Rivulet flow round a horizontal cylinder subject to a uniform surface shear stress
KAUST Grant NumberKUK-C1-013-04
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Abstract© 2014 © The Author, 2014. Published by Oxford University Press; all rights reserved. For Permissions, please email: email@example.com. The steady flow of a slowly varying rivulet with prescribed flux in the azimuthal direction round a large stationary horizontal cylinder subject to a prescribed uniform azimuthal surface shear stress is investigated. In particular, we focus on the case where the volume flux is downwards but the shear stress is upwards, for which there is always a solution corresponding to a rivulet flowing down at least part of one side of the cylinder. We consider both a rivulet with constant non-zero contact angle but slowly varying width (that is, de-pinned contact lines) and a rivulet with constant width but slowly varying contact angle (that is, pinned contact lines), and show that they have qualitatively different behaviour. When shear is present, a rivulet with constant non-zero contact angle can never run all the way from the top to the bottom of the cylinder, and so we consider the scenario in which an infinitely wide two-dimensional film of uniform thickness covers part of the upper half of the cylinder and 'breaks' into a single rivulet with constant non-zero contact angle. In contrast, a sufficiently narrow rivulet with constant width can run all the way from the top to the bottom of the cylinder, whereas a wide rivulet can do so only if its contact lines de-pin, and so we consider the scenario in which the contact lines of a wide rivulet de-pin on the lower half of the cylinder.
CitationPaterson C, Wilson SK, Duffy BR (2014) Rivulet flow round a horizontal cylinder subject to a uniform surface shear stress. The Quarterly Journal of Mechanics and Applied Mathematics 67: 567–597. Available: http://dx.doi.org/10.1093/qjmam/hbu018.
SponsorsThe first author (C.P.) gratefully acknowledges the financial support of the University of Strathclyde via a Postgraduate Research Scholarship. All three authors gratefully acknowledge valuable discussions about the rain-wind-induced vibrations of cables and related problems with Dr Ian J. Taylor and Mr (now Dr) Andrew C. Robertson (Department of Mechanical Engineering, University of Strathclyde). This work was begun while the second author (S.K.W.) was a Visiting Fellow in the Oxford Centre for Collaborative Applied Mathematics (OCCAM), Mathematical Institute, University of Oxford, United Kingdom, and completed while he was a Leverhulme Trust Research Fellow supported by award RF-2013-355. This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
PublisherOxford University Press (OUP)