矩形微管道内电势分布的数值模拟

Numerical simulation on potential distribution in rectangular microchannels

针对矩形微管道横截面上双电层场的控制方程是二维、二阶非线性Poisson-Boltzm ann方程,不易求得其解析解的问题,应用有限控制容积法得到双电层控制方程的完全数值解.对采用不同浓度KC l溶液时矩形微管道内的电势分布进行了数值模拟.仿真结果表明,溶液浓度较高时,电势在靠近管壁的区域内迅速下降到零,这是由于双电层厚度很小,管道中心区的电荷密度为零的缘故;在20μm×30μm的管道中,溶液浓度为10-8mol/L时,管道中心区域的电势不为零.这是因为双电层厚度变大,双电层在管道内发生重叠,管道中心区的电荷密度不为零的缘故.

The electrical double layer （EDL） field in the cross-section of rectangular microchannel is described by Poisson-Bohzmann equation which is a two-dimensional, nonlinear, and second-order partial differential equation. The Poisson-Boltzmann equation is numerically solved by employing the finite control volume method. The potential distribution in the rectangular microchannel with different KCl electrolyte solution concentrations is compared. The numerical simulation results show that the potential field drops to zero sharply in the region close to the wall when the electrolyte solution concentration is high, because the thickness of EDL is very small, and the electric charge density in the center of microchannel is zero. The potential in the center of the microchannel is not zero in the 20 μm×30μm microchannel when the electrolyte solution concentration is 10^-8 mol/L. The thickness of EDL becomes bigger, and EDLs in the rectangular microchannel are overlapped. So the net charge density in the center of microchannel is not zero.