### Abstract

Language | English |
---|---|

Pages | 567-597 |

Number of pages | 31 |

Journal | Quarterly Journal of Mechanics and Applied Mathematics |

Volume | 67 |

Issue number | 4 |

Early online date | 14 Sep 2014 |

DOIs | |

Publication status | Published - Nov 2014 |

### Fingerprint

### Keywords

- uniform surface shear stress
- rivulet flow
- horizontal cylinder

### Cite this

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*Quarterly Journal of Mechanics and Applied Mathematics*, vol. 67, no. 4, pp. 567-597. https://doi.org/10.1093/qjmam/hbu018

**Rivulet flow round a horizontal cylinder subject to a uniform surface shear stress.** / Paterson, Colin; Wilson, Stephen; Duffy, Brian.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Rivulet flow round a horizontal cylinder subject to a uniform surface shear stress

AU - Paterson, Colin

AU - Wilson, Stephen

AU - Duffy, Brian

PY - 2014/11

Y1 - 2014/11

N2 - 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.

AB - 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.

KW - uniform surface shear stress

KW - rivulet flow

KW - horizontal cylinder

UR - http://qjmam.oxfordjournals.org/

U2 - 10.1093/qjmam/hbu018

DO - 10.1093/qjmam/hbu018

M3 - Article

VL - 67

SP - 567

EP - 597

JO - Quarterly Journal of Mechanics and Applied Mathematics

T2 - Quarterly Journal of Mechanics and Applied Mathematics

JF - Quarterly Journal of Mechanics and Applied Mathematics

SN - 0033-5614

IS - 4

ER -