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

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Abstract

The local asymptotic behaviour is described for planar re-entrant corner flows of a Giesekus fluid with a solvent viscosity. Similar to the PTT model, Newtonian velocity and stress fields dominate near to the corner. However, in contrast to PTT, a weaker polymer stress singularity is obtained O(r-((1-0)(3-0)/4)) with slightly thinner stress boundary layers of thickness O(r(3-0)/2), where 0 is the Newtonian flow field eigenvalue and r the radial distance from the corner. In the benchmark case of a 270 corner, we thus have polymer stress singularities of O(r-2/3) for Oldroyd-B, O(r-0.3286) for PTT and O(r-0.2796) for Giesekus. The wall boundary layer thicknesses are O(r4/3) for Oldroyd-B, O(r1.2278) for Giesekus and O(r1.1518) for PTT. Similar to the PTT model, these results for the Giesekus model breakdown in both the limits of vanishing solvent viscosity and vanishing quadratic stress terms (i.e. the Oldroyd-B limit).
Original languageEnglish
Pages (from-to)538-543
Number of pages6
JournalJournal of Non-Newtonian Fluid Mechanics
Volume165
Issue number9-10
DOIs
Publication statusPublished - May 2010

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Viscosity
viscosity
Stress Singularity
Fluid
Fluids
fluids
Boundary Layer
Polymers
corner flow
Boundary layers
boundary layer thickness
Newtonian flow
polymers
Stress Field
Velocity Field
stress distribution
Flow Field
Breakdown
boundary layers
flow distribution

Keywords

  • Giesekus model
  • solvent viscosity
  • stress singularities
  • Giesekus fluids
  • radial distance
  • Corner flow
  • local asymptotic
  • stress field
  • re-entrant corner
  • stress boundary layer
  • Newtonians
  • Oldroyd-B
  • Eigen-value
  • polymer stress

Cite this

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

In: Journal of Non-Newtonian Fluid Mechanics, Vol. 165, No. 9-10, 05.2010, p. 538-543.

Research output: Contribution to journalArticle

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abstract = "The local asymptotic behaviour is described for planar re-entrant corner flows of a Giesekus fluid with a solvent viscosity. Similar to the PTT model, Newtonian velocity and stress fields dominate near to the corner. However, in contrast to PTT, a weaker polymer stress singularity is obtained O(r-((1-0)(3-0)/4)) with slightly thinner stress boundary layers of thickness O(r(3-0)/2), where 0 is the Newtonian flow field eigenvalue and r the radial distance from the corner. In the benchmark case of a 270 corner, we thus have polymer stress singularities of O(r-2/3) for Oldroyd-B, O(r-0.3286) for PTT and O(r-0.2796) for Giesekus. The wall boundary layer thicknesses are O(r4/3) for Oldroyd-B, O(r1.2278) for Giesekus and O(r1.1518) for PTT. Similar to the PTT model, these results for the Giesekus model breakdown in both the limits of vanishing solvent viscosity and vanishing quadratic stress terms (i.e. the Oldroyd-B limit).",
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AB - The local asymptotic behaviour is described for planar re-entrant corner flows of a Giesekus fluid with a solvent viscosity. Similar to the PTT model, Newtonian velocity and stress fields dominate near to the corner. However, in contrast to PTT, a weaker polymer stress singularity is obtained O(r-((1-0)(3-0)/4)) with slightly thinner stress boundary layers of thickness O(r(3-0)/2), where 0 is the Newtonian flow field eigenvalue and r the radial distance from the corner. In the benchmark case of a 270 corner, we thus have polymer stress singularities of O(r-2/3) for Oldroyd-B, O(r-0.3286) for PTT and O(r-0.2796) for Giesekus. The wall boundary layer thicknesses are O(r4/3) for Oldroyd-B, O(r1.2278) for Giesekus and O(r1.1518) for PTT. Similar to the PTT model, these results for the Giesekus model breakdown in both the limits of vanishing solvent viscosity and vanishing quadratic stress terms (i.e. the Oldroyd-B limit).

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