基于改进型泊松-玻尔兹曼方程的电渗流建模与分析

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.

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

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.