Holland, D. and Wilson, S.K. and Duffy, B.R. (2003) *Similarity solutions for slender rivulets with thermocapillarity.* Quarterly Journal of Mechanics and Applied Mathematics, 56 (3). pp. 411-439. ISSN 0033-5614

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## Abstract

We use the lubrication approximation to investigate the steady flow of slender non-uniform rivulets of a viscous fluid on an inclined plane that is either heated or cooled relative to the surrounding atmosphere. Four non-isothermal situations in which thermocapillary effects play a significant role are considered. We derive the general equations for a slender rivulet subject to gravity, surface tension, thermocapillarity and a constant surface shear stress. Similarity solutions describing a thermocapillary-driven rivulet widening or narrowing due to either gravitational or surface-tension effects on a non-uniformly heated or cooled substrate are obtained, and we present examples of these solutions when the substrate temperature gradient depends on the longitudinal coordinate according to a general power law. When gravitational effects are strong there is a unique solution representing both a narrowing pendent rivulet and a widening sessile rivulet whose transverse profile always has a single global maximum. When surface-tension effects are strong there is a one-parameter family of solutions representing both a narrowing and a widening rivulet whose transverse profile has either a single global maximum or two equal global maxima and a local minimum. Unique similarity solutions whose transverse profiles always have a single global maximum are also obtained for both a gravity-driven and a constant-surface-shear-stress-driven rivulet widening or narrowing due to thermocapillarity on a uniformly heated or cooled substrate. The solutions in both cases represent both a narrowing rivulet on a heated substrate and a widening rivulet on a cooled substrate (albeit with infinite width in the gravity-driven case).

Item type: | Article |
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ID code: | 2128 |

Notes: | added document |

Keywords: | thermocapillarity, applied mathematics, rivulets, transverse profiles, Mathematics, Mechanics of Materials, Mechanical Engineering, Applied Mathematics, Condensed Matter Physics |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Strathprints Administrator |

Date Deposited: | 29 Sep 2007 |

Last modified: | 04 Sep 2014 13:09 |

URI: | http://strathprints.strath.ac.uk/id/eprint/2128 |

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