Revisiting boundary layer flows of viscoelastic fluids

Paul Griffiths; Liam Escott

doi:10.1016/j.jnnfm.2022.104976

Revisiting boundary layer flows of viscoelastic fluids

Paul Griffiths, Liam Escott^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this article we reconsider high Reynolds number boundary layer flows of fluids with viscoelastic properties. We show that a number of previous studies that have attempted to address this problem are, in fact, incomplete. We correctly reformulate the problem and solve the governing equations using a Chebyshev collocation scheme. By analysing the decay of the solutions to the far-field we determine the correct stress boundary conditions required to solve problems of this form.

Our results show that both the fluid velocity within the boundary layer and the stress at the solid boundary increase due to the effect of viscoelasticity. As a consequence of this, we predict a thinning of the boundary layer as the value of the dimensionless viscoelastic flow parameter is increased. These results contradict a number of prominent studies in the literature but are supported by results owing from an asymptotic analysis based on the assumption of the smallness of the non-dimensional viscoelastic flow parameter.

Original language	English
Article number	104976
Number of pages	12
Journal	Journal of Non-Newtonian Fluid Mechanics
Volume	312
Early online date	22 Dec 2022
DOIs	https://doi.org/10.1016/j.jnnfm.2022.104976
Publication status	Published - Feb 2023

Bibliographical note

© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

Funding Information:
The authors wish to acknowledge support from the UKRI EPSRC, UK (Grant No. EP/V006614/2). We also wish to acknowledge the insightful comments of the anonymous reviewers.

Keywords

Boundary-layer
Viscoelastic
Self-similar

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10.1016/j.jnnfm.2022.104976Licence: CC BY 4.0

1-s2.0-S0377025722001951-main
© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
Final published version, 939 KBLicence: CC BY 4.0

Cite this

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title = "Revisiting boundary layer flows of viscoelastic fluids",

abstract = "In this article we reconsider high Reynolds number boundary layer flows of fluids with viscoelastic properties. We show that a number of previous studies that have attempted to address this problem are, in fact, incomplete. We correctly reformulate the problem and solve the governing equations using a Chebyshev collocation scheme. By analysing the decay of the solutions to the far-field we determine the correct stress boundary conditions required to solve problems of this form.Our results show that both the fluid velocity within the boundary layer and the stress at the solid boundary increase due to the effect of viscoelasticity. As a consequence of this, we predict a thinning of the boundary layer as the value of the dimensionless viscoelastic flow parameter is increased. These results contradict a number of prominent studies in the literature but are supported by results owing from an asymptotic analysis based on the assumption of the smallness of the non-dimensional viscoelastic flow parameter.",

keywords = "Boundary-layer, Viscoelastic, Self-similar",

author = "Paul Griffiths and Liam Escott",

note = "{\textcopyright} 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Funding Information: The authors wish to acknowledge support from the UKRI EPSRC, UK (Grant No. EP/V006614/2). We also wish to acknowledge the insightful comments of the anonymous reviewers.",

year = "2023",

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doi = "10.1016/j.jnnfm.2022.104976",

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AU - Griffiths, Paul

AU - Escott, Liam

N1 - © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Funding Information: The authors wish to acknowledge support from the UKRI EPSRC, UK (Grant No. EP/V006614/2). We also wish to acknowledge the insightful comments of the anonymous reviewers.

PY - 2023/2

Y1 - 2023/2

N2 - In this article we reconsider high Reynolds number boundary layer flows of fluids with viscoelastic properties. We show that a number of previous studies that have attempted to address this problem are, in fact, incomplete. We correctly reformulate the problem and solve the governing equations using a Chebyshev collocation scheme. By analysing the decay of the solutions to the far-field we determine the correct stress boundary conditions required to solve problems of this form.Our results show that both the fluid velocity within the boundary layer and the stress at the solid boundary increase due to the effect of viscoelasticity. As a consequence of this, we predict a thinning of the boundary layer as the value of the dimensionless viscoelastic flow parameter is increased. These results contradict a number of prominent studies in the literature but are supported by results owing from an asymptotic analysis based on the assumption of the smallness of the non-dimensional viscoelastic flow parameter.

AB - In this article we reconsider high Reynolds number boundary layer flows of fluids with viscoelastic properties. We show that a number of previous studies that have attempted to address this problem are, in fact, incomplete. We correctly reformulate the problem and solve the governing equations using a Chebyshev collocation scheme. By analysing the decay of the solutions to the far-field we determine the correct stress boundary conditions required to solve problems of this form.Our results show that both the fluid velocity within the boundary layer and the stress at the solid boundary increase due to the effect of viscoelasticity. As a consequence of this, we predict a thinning of the boundary layer as the value of the dimensionless viscoelastic flow parameter is increased. These results contradict a number of prominent studies in the literature but are supported by results owing from an asymptotic analysis based on the assumption of the smallness of the non-dimensional viscoelastic flow parameter.

KW - Boundary-layer

KW - Viscoelastic

KW - Self-similar

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DO - 10.1016/j.jnnfm.2022.104976

M3 - Article

SN - 0377-0257

VL - 312

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

M1 - 104976

ER -

Revisiting boundary layer flows of viscoelastic fluids

Abstract

Bibliographical note

Keywords

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