On Applicability of Poisson-Boltzmann Equation for Micro- and Nanoscale Electroosmotic Flows (Communications in Computational Physics, 2008)
The applicability of the Poisson-Boltzmann model for micro- and nanoscaleelectroosmotic flows is a very important theoretical and engineering problem. In thiscontribution we investigate this problem at two aspects: first the high ionic concentration effect on the Boltzmann distribution assumption in the diffusion layer is studiedby comparisons with the molecular dynamics (MD) simulation results; then the electrical double layer (EDL) interaction effect caused by low ionic concentrations in smallchannels is discussed by comparing with the dynamic model described by the coupledPoisson-Nernst-Planck (PNP) and Navier-Stokes (NS) equations. The results show thatthe Poisson-Boltzmann (PB) model is applicable in a very wide range: (i) the PB modelcan still provide good predictions of the ions density profiles up to a very high ionicconcentration (∼ 1 M) in the diffusion layer; (ii) the PB model predicts the net chargedensity accurately as long as the EDL thickness is smaller than the channel width andthen overrates the net charge density profile as the EDL thickness increasing, and thepredicted electric potential profile is still very accurate up to a very strong EDL interaction (λ/W ∼10).