Comparison of the Nernst–Planck model and the Poisson–Boltzmann model for electroosmotic flows in microchannels

Abstract

In the analysis of electroosmotic flows, the internal electric potential is usually modeled by the Poisson-Boltzmann equation. The Poisson-Boltzmann equation is derived from the assumption of thermodynamic equilibrium where the ionic distributions are not affected by fluid flows. Although this is a reasonable assumption for steady electroosmotic flows through straight microchannels, there are some important cases where convective transport of ions has nontrivial effects. In these cases, it is necessary to adopt the Nernst-Planck equation instead of the Poisson-Boltzmann equation to model the internal electric field. In the present work, the predictions of the Nernst-Planck equation are compared with those of the Poisson-Boltzmann equation for electroosmotic flows in various microchannels where the convective transport of ions is not negligible.