### Abstract

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

Pages | 527-537 |

Number of pages | 11 |

Journal | Journal of Non-Newtonian Fluid Mechanics |

Volume | 165 |

Issue number | 9-10 |

DOIs | |

Status | Published - May 2010 |

### Fingerprint

### Keywords

- solvent viscosity
- stress singularities
- radial distance
- order of magnitude estimate
- Phan-thien-tanner fluids
- local asymptotic
- velocity field
- matched asymptotic expansion
- stress behaviour
- eigen-value
- stress boundary layer
- re-entrant corner
- Newtonians
- Oldroyd-B
- polymer stress
- corner flow

### Cite this

**Re-entrant corner behaviour of the PTT fluid with a solvent viscosity.** / Evans, Jonathan D.

Research output: Contribution to journal › Article

*Journal of Non-Newtonian Fluid Mechanics*, vol. 165, no. 9-10, pp. 527-537. https://doi.org/10.1016/j.jnnfm.2010.01.011

}

TY - JOUR

T1 - Re-entrant corner behaviour of the PTT fluid with a solvent viscosity

AU - Evans, Jonathan D

PY - 2010/5

Y1 - 2010/5

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(r0) whilst the solvent stress behaviour is O(r-(1-0)). The polymer stress has the less singular behaviour O(r-4(1-0)/(5+0)), where 0[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(4-0)/3). These results confirm the order of magnitude estimates previously obtained by Renardy [14], the alternative derivation given here using the method of matched asymptotic expansions. Further, we complete previous analysis by providing solutions (particularly for the polymer stresses) in the asymptotic regions that arise. These results breakdown in the limit of vanishing solvent viscosity as well as the Oldroyd-B model limit.

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(r0) whilst the solvent stress behaviour is O(r-(1-0)). The polymer stress has the less singular behaviour O(r-4(1-0)/(5+0)), where 0[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(4-0)/3). These results confirm the order of magnitude estimates previously obtained by Renardy [14], the alternative derivation given here using the method of matched asymptotic expansions. Further, we complete previous analysis by providing solutions (particularly for the polymer stresses) in the asymptotic regions that arise. These results breakdown in the limit of vanishing solvent viscosity as well as the Oldroyd-B model limit.

KW - solvent viscosity

KW - stress singularities

KW - radial distance

KW - order of magnitude estimate

KW - Phan-thien-tanner fluids

KW - local asymptotic

KW - velocity field

KW - matched asymptotic expansion

KW - stress behaviour

KW - eigen-value

KW - stress boundary layer

KW - re-entrant corner

KW - Newtonians

KW - Oldroyd-B

KW - polymer stress

KW - corner flow

UR - http://www.scopus.com/inward/record.url?scp=77950628935&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1016/j.jnnfm.2010.01.011

U2 - 10.1016/j.jnnfm.2010.01.011

DO - 10.1016/j.jnnfm.2010.01.011

M3 - Article

VL - 165

SP - 527

EP - 537

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 - 9-10

ER -