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

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

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    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).

    Author(s):Yatim, YM, Wilson, Stephen K. ORCID logoORCID: https://orcid.org/0000-0001-7841-9643 and Duffy, B.R.
    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
    Depositing user: Mrs Carolynne Westwood
    Date deposited:07 Oct 2010 19:10
    Last modified:13 Feb 2020 07:20
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/27755
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