Asymptotically exact formulas for channel flows over liquid-infused surfaces
File(s)
Published version
Author(s)
Rodriguez-Broadbent, Henry
MIYOSHI, Hiroyuki
Crowdy, Darren
Type
Journal Article
Abstract
Analytical formulas are derived describing channel flows over liquid-infused surfaces. The formulas are
explicit, asymptotically exact, and readily evaluated; no numerical scheme beyond simple quadrature is
needed to calculate the flows. The formulas are obtained using a three-stage asymptotic analysis under
the assumptions that an array of aligned finite-length grooves on the lower wall of a channel are (i)
slender, (ii) well separated from the upper channel wall and (iii) well separated from each other. Despite
these apparently limiting assumptions it is found, by comparison with full numerical simulations, that the
formulas give excellent approximations to the flow across a much broader range of operating conditions.
Useful formulas for the hydrodynamic slip lengths of the liquid-infused surfaces are reported and tested
against both numerical simulations and other approximate formulas appearing in the literature. The
formulas are also expected to be useful in assessing the possibility of so-called shear-induced failure
of liquid-infused surfaces.
explicit, asymptotically exact, and readily evaluated; no numerical scheme beyond simple quadrature is
needed to calculate the flows. The formulas are obtained using a three-stage asymptotic analysis under
the assumptions that an array of aligned finite-length grooves on the lower wall of a channel are (i)
slender, (ii) well separated from the upper channel wall and (iii) well separated from each other. Despite
these apparently limiting assumptions it is found, by comparison with full numerical simulations, that the
formulas give excellent approximations to the flow across a much broader range of operating conditions.
Useful formulas for the hydrodynamic slip lengths of the liquid-infused surfaces are reported and tested
against both numerical simulations and other approximate formulas appearing in the literature. The
formulas are also expected to be useful in assessing the possibility of so-called shear-induced failure
of liquid-infused surfaces.
Date Issued
2024-08
Date Acceptance
2024-10-08
Citation
IMA Journal of Applied Mathematics, 2024, 89 (4), pp.623-660
ISSN
0272-4960
Publisher
Oxford University Press
Start Page
623
End Page
660
Journal / Book Title
IMA Journal of Applied Mathematics
Volume
89
Issue
4
Copyright Statement
© The Author(s) 2024. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/
4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/
4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
License URL
Identifier
https://academic.oup.com/imamat/article/89/4/623/7817827
Publication Status
Published
Date Publish Online
2024-10-10