Streaming potential and electroviscous effects in periodical pressure-driven microchannel flow

Abstract

An analytical solution for pressure-driven periodical electrokinetic flows in a two-dimensional uniform microchannel is presented based on the Poisson–Boltzmann equation for electrical double layer and the Navier–Stokes equations for incompressible viscous fluid. The analytical results indicate that the periodical streaming potential strongly depends on the periodical Reynolds number (Re=ωh2∕ν) which is a function of the frequency, the channel size, and the kinetic viscosity of fluids. For Re<1, the streaming potential behaves similarly to that of steady flow, whereas it decreases rapidly with Re as Re>1. In addition, the electroviscous force affects greatly both the periodical flow and streaming potential, particularly when the nondimensional electrokinetic diameter κh is small. The electroviscous force has been found to depend on three factors: first, the electroviscous parameter, which is defined as the ratio of the maximum electroviscous force to the pressure gradient; second, the distribution parameter describing the distribution of the electroviscous force over the cross section of the microchannel; third, the coupling coefficient, which is a function of both the periodical Reynolds number and electroviscous parameter, determining both the amplitude attenuation and phase offset of the electroviscous force.