Analysis of the electroviscous effects on pressure-driven flow in nanochannels using effective ionic concentrations

Abstract

The selection of proper boundary conditions is one of the most critical issues when predicting electroviscous effects. Despite numerous studies of the electroviscous effects in micro- and nanochannels with overlapped electric double layers, the boundary conditions for ionic concentrations remain controversial. In this study, the analytical model employing the effective ionic concentrations suitable for determining boundary conditions at the wall is proposed for better predictions of the electroviscous effects in an electrically charged channel with highly overlapped electric double layers. The introduction of the effective ionic concentration is validated using previous numerical results obtained from the lattice Poisson–Boltzmann method. Additionally, numerical results based on the proposed model for streaming conductance as a function of the KCl concentration (c 0) are shown to be in close agreement with the experimental data. The proposed model is not only highly accurate compared with the existing analytical model, but also applicable to a wider range than the self-consistent NP model. Out of the numerical works in this study, a new parameter (ζ/ζ 0)/(κH) a is introduced to quantify the effect of the electroviscosity, which is the dimensionless zeta potential divided by the dimensionless Debye–Huckel parameter, which was commonly employed in previous works. This study shows that the electroviscosity can be expressed as a function of (ζ/ζ 0)/(κH) a only and the electroviscous effects can be safely neglected when (ζ/ζ 0)/(κH)1/4 is less than 20 in silica nanofluidic channels.