Commun. Comput. Phys.,
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Volume 3.


On Applicability of Poisson-Boltzmann Equation for Micro- and Nanoscale Electroosmotic Flows

Moran Wang 1*, Shiyi Chen 2

1 Nanomaterials in Environment, Agriculture and Technology (NEAT), University of California, Davis, CA 95616, USA; and Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
2 Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA; and College of Engineering, Peking University, Beijing, China.

Received 6 November 2007; Accepted (in revised version) 20 December 2007
Available online 29 January 2008

Abstract

The applicability of the Poisson-Boltzmann model for micro- and nanoscale electroosmotic flows is a very important theoretical and engineering problem. In this contribution we investigate this problem at two aspects: first the high ionic concentration effect on the Boltzmann distribution assumption in the diffusion layer is studied by comparisons with the molecular dynamics (MD) simulation results; then the electrical double layer (EDL) interaction effect caused by low ionic concentrations in small channels is discussed by comparing with the dynamic model described by the coupled Poisson-Nernst-Planck (PNP) and Navier-Stokes (NS) equations. The results show that the Poisson-Boltzmann (PB) model is applicable in a very wide range: (i) the PB model can still provide good predictions of the ions density profiles up to a very high ionic concentration ($\sim$ 1 M) in the diffusion layer; (ii) the PB model predicts the net charge density accurately as long as the EDL thickness is smaller than the channel width and then overrates the net charge density profile as the EDL thickness increasing, and the predicted electric potential profile is still very accurate up to a very strong EDL interaction ($\lambda/W \sim 10$).


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PACS: 41.20.Cv, 66.30.Ah, 82.39.Wj
Key words: Poisson-Boltzmann model, electroosmotic flow, EDL interaction, Poisson-Nernst-Planck equation.

*Corresponding author.
Email: mmwang@ucdavis.edu (M. Wang), syc@jhu.edu (S. Chen)
 

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