The Stokes boundary layer for a thixotropic or antithixotropic fluid

Handle URI:
http://hdl.handle.net/10754/599967
Title:
The Stokes boundary layer for a thixotropic or antithixotropic fluid
Authors:
McArdle, Catriona R.; Pritchard, David; Wilson, Stephen K.
Abstract:
We present a mathematical investigation of the oscillatory boundary layer in a semi-infinite fluid bounded by an oscillating wall (the so-called 'Stokes problem'), when the fluid has a thixotropic or antithixotropic rheology. We obtain asymptotic solutions in the limit of small-amplitude oscillations, and we use numerical integration to validate the asymptotic solutions and to explore the behaviour of the system for larger-amplitude oscillations. The solutions that we obtain differ significantly from the classical solution for a Newtonian fluid. In particular, for antithixotropic fluids the velocity reaches zero at a finite distance from the wall, in contrast to the exponential decay for a thixotropic or a Newtonian fluid.For small amplitudes of oscillation, three regimes of behaviour are possible: the structure parameter may take values defined instantaneously by the shear rate, or by a long-term average; or it may behave hysteretically. The regime boundaries depend on the precise specification of structure build-up and breakdown rates in the rheological model, illustrating the subtleties of complex fluid models in non-rheometric settings. For larger amplitudes of oscillation the dominant behaviour is hysteretic. We discuss in particular the relationship between the shear stress and the shear rate at the oscillating wall. © 2012 Elsevier B.V.
Citation:
McArdle CR, Pritchard D, Wilson SK (2012) The Stokes boundary layer for a thixotropic or antithixotropic fluid. Journal of Non-Newtonian Fluid Mechanics 185-186: 18–38. Available: http://dx.doi.org/10.1016/j.jnnfm.2012.08.001.
Publisher:
Elsevier BV
Journal:
Journal of Non-Newtonian Fluid Mechanics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Oct-2012
DOI:
10.1016/j.jnnfm.2012.08.001
Type:
Article
ISSN:
0377-0257
Sponsors:
C.R.McA. is supported by a Doctoral Training Award funded by the Engineering and Physical Sciences Research Council. Part of this work was undertaken while S.K.W. was a Visiting Fellow in the Department of Mechanical and Aerospace Engineering in the School of Engineering and Applied Science at Princeton University, USA, and part was undertaken while he was a Visiting Fellow in the Oxford Centre for Collaborative Applied Mathematics (OCCAM) at the University of Oxford, England. This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). We are also grateful to Dr. Michele Taroni (formerly of OCCAM, University of Oxford) and Prof. Iain W. Stewart (University of Strathclyde) for their valuable suggestions on aspects of this work, and to two anonymous reviewers for their comments on the original version.
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Full metadata record

DC FieldValue Language
dc.contributor.authorMcArdle, Catriona R.en
dc.contributor.authorPritchard, Daviden
dc.contributor.authorWilson, Stephen K.en
dc.date.accessioned2016-02-28T06:33:27Zen
dc.date.available2016-02-28T06:33:27Zen
dc.date.issued2012-10en
dc.identifier.citationMcArdle CR, Pritchard D, Wilson SK (2012) The Stokes boundary layer for a thixotropic or antithixotropic fluid. Journal of Non-Newtonian Fluid Mechanics 185-186: 18–38. Available: http://dx.doi.org/10.1016/j.jnnfm.2012.08.001.en
dc.identifier.issn0377-0257en
dc.identifier.doi10.1016/j.jnnfm.2012.08.001en
dc.identifier.urihttp://hdl.handle.net/10754/599967en
dc.description.abstractWe present a mathematical investigation of the oscillatory boundary layer in a semi-infinite fluid bounded by an oscillating wall (the so-called 'Stokes problem'), when the fluid has a thixotropic or antithixotropic rheology. We obtain asymptotic solutions in the limit of small-amplitude oscillations, and we use numerical integration to validate the asymptotic solutions and to explore the behaviour of the system for larger-amplitude oscillations. The solutions that we obtain differ significantly from the classical solution for a Newtonian fluid. In particular, for antithixotropic fluids the velocity reaches zero at a finite distance from the wall, in contrast to the exponential decay for a thixotropic or a Newtonian fluid.For small amplitudes of oscillation, three regimes of behaviour are possible: the structure parameter may take values defined instantaneously by the shear rate, or by a long-term average; or it may behave hysteretically. The regime boundaries depend on the precise specification of structure build-up and breakdown rates in the rheological model, illustrating the subtleties of complex fluid models in non-rheometric settings. For larger amplitudes of oscillation the dominant behaviour is hysteretic. We discuss in particular the relationship between the shear stress and the shear rate at the oscillating wall. © 2012 Elsevier B.V.en
dc.description.sponsorshipC.R.McA. is supported by a Doctoral Training Award funded by the Engineering and Physical Sciences Research Council. Part of this work was undertaken while S.K.W. was a Visiting Fellow in the Department of Mechanical and Aerospace Engineering in the School of Engineering and Applied Science at Princeton University, USA, and part was undertaken while he was a Visiting Fellow in the Oxford Centre for Collaborative Applied Mathematics (OCCAM) at the University of Oxford, England. This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). We are also grateful to Dr. Michele Taroni (formerly of OCCAM, University of Oxford) and Prof. Iain W. Stewart (University of Strathclyde) for their valuable suggestions on aspects of this work, and to two anonymous reviewers for their comments on the original version.en
dc.publisherElsevier BVen
dc.subjectOscillatory boundary layeren
dc.subjectRheopexyen
dc.subjectStokes layeren
dc.subjectStokes's second problemen
dc.subjectThixotropyen
dc.titleThe Stokes boundary layer for a thixotropic or antithixotropic fluiden
dc.typeArticleen
dc.identifier.journalJournal of Non-Newtonian Fluid Mechanicsen
dc.contributor.institutionUniversity of Strathclyde, Glasgow, United Kingdomen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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