### Abstract

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

Pages | 827-840 |

Number of pages | 13 |

Journal | Physics of Fluids |

Volume | 15 |

Issue number | 4 |

DOIs | |

Publication status | Published - 19 Feb 2003 |

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### Keywords

- fluid dynamics
- physics
- lubrication
- viscosity

### Cite this

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**Strong temperature-dependent viscosity effects on a rivulet draining down a uniformly heated or cooled slowly varying substrate.** / Wilson, S.K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Strong temperature-dependent viscosity effects on a rivulet draining down a uniformly heated or cooled slowly varying substrate

AU - Wilson, S.K.

PY - 2003/2/19

Y1 - 2003/2/19

N2 - We use the lubrication approximation to investigate the steady locally unidirectional gravity-driven draining of a thin rivulet of Newtonian fluid with temperature-dependent viscosity down a slowly varying substrate that is either uniformly hotter or uniformly colder than the surrounding atmosphere. We consider the situation in which the Biot number ~and hence the variation of temperature across the rivulet! is small, but in which the variation of viscosity with temperature is sufficiently strong that thermoviscosity effects appear at leading order in the limit of small Biot number. Three different models for the dependence of viscosity on temperature ~specifically, the linear, exponential and Eyring models! are considered, but our attention is concentrated on the more realistic exponential and Eyring models ~which coincide at leading order in the limit of small Biot number!. We show that the effect of cooling the atmosphere is always to widen and deepen the rivulet, while the effect of heating the atmosphere is always to narrow and shallow it. We interpret our results as describing a slowly varying rivulet draining in the azimuthal direction from the top to the bottom of a large horizontal circular cylinder, and find that the behavior of the rivulet is rather different on the upper and lower parts of the cylinder ~i.e., for sessile and pendent rivulets!. Specifically, the effect of strong cooling of the atmosphere is to produce a wide rivulet with finite uniform thickness on the upper part of the cylinder, but a deep rivulet with finite semi-width on the lower part of the cylinder. On the other hand, the effect of strong heating of the atmosphere is to produce a narrow and shallow rivulet everywhere except near the top and the bottom of the cylinder.

AB - We use the lubrication approximation to investigate the steady locally unidirectional gravity-driven draining of a thin rivulet of Newtonian fluid with temperature-dependent viscosity down a slowly varying substrate that is either uniformly hotter or uniformly colder than the surrounding atmosphere. We consider the situation in which the Biot number ~and hence the variation of temperature across the rivulet! is small, but in which the variation of viscosity with temperature is sufficiently strong that thermoviscosity effects appear at leading order in the limit of small Biot number. Three different models for the dependence of viscosity on temperature ~specifically, the linear, exponential and Eyring models! are considered, but our attention is concentrated on the more realistic exponential and Eyring models ~which coincide at leading order in the limit of small Biot number!. We show that the effect of cooling the atmosphere is always to widen and deepen the rivulet, while the effect of heating the atmosphere is always to narrow and shallow it. We interpret our results as describing a slowly varying rivulet draining in the azimuthal direction from the top to the bottom of a large horizontal circular cylinder, and find that the behavior of the rivulet is rather different on the upper and lower parts of the cylinder ~i.e., for sessile and pendent rivulets!. Specifically, the effect of strong cooling of the atmosphere is to produce a wide rivulet with finite uniform thickness on the upper part of the cylinder, but a deep rivulet with finite semi-width on the lower part of the cylinder. On the other hand, the effect of strong heating of the atmosphere is to produce a narrow and shallow rivulet everywhere except near the top and the bottom of the cylinder.

KW - fluid dynamics

KW - physics

KW - lubrication

KW - viscosity

U2 - 10.1063/1.1543583

DO - 10.1063/1.1543583

M3 - Article

VL - 15

SP - 827

EP - 840

JO - Physics of Fluids

T2 - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 4

ER -