### Abstract

For small amplitudes of oscillation, three regimes of behaviour are possible: the structure parameter may take values defined instantaneously by the shear rate, or by a long-term average; or it may behave hysteretically. The regime boundaries depend on the precise specification of structure build-up and breakdown rates in the rheological model, illustrating the subtleties of complex fluid models in non-rheometric settings. For larger amplitudes of oscillation the dominant behaviour is hysteretic. We discuss in particular the relationship between the shear stress and the shear rate at the oscillating wall.

Original language | English |
---|---|

Pages (from-to) | 18-38 |

Number of pages | 21 |

Journal | Journal of Non-Newtonian Fluid Mechanics |

Volume | 185-186 |

Early online date | 20 Aug 2012 |

DOIs | |

Publication status | Published - Oct 2012 |

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### Keywords

- Stokes boundary layer
- thixotropic fluid
- antithixotropic fluid

### Cite this

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*Journal of Non-Newtonian Fluid Mechanics*, vol. 185-186, pp. 18-38. https://doi.org/10.1016/j.jnnfm.2012.08.001

**The Stokes boundary layer for a thixotropic or antithixotropic fluid.** / McArdle, Catriona; Pritchard, David; Wilson, Stephen.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The Stokes boundary layer for a thixotropic or antithixotropic fluid

AU - McArdle, Catriona

AU - Pritchard, David

AU - Wilson, Stephen

N1 - added document

PY - 2012/10

Y1 - 2012/10

N2 - We present a mathematical investigation of the oscillatory boundary layer in a semi-infinite fluid bounded by an oscillating wall (the so-called ‘Stokes problem’), when the fluid has a thixotropic or antithixotropic rheology. We obtain asymptotic solutions in the limit of small-amplitude oscillations, and we use numerical integration to validate the asymptotic solutions and to explore the behaviour of the system for larger-amplitude oscillations. The solutions that we obtain differ significantly from the classical solution for a Newtonian fluid. In particular, for antithixotropic fluids the velocity reaches zero at a finite distance from the wall, in contrast to the exponential decay for a thixotropic or a Newtonian fluid.For small amplitudes of oscillation, three regimes of behaviour are possible: the structure parameter may take values defined instantaneously by the shear rate, or by a long-term average; or it may behave hysteretically. The regime boundaries depend on the precise specification of structure build-up and breakdown rates in the rheological model, illustrating the subtleties of complex fluid models in non-rheometric settings. For larger amplitudes of oscillation the dominant behaviour is hysteretic. We discuss in particular the relationship between the shear stress and the shear rate at the oscillating wall.

AB - We present a mathematical investigation of the oscillatory boundary layer in a semi-infinite fluid bounded by an oscillating wall (the so-called ‘Stokes problem’), when the fluid has a thixotropic or antithixotropic rheology. We obtain asymptotic solutions in the limit of small-amplitude oscillations, and we use numerical integration to validate the asymptotic solutions and to explore the behaviour of the system for larger-amplitude oscillations. The solutions that we obtain differ significantly from the classical solution for a Newtonian fluid. In particular, for antithixotropic fluids the velocity reaches zero at a finite distance from the wall, in contrast to the exponential decay for a thixotropic or a Newtonian fluid.For small amplitudes of oscillation, three regimes of behaviour are possible: the structure parameter may take values defined instantaneously by the shear rate, or by a long-term average; or it may behave hysteretically. The regime boundaries depend on the precise specification of structure build-up and breakdown rates in the rheological model, illustrating the subtleties of complex fluid models in non-rheometric settings. For larger amplitudes of oscillation the dominant behaviour is hysteretic. We discuss in particular the relationship between the shear stress and the shear rate at the oscillating wall.

KW - Stokes boundary layer

KW - thixotropic fluid

KW - antithixotropic fluid

UR - http://www.sciencedirect.com/science/journal/03770257

U2 - 10.1016/j.jnnfm.2012.08.001

DO - 10.1016/j.jnnfm.2012.08.001

M3 - Article

VL - 185-186

SP - 18

EP - 38

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

ER -