School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore.
Electrophoresis. 2013 Mar;34(5):662-7. doi: 10.1002/elps.201200507. Epub 2013 Feb 5.
EOF of non-Newtonian power-law fluids in a cylindrical microchannel is analyzed theoretically. Specially, exact solutions of electroosmotic velocity corresponding to two special fluid behavior indices (n = 0.5 and 1.0) are found, while approximate solutions are derived for arbitrary values of fluid behavior index. It is found that because of the approximation for the first-order modified Bessel function of the first kind, the approximate solutions introduce largest errors for predicting electroosmotic velocity when the thickness of electric double layer is comparable to channel radius, but can accurately predict the electroosmotic velocity when the thickness of electric double layer is much smaller or larger than the channel radius. Importantly, the analysis reveals that the Helmholtz-Smoluchowski velocity of power-law fluids in cylindrical microchannels becomes dependent on geometric dimensions (radius of channel), standing in stark contrast to the Helmholtz-Smoluchowski velocity over planar surfaces or in parallel-plate microchannels. Such interesting and counterintuitive effects can be attributed to the nonlinear coupling among the electrostatics, channel geometry, and non-Newtonian hydrodynamics. Furthermore, a method for enhancement of EOFs of power-law fluids is proposed under a combined DC and AC electric field.
在圆柱形微通道中分析了非牛顿幂律流体的EOF。特别地，找到了对应于两个特殊流体行为指数（n = 0.5 和 1.0）的电渗速度的精确解，而对于任意流体行为指数则推导出了近似解。发现由于对第一类一阶修正贝塞尔函数的近似，当双电层厚度与通道半径相当时，近似解在预测电渗速度时会引入最大误差，但当双电层厚度远小于或大于通道半径时，近似解可以准确预测电渗速度。重要的是，分析表明，圆柱形微通道中幂律流体的亥姆霍兹-斯莫卢霍夫斯基速度取决于几何尺寸（通道半径），与平面表面或平行板微通道上的亥姆霍兹-斯莫卢霍夫斯基速度形成鲜明对比。这种有趣且违反直觉的效应可归因于静电、通道几何形状和非牛顿流体动力学之间的非线性耦合。此外，提出了一种在直流和交流电场组合下增强幂律流体EOF 的方法。
