Mortensen Niels Asger, Okkels Fridolin, Bruus Henrik
MIC, Department of Micro and Nanotechnology, Bldg. 345 east, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 May;71(5 Pt 2):057301. doi: 10.1103/PhysRevE.71.057301. Epub 2005 May 5.
We consider pressure-driven, steady-state Poiseuille flow in straight channels with various cross-sectional shapes: elliptic, rectangular, triangular, and harmonic-perturbed circles. A given shape is characterized by its perimeter P and area A which are combined into the dimensionless compactness number C= P2/A, while the hydraulic resistance is characterized by the well-known dimensionless geometrical correction factor alpha. We find that alpha depends linearly on C, which points out C as a single dimensionless measure characterizing flow properties as well as the strength and effectiveness of surface-related phenomena central to lab-on-a-chip applications. This measure also provides a simple way to evaluate the hydraulic resistance for the various shapes.
我们考虑在具有各种横截面形状（椭圆形、矩形、三角形和谐波扰动圆形）的直通道中，由压力驱动的稳态泊肃叶流。给定的形状由其周长(P)和面积(A)来表征，它们被组合成无量纲紧凑度数(C = P^2/A)，而水力阻力则由著名的无量纲几何校正因子(\alpha)来表征。我们发现(\alpha)与(C)呈线性关系，这表明(C)是一个单一的无量纲量度，它既表征了流动特性，也表征了对于芯片实验室应用至关重要的与表面相关现象的强度和有效性。这个量度还提供了一种简单的方法来评估各种形状的水力阻力。
