Analytical Solution of Combined Electroosmotic/Pressure Driven Flows in Two-Dimensional Straight Channels: Finite Debye Layer Effects

Analytical results for the velocity distribution, mass flow rate, pressure gradient, wall shear stress, and vorticity in mixed electroosmotic/pressure driven flows are presented for two-dimensional straight channel geometry. We particularly analyze the electric double-layer (EDL) region near the walls and define three new concepts based on the electroosmotic potential distribution. These are the effective EDL thickness, the EDL displacement thickness, and the EDL vorticity thickness. We show that imposing Helmholtz-Smoluchowski velocity at the edge of the EDL as the velocity matching condition between the EDL and the bulk flow region is incomplete under spatial bulk flow variations across the finite EDL. However, the Helmholtz-Smoluchowski velocity can be used as the appropriate slip velocity on the wall. We discuss the limitations of this approach in satisfying the global conservation laws.