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 th...

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Bibliographic Details
Published in:Journal of colloid and interface science 2006-06, Vol.298 (2), p.880-888
Main Authors: Xiao, Yan, Yang, Fuzheng, Pitchumani, Ranga
Format: Article
Language:English
Subjects:
Analytical model
Capillary flow
Chemistry
Dynamic contact angle
Exact sciences and technology
General and physical chemistry
Minichannels
Parallel plates
Tube
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Summary: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. Capillary rise in microchannel and tube configurations.
ISSN:0021-9797
1095-7103
DOI:10.1016/j.jcis.2006.01.005