Unsteady gravitydriven slender rivulets of a powerlaw fluid
Yatim, YM and Wilson, Stephen K. and Duffy, B.R. (2010) Unsteady gravitydriven slender rivulets of a powerlaw fluid. Journal of NonNewtonian Fluid Mechanics, 165 (2122). pp. 14231430. ISSN 03770257 (https://doi.org/10.1016/j.jnnfm.2010.06.017)
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Abstract
Unsteady gravitydriven flow of a thin slender rivulet of a nonNewtonian powerlaw 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 powerlaw index N there are two physically realisable solutions, with crosssectional profiles that are 'singlehumped' and 'doublehumped', 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 Dates: DateEventNovember 2010PublishedSubjects: Science > Mathematics > Probabilities. Mathematical statistics
Science > MathematicsDepartment: Faculty of Science > Mathematics and Statistics Depositing user: Mrs Carolynne Westwood Date deposited: 07 Oct 2010 19:10 Last modified: 21 Feb 2024 14:25 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/27755