Similarity solutions for unsteady shear-stress-driven flow of Newtonian and power-law fluids: slender rivulets and dry patches

Yazariah Mohd Yatim, Brian Duffy, Stephen Wilson

Research output: Contribution to journalArticle

7 Citations (Scopus)
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Abstract

Unsteady flow of a thin film of a Newtonian fluid or a non-Newtonian power-law fluid with power-law index N driven by a constant shear stress applied at the free surface, on a plane inclined at an angle α to the horizontal, is considered. Unsteady similarity solutions representing flow of slender rivulets and flow around slender dry patches are obtained. Specifically, solutions are obtained for converging sessile rivulets (0 < α < π/2) and converging dry patches in a pendent film (π/2 < α < π), as well as for diverging pendent rivulets and diverging dry patches in a sessile film. These solutions predict that at any time t, the rivulet and dry patch widen or narrow according to |x|3/2, and the film thickens or thins according to |x|, where x denotes distance down the plane, and that at any station x, the rivulet and dry patch widen or narrow like |t|−1, and the film thickens or thins like |t|−1, independent of N.
Original languageEnglish
Pages (from-to)53-69
Number of pages17
JournalJournal of Engineering Mathematics
Volume73
Issue number1
Early online date11 Oct 2011
DOIs
Publication statusPublished - Apr 2012

Keywords

  • dry patch
  • power law fluid
  • rivulet
  • unsteady flow
  • thin film
  • mathematical analysis

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