三维矩形微通道内电渗流动与换热的LB模拟
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摘要
采用一体化的格子Boltzmann方法(LBM)对三维矩形微通道内的电渗流动换热问题进行了模拟,获得了NP模型和PB模型下微通道截面的电势分布、无量纲速度分布及温度分布,分别与D-H近似解及解析解对比以验证正确性及精度。进一步对比分析了不同模型下壁面异质电势正电荷分布并模拟了三维壁面异质电势分布微通道内的电渗对流换热问题,结果表明PB模型描述电势场具有较大局限性,而电势分布情况对微通道内的流动模式与对流传热具有明显的影响。
Electroosmotic flow and heat transfer in a three dimensional rectangular microchannel is numerically investigated using a unified lattice Boltzmann method(LBM). The potential distributions, the dimensionless velocity distributions and the temperature distributions in the section of microchannel under both Poisson-Boltzmann model and Nernst-Planck model are compared with Debye-Huckel approximate solution and analytical solution respectively to validate the accurate and precise. Furthermore, the electroosmotic flow and heat transfer in the microchannel with different nonuniform potential distribution along the wall are simulated, and the positive charge distributions for different model are compared. It is found that the Poisson-Boltzmann model has considerable limitations to describe the electric potential field, which have an obvious impact on the flow mode and convective heat transfer in the microchannel.
Electroosmotic flow and heat transfer in a three dimensional rectangular microchannel is numerically investigated using a unified lattice Boltzmann method(LBM). The potential distributions, the dimensionless velocity distributions and the temperature distributions in the section of microchannel under both Poisson-Boltzmann model and Nernst-Planck model are compared with Debye-Huckel approximate solution and analytical solution respectively to validate the accurate and precise. Furthermore, the electroosmotic flow and heat transfer in the microchannel with different nonuniform potential distribution along the wall are simulated, and the positive charge distributions for different model are compared. It is found that the Poisson-Boltzmann model has considerable limitations to describe the electric potential field, which have an obvious impact on the flow mode and convective heat transfer in the microchannel.
引文
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[2] Wang J, Wang M, Li Z. Lattice Poisson-Boltzmann Simulations of Electro-osmotic Flows in Microchannels[J].Journal of Colloid and Interface Science, 2006, 296(2):729-736
[3] Chai Z, Shi B. Simulation of Electro-osmotic Flow in Microchannel with Lattice Boltzmann Method[J]. Physics Letters A, 2007, 364(3):183-188
[4] Masilamani K, Ganguly S, Feichtinger C, et al. Effects of Surface Roughness and Electrokinetic Heterogeneity on Electroosmotic Flow in Microchannel[J]. Fluid Dynamics Research, 2015, 47(3):035505
[5] Yang R J, Fu L M, Hwang C C. Electroosmotic Entry Flow in a Microchannel[J]. Journal of Colloid and Interface Science, 2001, 244(1):173-179
[6] Wang M, Kang Q. Modeling Electrokinetic flows in Microchannels Using Coupled Lattice Boltzmann Methods[J]. Journal of Computational Physics, 2010, 229(3):728-744
[7] Mohammadipoor O R, Niazmand H, Mirbozorgi S A. Numerical Simulation of Electroosmotic Flow in Flat Microchannels With Lattice Boltzmann Method[J]. Arabian Journal for Science and Engineering, 2014, 39(2):1291-1302
[8] Yang X, Shi B, Chai Z, et al. A Coupled Lattice Boltzmann Method to Solve Nernst-Planck Model for Simulating Electro-osmotic Flows[J]. Journal of Scientific Computing, 2014, 61(1):222-238
[9] Yoshida H, Kinjo T, Washizu H. Analysis of Electroosmotic Flow in a Microchannel with Undulated Surfaces[J]. Computers&Fluids, 2016, 124:237-245
[10] Luo K, Wu J, Yi H L, et al. Lattice Boltzmann Modelling of Electro-thermo-convection in a Planar Layer of Dielectric Liquid Subjected to Unipolar Injection and Thermal Gradient[J]. International Journal of Heat and Mass Transfer, 2016, 103:832-846
[11] Guo Z, Zheng C, Shi B. Discrete Lattice Effects on the Forcing Term in the Lattice Boltzmann Method[J]. Physical Review E, 2002, 65(4):046308
[12] Peng Y, Shu C, Chew Y T. Simplified Thermal Lattice Boltzmann Model for Incompressible Thermal Flows[J].Physical Review E, 2003, 68(2):026701
[13] Zhao-Li G, Chu-Guang Z, Bao-Chang S. Non-equilibrium Extrapolation Method for Velocity and Pressure Boundary Conditions in the Lattice Boltzmann Method[J]. Chinese Physics, 2002, 11(4):366
[14] Dutta P, Beskok A. Analytical Solution of Combined Electroosmotic/Pressure Driven Flows in Two-dimensional Straight Channels:Finite Debye Layer Effects[J]. Analytical chemistry, 2001, 73(9):1979-1986
[2] Wang J, Wang M, Li Z. Lattice Poisson-Boltzmann Simulations of Electro-osmotic Flows in Microchannels[J].Journal of Colloid and Interface Science, 2006, 296(2):729-736
[3] Chai Z, Shi B. Simulation of Electro-osmotic Flow in Microchannel with Lattice Boltzmann Method[J]. Physics Letters A, 2007, 364(3):183-188
[4] Masilamani K, Ganguly S, Feichtinger C, et al. Effects of Surface Roughness and Electrokinetic Heterogeneity on Electroosmotic Flow in Microchannel[J]. Fluid Dynamics Research, 2015, 47(3):035505
[5] Yang R J, Fu L M, Hwang C C. Electroosmotic Entry Flow in a Microchannel[J]. Journal of Colloid and Interface Science, 2001, 244(1):173-179
[6] Wang M, Kang Q. Modeling Electrokinetic flows in Microchannels Using Coupled Lattice Boltzmann Methods[J]. Journal of Computational Physics, 2010, 229(3):728-744
[7] Mohammadipoor O R, Niazmand H, Mirbozorgi S A. Numerical Simulation of Electroosmotic Flow in Flat Microchannels With Lattice Boltzmann Method[J]. Arabian Journal for Science and Engineering, 2014, 39(2):1291-1302
[8] Yang X, Shi B, Chai Z, et al. A Coupled Lattice Boltzmann Method to Solve Nernst-Planck Model for Simulating Electro-osmotic Flows[J]. Journal of Scientific Computing, 2014, 61(1):222-238
[9] Yoshida H, Kinjo T, Washizu H. Analysis of Electroosmotic Flow in a Microchannel with Undulated Surfaces[J]. Computers&Fluids, 2016, 124:237-245
[10] Luo K, Wu J, Yi H L, et al. Lattice Boltzmann Modelling of Electro-thermo-convection in a Planar Layer of Dielectric Liquid Subjected to Unipolar Injection and Thermal Gradient[J]. International Journal of Heat and Mass Transfer, 2016, 103:832-846
[11] Guo Z, Zheng C, Shi B. Discrete Lattice Effects on the Forcing Term in the Lattice Boltzmann Method[J]. Physical Review E, 2002, 65(4):046308
[12] Peng Y, Shu C, Chew Y T. Simplified Thermal Lattice Boltzmann Model for Incompressible Thermal Flows[J].Physical Review E, 2003, 68(2):026701
[13] Zhao-Li G, Chu-Guang Z, Bao-Chang S. Non-equilibrium Extrapolation Method for Velocity and Pressure Boundary Conditions in the Lattice Boltzmann Method[J]. Chinese Physics, 2002, 11(4):366
[14] Dutta P, Beskok A. Analytical Solution of Combined Electroosmotic/Pressure Driven Flows in Two-dimensional Straight Channels:Finite Debye Layer Effects[J]. Analytical chemistry, 2001, 73(9):1979-1986