Abstract
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 language | English |
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Article number | 5129664 |
Journal | Physics of Fluids |
Volume | 31 |
Issue number | 11 |
Early online date | 5 Nov 2019 |
DOIs | |
Publication status | Published - 30 Nov 2019 |
Funding
This work was supported by Sun Chemical Ltd. and the University of Bath through a 50:50 scholarship and FAPESP-SPRINT Grant No. 2018/22242-0.
ASJC Scopus subject areas
- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes