基于改进型泊松-玻尔兹曼方程的电渗流建模与分析

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

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(modifiedPoisson 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. 4 V,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±1 V,500 Hz电信号产生的最大电渗流速度为1 034. 31μm/s.

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 0.4 V and the ion concentration is less than 10-4 mol/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 500 μm and the gap of 25 μm is 1 034.31 μm/s at ±1 V potential with the frequency of 500 Hz.