Pressure-driven electrokinetic slip-flow in planar microchannels

Abstract

This paper presents an analytical solution for pressure-driven electrokinetic flows in planar microchannels with velocity slip at the walls. The Navier–Stokes equations for an incompressible viscous fluid have been solved along with the Poisson–Boltzmann equation for the electric double layer. Analytical expressions for the velocity profile, average electrical conductivity, and induced voltage are presented without invoking the Debye–Hückel approximation. It is known that an increase in the zeta-potential leads to an increase in the flow-induced voltage; however, it is demonstrated that the induced voltage reaches a maximum value at a certain zeta-potential depending on the slip coefficient and the Debye–Hückel parameter, while decreasing rapidly at higher zeta-potentials. The present parametric study indicates that liquid slip at the walls can increase the maximum induced voltage very significantly.