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 |
|---|---|
| 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 |
ASJC Scopus subject areas
- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes
Cite this
The extrudate swell singularity of Phan-Thien-Tanner and Giesekus fluids. / Evans, Jonathan D.; Evans, Morgan L.
In: Physics of Fluids, Vol. 31, No. 11, 5129664, 30.11.2019.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The extrudate swell singularity of Phan-Thien-Tanner and Giesekus fluids
AU - Evans, Jonathan D.
AU - Evans, Morgan L.
PY - 2019/11/30
Y1 - 2019/11/30
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85074719334&partnerID=8YFLogxK
U2 - 10.1063/1.5129664
DO - 10.1063/1.5129664
M3 - Article
AN - SCOPUS:85074719334
VL - 31
JO - Physics of Fluids
JF - Physics of Fluids
SN - 1070-6631
IS - 11
M1 - 5129664
ER -