Xuan Xiangchun, Li Dongqing
Department of Mechanical and Industrial Engineering, University of Toronto, ON, Canada.
J Colloid Interface Sci. 2005 Sep 1;289(1):291-303. doi: 10.1016/j.jcis.2005.03.069.
General solutions are developed for direct current (DC) and alternating current (AC) electroosmotic flows in microfluidic channels with arbitrary cross-sectional geometry and arbitrary distribution of wall charge (zeta potential). The applied AC electric field can also be of arbitrary waveform. By proposing a nondimensional time scale varpi defined as the ratio of the diffusion time of momentum across the electric double-layer thickness to the period of the applied electric field, we demonstrate analytically that the Helmholtz-Smoluchowski electroosmotic velocity is an appropriate slip condition for AC electroosmotic flows in typical microfluidic applications. With this slip condition approach, electroosmotic flows in rectangular and asymmetric trapezoidal microchannels with nonuniform wall charge, as examples, are investigated. The unknown constants in the proposed general solutions are numerically determined with a least-squares method through matching the boundary conditions. We find that the wall charge affects significantly the electroosmotic flow while the channel geometry does not. Moreover, the flow feature is characterized by another nondimensional time scale Omega defined as the ratio of the diffusion time of momentum across the channel hydraulic radius to the period of the applied electric field. The onset of phase shift between AC electroosmotic velocity and applied electric field is also examined analytically.
针对具有任意横截面几何形状和任意壁电荷（zeta 电位）分布的微流控通道中的直流（DC）和交流（AC）电渗流，开发了通用解。所施加的交流电场也可以是任意波形。通过提出一个无量纲时间尺度 varpi，其定义为动量在双电层厚度上的扩散时间与所施加电场周期的比值，我们通过分析证明，在典型的微流控应用中，亥姆霍兹 - 斯莫卢霍夫斯基电渗速度是交流电渗流的合适滑移条件。采用这种滑移条件方法，以具有不均匀壁电荷的矩形和不对称梯形微通道中的电渗流为例进行了研究。通过匹配边界条件，用最小二乘法数值确定了所提出的通用解中的未知常数。我们发现壁电荷对电渗流有显著影响，而通道几何形状则没有。此外，流动特性由另一个无量纲时间尺度 Omega 表征，其定义为动量在通道水力半径上的扩散时间与所施加电场周期的比值。还对交流电渗速度与所施加电场之间的相移起始进行了分析研究。
