A rivulet of a power-law fluid with constant contact angle draining down a slowly varying substrate

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Al Mukahal, F. H. H. and Duffy, B. R. and Wilson, S. K. (2015) A rivulet of a power-law fluid with constant contact angle draining down a slowly varying substrate. Physics of Fluids, 27 (5). 052101. ISSN 1070-6631 (https://doi.org/10.1063/1.4919342)

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Abstract

Locally unidirectional steady gravity-driven flow of a thin rivulet of a power-law fluid with prescribed volume flux down a locally planar substrate is considered. First the solution for unidirectional flow of a uniform rivulet down a planar substrate is obtained, and then it is used to obtain the solution for a slowly varying rivulet with prescribed constant (nonzero) contact angle down a slowly varying substrate, specifically flow in the azimuthal direction around the outside of a large horizontal circular cylinder. The solution is shown to depend strongly on the value of the power-law index of the fluid. For example, a rivulet of strongly shear-thinning fluid "self-channels" its flow down a narrow central channel between two "levees" of slowly moving fluid that form at its sides, and in the central channel there is a "plug-like" flow except in a boundary layer near the substrate. On the other hand, in a rivulet of a strongly shear-thickening fluid the velocity profile is linear except in a boundary layer near the free surface. Another notable qualitative departure from Newtonian behaviour is that, whereas the mass of a rivulet of a Newtonian or a shear-thinning fluid is theoretically infinite, the mass of a rivulet of a shear-thickening fluid is finite.

ORCID iDs

Al Mukahal, F. H. H., Duffy, B. R. ORCID logoORCID: https://orcid.org/0000-0003-2687-7938 and Wilson, S. K. ORCID logoORCID: https://orcid.org/0000-0001-7841-9643;
  • Item type:Article
    ID code:52775
    Dates:
    Date
    Event
    6 May 2015
    Published
    8 April 2015
    Accepted
    Notes:Copyright (2015) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of Fluids (1994-present) 27, 052101 (2015); doi: 10.1063/1.4919342 and may be found at (URL/http://scitation.aip.org/content/aip/journal/pof2/27/5/10.1063/1.4919342).
    Subjects:Science > Physics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:21 Apr 2015 14:19
    Last modified:02 Dec 2024 01:16
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/52775
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