Periodical pressure-driven flows in microchannel with wall slip velocity and electro-viscous effects

Abstract

In a microfluidic system, the flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in the microchannel. The flow-electricity interaction in a complex microfluidic system subjected to a joint action of wall slip and electro-viscosity is an important topic. An analytical solution for the periodical pressure-driven flow in a two-dimensional uniform microchannel, with consideration of wall slip and electro-viscous effect is obtained based on the Poisson-Boltzmann equation for the Electric Double Layer (EDL) and the Navier-Stokes equations for the liquid flow. The analytic solutions agree well with the numerical solutions. The analytical results indicate that the periodical flow velocity and the Flow-Induced Electric Field (FIEF) strongly depend on the frequency Reynolds number ( Re = ω h 2/ v), that is a function of the frequency, the channel size and the kinetic viscosity of fluids. For Re<1 the flow velocity and the FIEF behave similarly to those in a steady flow, whereas they decrease rapidly with Re as Re>1. In addition, the electro-viscous effect greatly influences the periodical flow velocity and the FIEF, particularly, when the electrokinetic radius κ H is small. Furthermore, the wall slip velocity amplifies the FIEF and enhances the electro-viscous effect on the flow.