On slip velocity boundary conditions for electroosmotic flow near sharp corners

Abstract

The Helmholtz–Smoluchowski (HS) slip velocity boundary condition is often used in computational models of microchannel flows because it allows the motion of the electric double layer (EDL) to be approximated without resolving the charge density profiles close to the walls while dramatically reducing the computational effort required to solve the flow model. The approximation works well for straight channel flows but breaks down in areas of high wall curvature such as sharp corners, where large nonphysical velocities are generated. Many microfluidic applications such as the on-chip focusing and separation of biomolecules rely on the interaction of electroosmosis and electrophoresis in complex channel geometries. In order for these effects to be properly treated using the slip velocity boundary condition, the errors introduced into the solution at corners must be understood. In this article, a complete model for the ion concentrations, electric field, and fluid flow in complex microchannel geometries is presented and is used to compute a pure electroosmotic flow in a two-dimensional microchannel cross slot. The full model solution near the corner at the edge of the EDL is compared to the approximate solution computed by using the HS boundary condition, and it is shown that the accuracy of the approximate solution may be greatly increased by “patching” the full solution as a boundary condition for the approximate solution at the edge of the double layer region. Finally, an empirically derived modified slip velocity boundary condition for electroosmotic flow is proposed. It is shown to improve the accuracy of the flow solution at sharp corners by about 60% when compared to the original boundary condition while also delivering a modest improvement in computational performance because of the elimination of a singularity in the velocity field.