Stick-slip and slip-stick singularities of the Phan-Thien-Tanner fluid

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The stress singularity of the Phan-Thien-Tanner (PTT) fluid is determined for steady planar stick-slip and slip-stick flows. In the presence of a solvent viscosity, we show that the velocity field is Newtonian dominated local to the singularity. The velocity vanishes as v=O(r12), with r the radial distance from the singular point at the meeting of the solid (stick) and free (slip) surfaces. The solvent stresses thus behave as O(r-12). The polymer stresses are only slightly less singular O(r-411), but require boundary layers at both the stick and slip surfaces for their resolution. The stick surface boundary layer is of thickness O(r76) whilst the slip surface boundary layer is very slightly thicker O(r2320). Solutions are constructed for stick-slip and slip-stick flow regimes, both of which share the same asymptotic structure and singularity. The behaviour described here breaks down in the limit of vanishing solvent viscosity as well as the Oldroyd-B limit.
LanguageEnglish
Pages12-19
Number of pages8
JournalJournal of Non-Newtonian Fluid Mechanics
Volume199
Early online date11 Jun 2013
DOIs
StatusPublished - Sep 2013

Fingerprint

Stick-slip
slip
Slip
Singularity
Boundary Layer
Fluid
Boundary layers
Fluids
fluids
Viscosity
boundary layers
Stress Singularity
Singular Point
Velocity Field
Breakdown
Vanish
Polymers
viscosity
velocity distribution
breakdown

Cite this

Stick-slip and slip-stick singularities of the Phan-Thien-Tanner fluid. / Evans, J.D.

In: Journal of Non-Newtonian Fluid Mechanics, Vol. 199, 09.2013, p. 12-19.

Research output: Contribution to journalArticle

@article{d8b2f9a52ce546baa288ae8ffa2bdb04,
title = "Stick-slip and slip-stick singularities of the Phan-Thien-Tanner fluid",
abstract = "The stress singularity of the Phan-Thien-Tanner (PTT) fluid is determined for steady planar stick-slip and slip-stick flows. In the presence of a solvent viscosity, we show that the velocity field is Newtonian dominated local to the singularity. The velocity vanishes as v=O(r12), with r the radial distance from the singular point at the meeting of the solid (stick) and free (slip) surfaces. The solvent stresses thus behave as O(r-12). The polymer stresses are only slightly less singular O(r-411), but require boundary layers at both the stick and slip surfaces for their resolution. The stick surface boundary layer is of thickness O(r76) whilst the slip surface boundary layer is very slightly thicker O(r2320). Solutions are constructed for stick-slip and slip-stick flow regimes, both of which share the same asymptotic structure and singularity. The behaviour described here breaks down in the limit of vanishing solvent viscosity as well as the Oldroyd-B limit.",
author = "J.D. Evans",
year = "2013",
month = "9",
doi = "10.1016/j.jnnfm.2013.06.001",
language = "English",
volume = "199",
pages = "12--19",
journal = "Journal of Non-Newtonian Fluid Mechanics",
issn = "0377-0257",
publisher = "Elsevier",

}

TY - JOUR

T1 - Stick-slip and slip-stick singularities of the Phan-Thien-Tanner fluid

AU - Evans, J.D.

PY - 2013/9

Y1 - 2013/9

N2 - The stress singularity of the Phan-Thien-Tanner (PTT) fluid is determined for steady planar stick-slip and slip-stick flows. In the presence of a solvent viscosity, we show that the velocity field is Newtonian dominated local to the singularity. The velocity vanishes as v=O(r12), with r the radial distance from the singular point at the meeting of the solid (stick) and free (slip) surfaces. The solvent stresses thus behave as O(r-12). The polymer stresses are only slightly less singular O(r-411), but require boundary layers at both the stick and slip surfaces for their resolution. The stick surface boundary layer is of thickness O(r76) whilst the slip surface boundary layer is very slightly thicker O(r2320). Solutions are constructed for stick-slip and slip-stick flow regimes, both of which share the same asymptotic structure and singularity. The behaviour described here breaks down in the limit of vanishing solvent viscosity as well as the Oldroyd-B limit.

AB - The stress singularity of the Phan-Thien-Tanner (PTT) fluid is determined for steady planar stick-slip and slip-stick flows. In the presence of a solvent viscosity, we show that the velocity field is Newtonian dominated local to the singularity. The velocity vanishes as v=O(r12), with r the radial distance from the singular point at the meeting of the solid (stick) and free (slip) surfaces. The solvent stresses thus behave as O(r-12). The polymer stresses are only slightly less singular O(r-411), but require boundary layers at both the stick and slip surfaces for their resolution. The stick surface boundary layer is of thickness O(r76) whilst the slip surface boundary layer is very slightly thicker O(r2320). Solutions are constructed for stick-slip and slip-stick flow regimes, both of which share the same asymptotic structure and singularity. The behaviour described here breaks down in the limit of vanishing solvent viscosity as well as the Oldroyd-B limit.

UR - http://www.scopus.com/inward/record.url?scp=84880179138&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1016/j.jnnfm.2013.06.001

U2 - 10.1016/j.jnnfm.2013.06.001

DO - 10.1016/j.jnnfm.2013.06.001

M3 - Article

VL - 199

SP - 12

EP - 19

JO - Journal of Non-Newtonian Fluid Mechanics

T2 - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

ER -