A detailed analysis of small-scale locally unidirectional gravity-driven rivulet flow with prescribed volume flux down an inclined slippery substrate for a rivulet with either constant width (i.e., pinned contact lines) or constant contact angle is undertaken. In particular, we determine the effect of varying the Navier slip length λ (i.e., the strength of the slip at the solid–fluid interface) on the rivulet. The present analysis shows that the shape and size of the rivulet and the velocity within it depend strongly on the value of λ. Increasing the value of λ reduces the viscous resistance at the substrate and, hence, leads to a larger velocity within the rivulet, and so the prescribed flux is achieved with a smaller rivulet. In particular, in the limit of strong slip, λ → ∞, for a rivulet of a perfectly wetting fluid and a rivulet with constant width, the velocity becomes large and plug-like like O(λ1/2) ≫ 1, and the rivulet becomes shallow like O(λ−1/2) ≪ 1, while for a rivulet with positive constant contact angle, the velocity becomes large and plug-like like O(λ2/3) ≫ 1, and the rivulet becomes narrow like O(λ−1/3) ≪ 1 and shallow like O(λ−1/3) ≪ 1.
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July 2020
Research Article|
July 27 2020
Rivulet flow down a slippery substrate
Abdulwahed S. Alshaikhi
;
Abdulwahed S. Alshaikhi
a)
Department of Mathematics and Statistics, University of Strathclyde
, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, United Kingdom
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Stephen K. Wilson
;
Stephen K. Wilson
b)
Department of Mathematics and Statistics, University of Strathclyde
, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, United Kingdom
b)Author to whom correspondence should be addressed: s.k.wilson@strath.ac.uk
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Brian R. Duffy
Brian R. Duffy
c)
Department of Mathematics and Statistics, University of Strathclyde
, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, United Kingdom
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b)Author to whom correspondence should be addressed: s.k.wilson@strath.ac.uk
Physics of Fluids 32, 072011 (2020)
Article history
Received:
May 12 2020
Accepted:
June 27 2020
Citation
Abdulwahed S. Alshaikhi, Stephen K. Wilson, Brian R. Duffy; Rivulet flow down a slippery substrate. Physics of Fluids 1 July 2020; 32 (7): 072011. https://doi.org/10.1063/5.0013572
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