### 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 language | English |
---|---|

Pages (from-to) | 1-6 |

Number of pages | 7 |

Journal | Journal of Non-Newtonian Fluid Mechanics |

Volume | 207 |

Early online date | 13 Mar 2014 |

DOIs | |

Publication status | Published - May 2014 |

Externally published | Yes |

### Fingerprint

### 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

*Journal of Non-Newtonian Fluid Mechanics*,

*207*, 1-6. https://doi.org/10.1016/j.jnnfm.2014.02.004

**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.

Research output: Contribution to journal › Article

*Journal of Non-Newtonian Fluid Mechanics*, vol. 207, pp. 1-6. https://doi.org/10.1016/j.jnnfm.2014.02.004

}

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 -