Ouali, F.F. ORCID: 0000-0002-6530-6786, McHale, G., Javed, H., Trabi, C., Shirtcliffe, N.J. and Newton, M.I. ORCID: 0000-0003-4231-1002, 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 | ||||
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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 | ||||
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Rights: | © 2013 Springer | ||||
Divisions: | Schools > School of Science and Technology | ||||
Record created by: | EPrints Services | ||||
Date Added: | 09 Oct 2015 10:11 | ||||
Last Modified: | 29 Sep 2021 08:18 | ||||
URI: | https://irep.ntu.ac.uk/id/eprint/9177 |
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