微通道内幂律流体电渗流的量纲分析

Dimensional analysis of electroosmotic flow of power-law fluids in microchannels

运用量纲分析法对微通道内非牛顿幂律流体电渗流(EOF)进行公式推导和参数分析,得出了EOF速度和外加电场、稠度系数、Zeta电势之间存在的数学关系,并基于Poisson-Nernst-Planck模型有限元法对幂律流体EOF进行模拟分析,验证了上述数学关系的正确性。结果表明微通道内幂律流体EOF速度与外加电场、Zeta电势以及稠度系数均成幂函数关系,并且稠度系数的指数为幂律指数的负倒数。该结论对研究非牛顿幂律流体在微通道内的EOF理论研究和实验优化具有参考价值。

The dimensional analysis method was used to deduce the formulas and analyze the parameters of electroosmotic flow（ EOF） of power-law fluids in microchannels. The mathematical relationship between the velocity of EOF of power-law fluids and the applied electric field,the consistency coefficient,the zeta potential was obtained.Based on the poisson-nernst-planck（ PNP） model,the finite element method was used to simulate numerically the flow characteristics of EOF of power-law fluids in a microchannel and the results verified the correction of the mathematical relationship. The results showed that the EOF of power-law fluids in microchannels has a power function relationship with the applied electric field,the Zeta potential and the consistency coefficient. Particularly,the exponent of consistency coefficient was negative derivative of power-law index. The conclusions have an extensive scope of application and can provide a reference value to theoretical research and experimental application of electroosmotic flow of power-law fluids in microchannels.