The extrudate swell singularity of Phan-Thien-Tanner and Giesekus fluids

Jonathan D. Evans, Morgan L. Evans

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The stress singularity for Phan-Thien-Tanner (PTT) and Giesekus viscoelastic fluids is determined for extrudate swell (commonly termed die swell). In the presence of a Newtonian solvent viscosity, the solvent stress dominates the polymer stresses local to the contact point between the solid (no-slip) surface inside the die and the free (slip) surface outside the die. The velocity field thus vanishes like rλ0, where r is the radial distance from the contact point and λ0 is the smallest Newtonian eigenvalue (dependent upon the angle of separation between the solid and free surfaces). The solvent stress thus behaves like r-(1-λ0) and dominates the polymer stresses, which are like r-4(1-λ0)/(5+λ0) for PTT and r-(1-λ0)(3-λ0)/4 for Giesekus. The polymer stresses require boundary layers at both the solid and free surfaces, the thicknesses of which are derived. These results do not hold for the Oldroyd-B fluid.

Original languageEnglish
Article number5129664
JournalPhysics of Fluids
Issue number11
Early online date5 Nov 2019
Publication statusPublished - 30 Nov 2019

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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