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

Research output: Contribution to journalArticle

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Abstract

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.
LanguageEnglish
Pages527-537
Number of pages11
JournalJournal of Non-Newtonian Fluid Mechanics
Volume165
Issue number9-10
DOIs
StatusPublished - May 2010

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Viscosity
viscosity
Fluid
Fluids
fluids
Polymers
polymers
Velocity Field
velocity distribution
corner flow
Newtonian flow
Matched Asymptotic Expansions
Flow Field
Breakdown
Boundary Layer
Vanish
boundary layers
Flow fields
flow distribution
Boundary layers

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.

In: Journal of Non-Newtonian Fluid Mechanics, Vol. 165, No. 9-10, 05.2010, p. 527-537.

Research output: Contribution to journalArticle

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