A generalized analysis of capillary flows in channels

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. (c) 2006 Elsevier Inc. All rights reserved.