东北大学学报（自然科学版）

东北大学学报:自然科学版 ›› 2019, Vol. 40 ›› Issue (3): 447-451.DOI: 10.12068/j.issn.1005-3026.2019.03.027

• 物理学 • 上一篇    下一篇

基于改进型泊松-玻尔兹曼方程的电渗流建模与分析

胡晟， 吕江涛， 司光远   

  1. (东北大学秦皇岛分校 控制工程学院， 河北 秦皇岛066004)
  • 收稿日期:2018-01-24 修回日期:2018-01-24 出版日期:2019-03-15 发布日期:2019-03-08
  • 通讯作者: 胡晟
  • 作者简介:胡晟(1984-)，男，云南景洪人，东北大学秦皇岛分校讲师，博士.
  • 基金资助:
    河北省自然科学基金资助项目(F2017501059)； 辽宁省博士启动基金资助项目(20170520325)； 中央高校基本科研业务费专项资金资助项目(N172304033).

Analysis and Modeling of Electro-osmosis Based on the Modified Poisson-Boltzmann Equation

HU Sheng， LYU Jiang-tao， SI Guang-yuan   

  1. School of Control Engineering， Northeastern University at Qinhuangdao， Qinhuangdao 066004， China.
  • Received:2018-01-24 Revised:2018-01-24 Online:2019-03-15 Published:2019-03-08
  • Contact: HU Sheng
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摘要： 建立了双电层的离子分布模型，基于经典Poisson-Boltzmann(PB)方程和改进型MPB(modified Poisson Boltzmann)方程对不同浓度和激励电压的离子分布进行了理论研究.结果发现在电压高于0.4V，且自由离子浓度小于10-4mol/L时，双电层内部的扩散层厚度存在较大的误差.这直接导致了基于Debye长度模拟电渗流运动与实际观测不符，主要因为Debye-Hückel公式具有线性关系不适用于仿真高电压条件下的电渗流运动.因此借助非线性MPB方程求解扩散层厚度，更能精确得到正、负电极宽度为500μm，间距为25μm，在±1V，500Hz电信号产生的最大电渗流速度为1034.31μm/s.

关键词: 交流电渗流, 双电层, PB方程, MPB方程, 有限元法

Abstract: The ion distribution for different concentrations and applied voltage is studied by modeling the ion distribution in electric double layer(EDL)based on the Poisson-Boltzmann(PB)and modified Poisson-Boltzmann(MPB)equations. The results indicate that some errors exist in the thickness of diffusion in EDL if the applied voltage is more than 0.4V and the ion concentration is less than 10-4mol/L. The simulated electro-osmotic flow by using Debye length is not in agreement with the practical observation result mainly because the Debye-Hückel equation is of linear relationship and not compatible with the calculating electro-osmotic flow under higher voltage conditions. By use of the MPB equation with non-linear characteristics， the maximal electro-osmotic flow generated by two co-planar metal electrodes with the width of 500μm and the gap of 25μm is 1034.31μm/s at ±1V potential with the frequency of 500Hz.

Key words: AC electro-osmosis, electric double layer(EDL), PB equation, MPB equation, finite element method

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