### Abstract

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

Title of host publication | Numerical Analysis and Applied Mathematics, Vols I-III |

Editors | T E Simos, G Psihoyios, C Tsitouras |

Publisher | American Institute of Physics |

Pages | 1676-1679 |

Number of pages | 4 |

Volume | 1281 |

ISBN (Print) | 978-0-7354-0834-0 |

DOIs | |

Publication status | Published - 2010 |

### Publication series

Name | AIP Conference Proceedings |
---|---|

Publisher | American Institute of Physics |

### Fingerprint

### Cite this

*Numerical Analysis and Applied Mathematics, Vols I-III*(Vol. 1281, pp. 1676-1679). (AIP Conference Proceedings). American Institute of Physics. https://doi.org/10.1063/1.3498161

**Re-Entrant Corner Singularity of the PTT Fluid.** / Evans, Jonathan D.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Numerical Analysis and Applied Mathematics, Vols I-III.*vol. 1281, AIP Conference Proceedings, American Institute of Physics, pp. 1676-1679. https://doi.org/10.1063/1.3498161

}

TY - CHAP

T1 - Re-Entrant Corner Singularity of the PTT Fluid

AU - Evans, Jonathan D

N1 - International Conference on Numerical Analysis and Applied Mathematics. 19-25 September 2010. Rhodes, Greece.

PY - 2010

Y1 - 2010

N2 - The local asymptotic behaviour is given for planar re-entrant corner flows of Phan-Thien-Tanner fluids with a solvent viscosity. The solvent stress and Newtonian velocity field dominate in all regions, with the polymer stress being uniformly subdominant. At small radial distances r to the corner, the velocity field vanishes as O (r(lambda 0)) whilst the solvent stress behaviour is O(r(-(1-lambda 0))). The polymer stress has the less singular behaviour O (r(-4(1-lambda 0)/(5+lambda 0))), where lambda(0) is an element of [1/2, 1) is the Newtonian flow-field eigenvalue. Stress boundary layers are needed at the walls for the polymer stress solution, which are of thickness O (r((4-lambda 0)/3)). These results confirm the order of magnitude estimates previously obtained by Renardy [13], the alternative derivation given here using the method of matched asymptotic expansions. These results breakdown in the limit of vanishing solvent viscosity as well as vanishing quadratic stress terms (i.e. the Oldroyd-B limit). It is also implicitly assumed that there are no regions of recirculation at the upstream wall i.e. we consider flow in the absence of a lip vortex.

AB - The local asymptotic behaviour is given for planar re-entrant corner flows of Phan-Thien-Tanner fluids with a solvent viscosity. The solvent stress and Newtonian velocity field dominate in all regions, with the polymer stress being uniformly subdominant. At small radial distances r to the corner, the velocity field vanishes as O (r(lambda 0)) whilst the solvent stress behaviour is O(r(-(1-lambda 0))). The polymer stress has the less singular behaviour O (r(-4(1-lambda 0)/(5+lambda 0))), where lambda(0) is an element of [1/2, 1) is the Newtonian flow-field eigenvalue. Stress boundary layers are needed at the walls for the polymer stress solution, which are of thickness O (r((4-lambda 0)/3)). These results confirm the order of magnitude estimates previously obtained by Renardy [13], the alternative derivation given here using the method of matched asymptotic expansions. These results breakdown in the limit of vanishing solvent viscosity as well as vanishing quadratic stress terms (i.e. the Oldroyd-B limit). It is also implicitly assumed that there are no regions of recirculation at the upstream wall i.e. we consider flow in the absence of a lip vortex.

UR - http://dx.doi.org/10.1063/1.3498161

U2 - 10.1063/1.3498161

DO - 10.1063/1.3498161

M3 - Chapter

SN - 978-0-7354-0834-0

VL - 1281

T3 - AIP Conference Proceedings

SP - 1676

EP - 1679

BT - Numerical Analysis and Applied Mathematics, Vols I-III

A2 - Simos, T E

A2 - Psihoyios, G

A2 - Tsitouras, C

PB - American Institute of Physics

ER -