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

F. H. H. Al Mukahal, B. R. Duffy, S. K. Wilson

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.
LanguageEnglish
Article number052101
Number of pages20
JournalPhysics of Fluids
Volume27
Issue number5
DOIs
Publication statusPublished - 6 May 2015

Fingerprint

drainage
fluids
shear thinning
boundary layers
shear
circular cylinders
channel flow
plugs
velocity distribution
gravitation

Keywords

  • power law fluid
  • gravity driven flow
  • rivulets
  • rivulet flow

Cite this

@article{50bc82c5ff824cc8a854719143128213,
title = "A rivulet of a power-law fluid with constant contact angle draining down a slowly varying substrate",
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.",
keywords = "power law fluid , gravity driven flow, rivulets, rivulet flow",
author = "{Al Mukahal}, {F. H. H.} and Duffy, {B. R.} and Wilson, {S. K.}",
note = "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).",
year = "2015",
month = "5",
day = "6",
doi = "10.1063/1.4919342",
language = "English",
volume = "27",
journal = "Physics of Fluids",
issn = "1070-6631",
number = "5",

}

A rivulet of a power-law fluid with constant contact angle draining down a slowly varying substrate. / Al Mukahal, F. H. H.; Duffy, B. R.; Wilson, S. K.

In: Physics of Fluids, Vol. 27, No. 5, 052101, 06.05.2015.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A rivulet of a power-law fluid with constant contact angle draining down a slowly varying substrate

AU - Al Mukahal, F. H. H.

AU - Duffy, B. R.

AU - Wilson, S. K.

N1 - 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).

PY - 2015/5/6

Y1 - 2015/5/6

N2 - 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.

AB - 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.

KW - power law fluid

KW - gravity driven flow

KW - rivulets

KW - rivulet flow

UR - http://scitation.aip.org/content/aip/journal/pof2/browse

U2 - 10.1063/1.4919342

DO - 10.1063/1.4919342

M3 - Article

VL - 27

JO - Physics of Fluids

T2 - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 5

M1 - 052101

ER -