Division of Mechanics, Research Center for Applied Sciences, Academia Sinica, Taipei, Taiwan.
Electrophoresis. 2011 Jun;32(11):1268-72. doi: 10.1002/elps.201000692. Epub 2011 May 2.
The paper presents semi-analytical solutions to electro-osmotic (EO) flow through polygonal ducts under the Debye-Hückel approximation. Analytical series solutions assisted with numerical collocations are found to yield very fast convergence. The solutions have practical applications as the pores of EO membranes are mostly hexagonal, stacked densely in a beehive-like matrix. In addition, we develop simple asymptotic approximations that would be applicable to all EO tube flows of small as well as large dimensionless electrokinetic width. This facilitates investigation of analytical structures of general EO flows in all shapes of tubes, including the present geometries. In particular, for thick electrical double layers, the flow rate of EO is related to the corresponding viscous Poiseuille flow rate, while for thin electrical double layers, the flow rate is shown to be characterized by the cross-sectional area and the perimeter length of the tubes.
本文提出了在德拜-休克尔近似下通过多边形管道的电渗透（EO）流动的半解析解。发现解析级数解与数值配置相结合，可以非常快速地收敛。这些解具有实际应用价值，因为 EO 膜的孔大多为六边形，在蜂窝状基质中密集堆叠。此外，我们还开发了简单的渐近近似，适用于所有 EO 管流的小和大无量纲电动宽度。这便于研究所有形状的 EO 管中一般 EO 流动的分析结构，包括当前的几何形状。特别是对于厚的电双层，EO 的流速与相应的粘性泊肃叶流速有关，而对于薄的电双层，流速表现为由管的横截面面积和周长长度决定。
