Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels

OUALI, F.F., MCHALE, G., JAVED, H., TRABI, C., SHIRTCLIFFE, N.J. and NEWTON, M.I., 2013. Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels. Microfluidics and Nanofluidics, 15 (3), pp. 309-326. ISSN 1613-4982

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Abstract

The spontaneous capillary-driven filling of microchannels is important for a wide range of applications. These channels are often rectangular in cross-section, can be closed or open, and horizontal or vertically orientated. In this work, we develop the theory for capillary imbibition and rise in channels of rectangular cross-section, taking into account rigidified and non-rigidified boundary conditions for the liquid–air interfaces and the effects of surface topography assuming Wenzel or Cassie-Baxter states. We provide simple interpolation formulae for the viscous friction associated with flow through rectangular cross-section channels as a function of aspect ratio. We derive a dimensionless cross-over time, T c, below which the exact numerical solution can be approximated by the Bousanquet solution and above which by the visco-gravi- tational solution. For capillary rise heights significantly below the equilibrium height, this cross-over time is T c & (3 X e /2) 2/3 and has an associated dimensionless cross-over rise height X c & (3 X e /2) 1/3, where X e = 1/ G is the dimensionless equilibrium rise height and G is a dimensionless form of the acceleration due to gravity. We also show from wetting considerations that for rectangular channels, fingers of a wetting liquid can be expected to imbibe in advance of the main meniscus along the corners of the channel walls.

Item Type: Journal article
Publication Title: Microfluidics and Nanofluidics
Creators: Ouali, F.F., McHale, G., Javed, H., Trabi, C., Shirtcliffe, N.J. and Newton, M.I.
Publisher: Springer
Date: 2013
Volume: 15
Number: 3
ISSN: 1613-4982
Identifiers:
NumberType
10.1007/s10404-013-1145-5DOI
Rights: © 2013 Springer
Divisions: Schools > School of Science and Technology
Depositing User: EPrints Services
Date Added: 09 Oct 2015 10:11
Last Modified: 23 Aug 2016 09:08
URI: http://irep.ntu.ac.uk/id/eprint/9177

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