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Rise in optimized capillary channels

Published online by Cambridge University Press:  14 August 2013

B. Figliuzzi  and
C. R. Buie
B. Figliuzzi*
Affiliation:
Department of mechanical Engineering, Massachusetts Institute of Technology, Cambridge, 77 Massachusetts Avenue, MA 02139, USA
C. R. Buie
Affiliation:
Department of mechanical Engineering, Massachusetts Institute of Technology, Cambridge, 77 Massachusetts Avenue, MA 02139, USA
*
†Email address for correspondence: crb@mit.edu
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Abstract

Many technological applications rely on the phenomenon of wicking flow induced by capillarity. However, despite a continuing interest in the subject, the influence of the capillary geometry on the wicking dynamics remains underexploited. In numerous applications, the ability to promote wicking in a capillary is a key issue. In this article, a model describing the capillary rise of a liquid in a capillary of varying circular cross-section is presented. The wicking dynamics is described by an ordinary differential equation with a term dependent upon the shape of the capillary channel. Using optimal control theory, we were able to design optimized capillaries which promote faster wicking than uniform cylinders. Numerical simulations show that the height of the rising liquid was up to 50 % greater with the optimized shapes than with a uniform cylinder of optimal radius. Experiments on specially designed capillaries with silicone oil show a good agreement with the theory. The methods presented can be useful in the design and optimization of systems employing capillary-driven transport including micro-heat pipes or oil extracting devices.

JFM classification

Interfacial Flows (free surface): Capillary flows Flow Control: Control theory Flow Control: Flow Control

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 731 , 25 September 2013 , pp. 142 - 161
Copyright
©2013 Cambridge University Press 

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