Rivulet flow round a horizontal cylinder subject to a uniform surface shear stress

Colin Paterson, Stephen Wilson, Brian Duffy

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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 (i.e. de-pinned contact lines) and a rivulet with constant width but slowly varying contact angle (i.e. 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.
LanguageEnglish
Pages567-597
Number of pages31
JournalQuarterly Journal of Mechanics and Applied Mathematics
Volume67
Issue number4
Early online date14 Sep 2014
DOIs
Publication statusPublished - Nov 2014

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Shear Stress
shear stress
Contact angle
Shear stress
Contact Line
Horizontal
Contact Angle
Fluxes
Steady flow
Contacts (fluid mechanics)
Scenarios
steady flow
Steady Flow
Cover
shear

Keywords

  • uniform surface shear stress
  • rivulet flow
  • horizontal cylinder

Cite this

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abstract = "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 (i.e. de-pinned contact lines) and a rivulet with constant width but slowly varying contact angle (i.e. 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.",
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Rivulet flow round a horizontal cylinder subject to a uniform surface shear stress. / Paterson, Colin; Wilson, Stephen; Duffy, Brian.

In: Quarterly Journal of Mechanics and Applied Mathematics, Vol. 67, No. 4, 11.2014, p. 567-597.

Research output: Contribution to journalArticle

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