Yatim, YM and Wilson, Stephen K. and Duffy, B.R. (2010) *Unsteady gravity-driven slender rivulets of a power-law fluid.* Journal of Non-Newtonian Fluid Mechanics, 165 (21-22). pp. 1423-1430. ISSN 0377-0257

## 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).

Item type: | Article |
---|---|

ID code: | 27755 |

Keywords: | power-law fluid, rivulet, similarity solution, unsteady flow, Probabilities. Mathematical statistics, Mathematics, Materials Science(all), Chemical Engineering(all), Mechanical Engineering, Applied Mathematics, Condensed Matter Physics |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Mrs Carolynne Westwood |

Date Deposited: | 07 Oct 2010 20:10 |

Last modified: | 27 Mar 2014 09:10 |

URI: | http://strathprints.strath.ac.uk/id/eprint/27755 |

### Actions (login required)

View Item |