### Abstract

Language | English |
---|---|

Pages | 79-91 |

Number of pages | 13 |

Journal | Journal of Non-Newtonian Fluid Mechanics |

Volume | 157 |

Issue number | 1-2 |

DOIs | |

Status | Published - 2009 |

### Fingerprint

### Keywords

- Phan-Thien-Tanner (PTT)
- Boundary layers
- Self-similar solutions
- Natural stress basis
- Stress singularity
- Re-entrant corner

### Cite this

*Journal of Non-Newtonian Fluid Mechanics*,

*157*(1-2), 79-91. https://doi.org/10.1016/j.jnnfm.2008.09.008

**Re-entrant corner flow for PTT fluids in the natural stress basis.** / Evans, Jonathan D; Sibley, David N.

Research output: Contribution to journal › Article

*Journal of Non-Newtonian Fluid Mechanics*, vol. 157, no. 1-2, pp. 79-91. https://doi.org/10.1016/j.jnnfm.2008.09.008

}

TY - JOUR

T1 - Re-entrant corner flow for PTT fluids in the natural stress basis

AU - Evans, Jonathan D

AU - Sibley, David N

PY - 2009

Y1 - 2009

N2 - We revisit the situation of steady planar flow of Phan–Thien–Tanner (PTT) fluids around re-entrant corners of angles π/α where 1/2 ≤ α < 1. The model is considered in the absence of a solvent viscosity, under which a class of self-similar solutions has been identified with stress singularities of O(r−2(1− α )) and stream function behaviour O(r α (1+ α)) (r being the radial distance from the corner). The asymptotic analysis is completed by providing a solution for the downstream boundary layer using natural stress variables. We show that the matching of the outer (core) solution into the downstream boundary layer imposes a restriction on the range of α ε (2/3, 1) for which these self-similar solutions are applicable, i.e. they only hold for corner angles between 180◦ and 270◦.

AB - We revisit the situation of steady planar flow of Phan–Thien–Tanner (PTT) fluids around re-entrant corners of angles π/α where 1/2 ≤ α < 1. The model is considered in the absence of a solvent viscosity, under which a class of self-similar solutions has been identified with stress singularities of O(r−2(1− α )) and stream function behaviour O(r α (1+ α)) (r being the radial distance from the corner). The asymptotic analysis is completed by providing a solution for the downstream boundary layer using natural stress variables. We show that the matching of the outer (core) solution into the downstream boundary layer imposes a restriction on the range of α ε (2/3, 1) for which these self-similar solutions are applicable, i.e. they only hold for corner angles between 180◦ and 270◦.

KW - Phan-Thien-Tanner (PTT)

KW - Boundary layers

KW - Self-similar solutions

KW - Natural stress basis

KW - Stress singularity

KW - Re-entrant corner

UR - http://www.scopus.com/inward/record.url?scp=58249140591&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1016/j.jnnfm.2008.09.008

U2 - 10.1016/j.jnnfm.2008.09.008

DO - 10.1016/j.jnnfm.2008.09.008

M3 - Article

VL - 157

SP - 79

EP - 91

JO - Journal of Non-Newtonian Fluid Mechanics

T2 - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

IS - 1-2

ER -