Al Mukahal F H H, Duffy B R, Wilson S K
Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK.
Department of Mathematics and Statistics, King Faisal University, PO Box 400, Hafouf 31982, Kingdom of Saudi Arabia.
Proc Math Phys Eng Sci. 2017 Nov;473(2207):20170524. doi: 10.1098/rspa.2017.0524. Epub 2017 Nov 15.
Motivated by the need for a better understanding of the transport of solutes in microfluidic flows with free surfaces, the advection and dispersion of a passive solute in steady unidirectional flow of a thin uniform rivulet on an inclined planar substrate driven by gravity and/or a uniform longitudinal surface shear stress are analysed. Firstly, we describe the short-time advection of both an initially semi-infinite and an initially finite slug of solute of uniform concentration. Secondly, we describe the long-time Taylor-Aris dispersion of an initially finite slug of solute. In particular, we obtain the general expression for the effective diffusivity for Taylor-Aris dispersion in such a rivulet, and discuss in detail its different interpretations in the special case of a rivulet on a vertical substrate.
出于更好地理解具有自由表面的微流体流动中溶质输运的需求，分析了在重力和/或均匀纵向表面剪切应力驱动下，倾斜平面基底上薄均匀细流的稳定单向流动中被动溶质的平流和扩散。首先，我们描述了初始时半无限长和初始时有限长度的均匀浓度溶质段的短时平流。其次，我们描述了初始时有限长度溶质段的长时泰勒 - 阿里斯扩散。特别地，我们得到了这种细流中泰勒 - 阿里斯扩散有效扩散率的一般表达式，并详细讨论了在垂直基底上细流的特殊情况下其不同的解释。
