A Coupled Lattice Boltzmann Method to Solve Nernst–Planck Model for Simulating Electro-osmotic Flows

In this paper, we focus on the nonlinear coupling mechanism of the Nernst–Planck model and propose a coupled lattice Boltzmann method (LBM) to solve it. In this method, a new LBM for the Nernst–Planck equation is developed, a multi-relaxation-time (MRT)-LBM for flow field and an LBM for the Poisson equation are used. And then, we discuss the choice of the model and found that the MRT-LBM is much more stable and accurate than the LBGK model. A reasonable iterative sequence and evolution number for each LBM are proposed by considering the properties of the coupled LBM. The accuracy and stability of the presented coupled LBM are also discussed through simulating electro-osmotic flows (EOF) in micro-channels. Furthermore, to test the applicability of it, the EOF with non-uniform surface potential in micro-channels based on the Nernst–Planck model is simulated. And we investigate the effects of non-uniform surface potential on the pattern of the EOF at different external applied electric fields. Finally, a comparison of the difference between the Nernst–Planck model and the Poisson–Boltzmann model is presented.

[1]  Baochang Shi,et al.  Multi-relaxation-time lattice Boltzmann model for incompressible flow , 2006 .

[2]  Drona Kandhai,et al.  Coupled lattice‐Boltzmann and finite‐difference simulation of electroosmosis in microfluidic channels , 2004 .

[3]  J. S. Lee,et al.  Comparison of the Nernst-Planck model and the Poisson-Boltzmann model for electroosmotic flows in microchannels. , 2007, Journal of colloid and interface science.

[4]  B. Shi,et al.  Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method , 2002 .

[5]  Zhenhua Chai,et al.  Lattice Boltzmann Simulation Of Viscous Dissipation In Electro-Osmotic Flow In Microchannels , 2007 .

[6]  Ameeya Kumar Nayak,et al.  Electroosmotic flow in micro/nanochannels with surface potential heterogeneity: An analysis through the Nernst–Planck model with convection effect , 2009 .

[7]  Baochang Shi,et al.  Lattice Boltzmann model for nonlinear convection-diffusion equations. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Baoming Li,et al.  Lattice Boltzmann Simulation of Electroosmotic Flows in Micro- and Nanochannels , 2004 .

[9]  Howard A. Stone,et al.  ENGINEERING FLOWS IN SMALL DEVICES , 2004 .

[10]  P. Lallemand,et al.  Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  Xiaoyi He,et al.  Lattice Boltzmann simulation of electrochemical systems , 2000 .

[12]  Zhenhua Chai,et al.  A novel lattice Boltzmann model for the Poisson equation , 2008 .

[13]  Edward Ng,et al.  Study of EDL effect on 3‐D developing flow in microchannel with Poisson–Boltzmann and Nernst–Planck models , 2007 .

[14]  Cyrus K. Aidun,et al.  Lattice-Boltzmann Method for Complex Flows , 2010 .

[15]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[16]  Sauro Succi,et al.  Electrorheology in nanopores via lattice Boltzmann simulation. , 2004, The Journal of chemical physics.

[17]  Lung-Ming Fu,et al.  Electroosmotic entry flow in a microchannel , 2001 .

[18]  B. Shi,et al.  Discrete lattice effects on the forcing term in the lattice Boltzmann method. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  R. Benzi,et al.  The lattice Boltzmann equation: theory and applications , 1992 .

[20]  L. Fu,et al.  Analysis of electroosmotic flow with step change in zeta potential. , 2003, Journal of colloid and interface science.

[21]  S. Succi,et al.  A Lattice Boltzmann Model for Anisotropic Crystal Growth from Melt , 2002 .

[22]  Bin Deng,et al.  A new scheme for source term in LBGK model for convection-diffusion equation , 2008, Comput. Math. Appl..

[23]  M. Gad-el-Hak.  The MEMS Handbook , 2001 .

[24]  Zhenhua Chai,et al.  Simulation of electro-osmotic flow in microchannel with lattice Boltzmann method , 2007 .

[25]  Zhan Chen,et al.  Comparison of the Mobile Charge Distribution Models in Mixed Ionic-Electronic Conductors , 2004 .

[26]  Chuguang Zheng,et al.  Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Moran Wang,et al.  Modeling electrokinetic flows in microchannels using coupled lattice Boltzmann methods , 2010, J. Comput. Phys..