A numerical analysis of finite Debye-length effects in induced-charge electro-osmosis

TL;DR

This paper compares three numerical models to analyze how finite Debye-length effects influence induced-charge electro-osmosis flows, revealing significant overestimations by slip-velocity models especially at nanoscales.

Contribution

It introduces and compares three numerical models for ICEO flow, highlighting the importance of finite Debye-length effects and their impact on flow velocity predictions.

Findings

Slip-velocity models overestimate ICEO flow compared to full models.

Discrepancies increase with Debye length relative to electrode size.

Finite Debye-length effects can cause over 100% velocity errors for certain electrode geometries.

Abstract

For a microchamber filled with a binary electrolyte and containing a flat un-biased center electrode at one wall, we employ three numerical models to study the strength of the resulting induced-charge electro-osmotic (ICEO) flow rolls: (i) a full nonlinear continuum model resolving the double layer, (ii) a linear slip-velocity model not resolving the double layer and without tangential charge transport inside this layer, and (iii) a nonlinear slip-velocity model extending the linear model by including the tangential charge transport inside the double layer. We show that compared to the full model, the slip-velocity models significantly overestimate the ICEO flow. This provides a partial explanation of the quantitative discrepancy between observed and calculated ICEO velocities reported in the literature. The discrepancy increases significantly for increasing Debye length relative to the electrode size, i.e. for nanofluidic systems. However, even for electrode dimensions in the micrometer range, the discrepancies in velocity due to the finite Debye length can be more than 10% for an electrode of zero height and more than 100% for electrode heights comparable to the Debye length.