Analytical solution of combined eloectoossmotic/pressure driven flows in two-dimensional straight channels: Finite debye layer effects

Analytical results for the velocity distribution,mass flow rate, pressure g radient, 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 wal ls and define three new concepts based on the electroosmotic: potential dis tribution. These are the effective EDL thickness, the EDL displacement thic kness, and the EDL vorticity thickness. We show that imposing Helmholtz-Smo luchowski velocity at the edge of the EDL as the velocity matching conditio n between the EDL and the hulk 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 disc uss the limitations of this approach in satisfying the global conservation laws.