Stability of the boundary layer on a rotating disk for power-law fluids

P. T. Griffiths, S. O. Stephen, A. P. Bassom, S. J. Garrett

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The stability of the flow due to a rotating disk is considered for non-Newtonian fluids, specifically shear-thinning fluids that satisfy the power-law (Ostwald-de Waele) relationship. In this case the basic flow is not an exact solution of the Navier-Stokes equations, however, in the limit of large Reynolds number the flow inside the three-dimensional boundary layer can be determined via a similarity solution. An asymptotic analysis is presented in the limit of large Reynolds number. It is shown that the stationary spiral instabilities observed experimentally in the Newtonian case can be described for shear-thinning fluids by a linear stability analysis. Predictions for the wavenumber and wave angle of the disturbances suggest that shear-thinning fluids may have a stabilising effect on the flow.

Original languageEnglish
Pages (from-to)1-6
Number of pages7
JournalJournal of Non-Newtonian Fluid Mechanics
Volume207
Early online date13 Mar 2014
DOIs
Publication statusPublished - May 2014
Externally publishedYes

Fingerprint

Power-law Fluid
Rotating Disk
rotating disks
Rotating disks
Shear Thinning
shear thinning
Shear thinning
Boundary Layer
boundary layers
Boundary layers
Fluids
fluids
Fluid
Reynolds number
three dimensional boundary layer
Linear stability analysis
Asymptotic analysis
Similarity Solution
Non-Newtonian Fluid
Linear Stability Analysis

Keywords

  • Crossflow vortices
  • Instability
  • Power-law fluid
  • Rotating disk flow

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanical Engineering
  • Applied Mathematics

Cite this

Stability of the boundary layer on a rotating disk for power-law fluids. / Griffiths, P. T.; Stephen, S. O.; Bassom, A. P.; Garrett, S. J.

In: Journal of Non-Newtonian Fluid Mechanics, Vol. 207, 05.2014, p. 1-6.

Research output: Contribution to journalArticle

Griffiths, P. T. ; Stephen, S. O. ; Bassom, A. P. ; Garrett, S. J. / Stability of the boundary layer on a rotating disk for power-law fluids. In: Journal of Non-Newtonian Fluid Mechanics. 2014 ; Vol. 207. pp. 1-6.
@article{ac7070e0ef9f4998bf61d7e07176571b,
title = "Stability of the boundary layer on a rotating disk for power-law fluids",
abstract = "The stability of the flow due to a rotating disk is considered for non-Newtonian fluids, specifically shear-thinning fluids that satisfy the power-law (Ostwald-de Waele) relationship. In this case the basic flow is not an exact solution of the Navier-Stokes equations, however, in the limit of large Reynolds number the flow inside the three-dimensional boundary layer can be determined via a similarity solution. An asymptotic analysis is presented in the limit of large Reynolds number. It is shown that the stationary spiral instabilities observed experimentally in the Newtonian case can be described for shear-thinning fluids by a linear stability analysis. Predictions for the wavenumber and wave angle of the disturbances suggest that shear-thinning fluids may have a stabilising effect on the flow.",
keywords = "Crossflow vortices, Instability, Power-law fluid, Rotating disk flow",
author = "Griffiths, {P. T.} and Stephen, {S. O.} and Bassom, {A. P.} and Garrett, {S. J.}",
year = "2014",
month = "5",
doi = "10.1016/j.jnnfm.2014.02.004",
language = "English",
volume = "207",
pages = "1--6",
journal = "Journal of Non-Newtonian Fluid Mechanics",
issn = "0377-0257",
publisher = "Elsevier",

}

TY - JOUR

T1 - Stability of the boundary layer on a rotating disk for power-law fluids

AU - Griffiths, P. T.

AU - Stephen, S. O.

AU - Bassom, A. P.

AU - Garrett, S. J.

PY - 2014/5

Y1 - 2014/5

N2 - The stability of the flow due to a rotating disk is considered for non-Newtonian fluids, specifically shear-thinning fluids that satisfy the power-law (Ostwald-de Waele) relationship. In this case the basic flow is not an exact solution of the Navier-Stokes equations, however, in the limit of large Reynolds number the flow inside the three-dimensional boundary layer can be determined via a similarity solution. An asymptotic analysis is presented in the limit of large Reynolds number. It is shown that the stationary spiral instabilities observed experimentally in the Newtonian case can be described for shear-thinning fluids by a linear stability analysis. Predictions for the wavenumber and wave angle of the disturbances suggest that shear-thinning fluids may have a stabilising effect on the flow.

AB - The stability of the flow due to a rotating disk is considered for non-Newtonian fluids, specifically shear-thinning fluids that satisfy the power-law (Ostwald-de Waele) relationship. In this case the basic flow is not an exact solution of the Navier-Stokes equations, however, in the limit of large Reynolds number the flow inside the three-dimensional boundary layer can be determined via a similarity solution. An asymptotic analysis is presented in the limit of large Reynolds number. It is shown that the stationary spiral instabilities observed experimentally in the Newtonian case can be described for shear-thinning fluids by a linear stability analysis. Predictions for the wavenumber and wave angle of the disturbances suggest that shear-thinning fluids may have a stabilising effect on the flow.

KW - Crossflow vortices

KW - Instability

KW - Power-law fluid

KW - Rotating disk flow

U2 - 10.1016/j.jnnfm.2014.02.004

DO - 10.1016/j.jnnfm.2014.02.004

M3 - Article

VL - 207

SP - 1

EP - 6

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

ER -