Commun. Comput. Phys., 2 (2007), pp. 1055-1070.


Lattice Poisson-Boltzmann Simulations of Electroosmotic Flows in Charged Anisotropic Porous Media

Moran Wang 1*, Ning Pan 2, Jinku Wang 3, Shiyi Chen 4

1 Department of Biological & Agricultural Engineering, University of California, Davis, CA 95616, USA / Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
2 Department of Biological & Agricultural Engineering, University of California, Davis, CA 95616, USA.
3 School of Aerospace, Tsinghua University, Beijing, China.
4 Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA/College of Engineering, Peking University, Beijing, China.

Received 7 November 2006; Accepted (in revised version) 7 March 2007
Available online 15 June 2007

Abstract

This paper presents numerical analysis of electroosmotic flows (EOF) in charged anisotropic porous media using the lattice Poisson-Boltzmann method (LPBM), which combines two sets of lattice evolution methods solving the nonlinear Poisson equation for electric potential distribution and the Navier-Stokes equations for fluid flow respectively. Consistent boundary condition implementations are proposed for solving both the electrodynamics and the hydrodynamics on a same grid set. The anisotropic structure effects on EOF characteristics are therefore studied by modeling the electrically driven flows through ellipse arrays packed in a microchannel whose shape and orientation angle are used to control the anisotropy of porous media. The results show that flow rates increase with the axis length along the external electric field direction for a certain porosity and decrease with the angle between the semimajor axis and the bulk flow direction when the orientation angle is smaller than $\pi/2$. After introducing random factors into the microstructures of porous media, the statistical results of flow rate show that the anisotropy of microstructure decreases the permeability of EOFs in porous media.


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PACS: 47.56.+r; 47.57.jd
Key words: Electroosmotic flow, anisotropic porous media, lattice Poisson-Boltzmann method.

*Corresponding author.
Email: mmwang@ucdavis.edu (M. R. Wang), npan@ucdavis.edu (N. Pan), wjk01@mails.tsinghua.edu.cn (J. K. Wang), syc@jhu.edu (S. Y. Chen)
 

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