基于改进型泊松-玻尔兹曼方程的电渗流建模与分析
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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(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 flowby 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 flowunder higher voltage conditions. By use of the MPB equation with non-linear characteristics,the maximal electro-osmotic flowgenerated 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.
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 flowby 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 flowunder higher voltage conditions. By use of the MPB equation with non-linear characteristics,the maximal electro-osmotic flowgenerated 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.
引文
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[3]Dittrich P S,Manz A.Lab-on-a-chip:microfluidics in drug discovery[J].Nature Reviews Drug Discovery,2006,5(3):210-218.
[4]Zou Z W,Jang A,Macknight E,et al.Environmentally friendly disposable sensors with microfabricated on-chip planar bismuth electrode for in situ heavy metal ions measurement[J].Sensors and Actuators B:Chemical,2008,134(1):18-24.
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[6]Zhao B S,Koo Y M,Chung D S.Separations based on the mechanical forces of light[J].Analytica Chimica Acta,2006,556(1):97-103.
[7]Shields C W,Reyes C D,Lopez G P.Microfluidic cell sorting:a review of the advances in the separation of cells from debulking to rare cell isolation[J].Lab on a Chip,2015,15(5):1230-1249.
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