Xiao Yan, Yang Fuzheng, Pitchumani Ranga
Advanced Materials and Technologies Laboratory, Department of Mechanical Engineering, University of Connecticut, Storrs, CT 06269-3139, USA.
J Colloid Interface Sci. 2006 Jun 15;298(2):880-8. doi: 10.1016/j.jcis.2006.01.005. Epub 2006 Feb 15.
Investigations on the motion of a fluid in capillary geometries have been extensively reported in the literature using both experimental and theoretical approaches. In this paper, the theories for capillary flow are generalized to a unified nonlinear second-order differential equation which takes the effects of the entrance, the inertial forces, and the dynamic contact angle into account. An analytical solution of the differential equation is obtained in the form of a double Dirichlet series. The readily evaluated analytical solution is compared with experimental and numerical results in the literature, which shows a good agreement. It is demonstrated that this analytical approach can be used to predict capillary flows for a wide range of fluids and parallel-plate and tube geometries in a unified manner.
关于毛细管几何形状中流体运动的研究，在文献中已广泛报道，采用了实验和理论两种方法。本文将毛细管流动理论推广到一个统一的非线性二阶微分方程，该方程考虑了入口、惯性力和动态接触角的影响。以双狄利克雷级数的形式得到了该微分方程的解析解。将易于评估的解析解与文献中的实验和数值结果进行了比较，结果显示出良好的一致性。结果表明，这种解析方法可用于以统一的方式预测广泛的流体以及平行板和管几何形状中的毛细管流动。
