Abstract

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 that varying the Navier slip length lambda (i.e, the strength of the slip at the solid-fluid interface) has 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 lambda. Increasing the value of lambda 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, lambda -> infinity, for a rivulet of a perfectly wetting fluid and a rivulet with constant width the velocity becomes large and plug-like like O(lambda^(1/2)) >> 1 and the rivulet becomes shallow like O(lambda^(-1/2)) << 1, while for a rivulet with positive constant contact angle the velocity becomes large and plug-like like O(lambda^(2/3)) >> 1 and the rivulet becomes narrow like O(lambda^(-1/3)) << 1 and shallow like O(lambda^(-1/3)) << 1.
Original languageEnglish
Article number072011
Number of pages11
JournalPhysics of Fluids
DOIs
Publication statusPublished - 27 Jul 2020

Keywords

  • rivulet flows
  • microfluidics
  • nanofluidics
  • mathematical physics
  • fluid dynamics

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