### Abstract

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

Pages | 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 |

### Fingerprint

### Keywords

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

### Cite this

*Journal of Non-Newtonian Fluid Mechanics*,

*165*(21-22), 1423-1430. https://doi.org/10.1016/j.jnnfm.2010.06.017

}

*Journal of Non-Newtonian Fluid Mechanics*, vol. 165, no. 21-22, pp. 1423-1430. https://doi.org/10.1016/j.jnnfm.2010.06.017

**Unsteady gravity-driven slender rivulets of a power-law fluid.** / Yatim, YM; Wilson, Stephen K.; Duffy, B.R.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Unsteady gravity-driven slender rivulets of a power-law fluid

AU - Yatim, YM

AU - Wilson, Stephen K.

AU - Duffy, B.R.

PY - 2010/11

Y1 - 2010/11

N2 - 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).

AB - 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).

KW - power-law fluid

KW - rivulet

KW - similarity solution

KW - unsteady flow

UR - http://www.scopus.com/inward/record.url?scp=77957338943&partnerID=8YFLogxK

U2 - 10.1016/j.jnnfm.2010.06.017

DO - 10.1016/j.jnnfm.2010.06.017

M3 - Article

VL - 165

SP - 1423

EP - 1430

JO - Journal of Non-Newtonian Fluid Mechanics

T2 - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

IS - 21-22

ER -