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Wicking of a liquid bridge connected to a moving porous surface

Published online by Cambridge University Press:  12 June 2012

A. D. Gat ,
H. K. Navaz  and
M. Gharib
A. D. Gat*
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
H. K. Navaz
Affiliation:
Department of Mechanical Engineering, University of Kettering, Flint, MI 48504, USA
M. Gharib
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: amirgat@caltech.edu
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Abstract

We study the coupled problem of a liquid bridge connected to a porous surface and an impermeable surface, where the gap between the surfaces is an externally controlled function of time. The relative motion between the surfaces influences the pressure distribution and geometry of the liquid bridge, thus affecting the shape of liquid penetration into the porous material. Utilizing the lubrication approximation and Darcy’s phenomenological law, we obtain an implicit integral relation between the relative motion between the surfaces and the shape of liquid penetration. A method to control the shape of liquid penetration is suggested and illustrated for the case of conical penetration shapes with an arbitrary cone opening angle. We obtain explicit analytic expressions for the case of constant relative speed of the surfaces as well as for the relative motion between the surfaces required to create conical penetration shapes. Our theoretical results are compared with experiments and reasonable agreement between the analytical and experimental data is observed.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Liquid bridges Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 703 , 25 July 2012 , pp. 315 - 325
Copyright
Copyright © Cambridge University Press 2012

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