### Abstract

Unsteady gravity-driven flow of a thin slender rivulet of a non-Newtonian power-law fluid on a plane inclined at an angle α to the horizontal is considered. Unsteady similarity solutions are obtained for both converging sessile rivulets (when 0 < α < π/2) in the case x < 0 with t < 0, and diverging pendent rivulets (when π/2 < α < π) in the case x > 0 with t > 0, where x denotes a coordinate measured down the plane and t denotes time. Numerical and asymptotic methods are used to show that for each value of the power-law index N there are two physically realisable solutions, with cross-sectional profiles that are 'single-humped' and 'double-humped', respectively. Each solution predicts that at any time t the rivulet widens or narrows according to |x | (2N+1)/2(N+1) and thickens or thins according to |x | N/(N+1) as it flows down the plane; moreover, at any station x, it widens or narrows according to |t | −N/2(N+1) and thickens or thins according to |t | −N/(N+1). The length of a truncated rivulet of fixed volume is found to behave according to |t | N/(2N+1).

Original language | English |
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Pages (from-to) | 1423-1430 |

Number of pages | 7 |

Journal | Journal of Non-Newtonian Fluid Mechanics |

Volume | 165 |

Issue number | 21-22 |

DOIs | |

Publication status | Published - Nov 2010 |

### Keywords

- power-law fluid
- rivulet
- similarity solution
- unsteady flow

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## Cite this

Yatim, YM., Wilson, S. K., & Duffy, B. R. (2010). Unsteady gravity-driven slender rivulets of a power-law fluid.

*Journal of Non-Newtonian Fluid Mechanics*,*165*(21-22), 1423-1430. https://doi.org/10.1016/j.jnnfm.2010.06.017