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

Ouali, FF ORCID: https://orcid.org/0000-0002-6530-6786, McHale, G, Javed, H, Trabi, C, Shirtcliffe, NJ and Newton, MI ORCID: https://orcid.org/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
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:	Number Type 10.1007/s10404-013-1145-5 DOI
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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