a step change in the zeta (ζ) potential. The stream function is determined from the creeping flow approximation to the Navier‐Stokes equations assuming a fixed volumetric axial flow, a constant electric field, and thin symmetric double layers. The resulting biharmonic equation is solved using a double‐sided Laplace transformation, which is then inverted by Heaviside expansion. The resulting series solution provides closed‐form expressions for the velocity and pressure fields that help explain how the recirculating flows generated by an abrupt change in the surface potential may contribute both locally and globally to the hydrodynamic dispersion in straight microchannels.