Flow of a thixotropic or antithixotropic fluid in a slowly varying channel: the weakly advective regime

David Pritchard, Stephen Wilson, Catriona McArdle

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4 Citations (Scopus)

Abstract

A general formulation of the governing equations for the slow, steady, two-dimensional flow of a thixotropic or antithixotropic fluid in a channel of slowly varying width is described. These equations are equivalent to the equations of classical lubrication theory for a Newtonian fluid, but incorporate the evolving microstructure of the fluid, described in terms of a scalar structure parameter. We demonstrate how the lubrication equations can be further simplified in the weakly advective regime in which the advective Deborah number is comparable to the aspect ratio of the flow, and present illustrative analytical and semi-analytical solutions for particular choices of the constitutive and kinetic laws, including a purely viscous Moore-Mewis-Wagner model and a regularised viscoplastic Houska model. The lubrication results also allow the calibration and validation of cross-sectionally averaged, or otherwise reduced, descriptions of thixotropic channel flow which provide a first step towards models of thixotropic flow in porous media, and we employ them to explain why such descriptions may be inadequate.
LanguageEnglish
Pages140-157
Number of pages18
JournalJournal of Non-Newtonian Fluid Mechanics
Volume238
Early online date4 Aug 2016
DOIs
Publication statusPublished - 1 Dec 2016

Fingerprint

Lubrication
lubrication
Fluid
Fluids
fluids
Lubrication Theory
Flow in Porous Media
Channel Flow
Newtonian Fluid
Channel flow
Aspect Ratio
two dimensional flow
Porous materials
Newtonian fluids
Aspect ratio
Microstructure
Governing equation
Analytical Solution
Calibration
channel flow

Keywords

  • thixotropic fluid
  • antithixotropic fluid
  • slowly varying channel
  • lubrication theory
  • structure parameter
  • weakly advective regime

Cite this

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title = "Flow of a thixotropic or antithixotropic fluid in a slowly varying channel: the weakly advective regime",
abstract = "A general formulation of the governing equations for the slow, steady, two-dimensional flow of a thixotropic or antithixotropic fluid in a channel of slowly varying width is described. These equations are equivalent to the equations of classical lubrication theory for a Newtonian fluid, but incorporate the evolving microstructure of the fluid, described in terms of a scalar structure parameter. We demonstrate how the lubrication equations can be further simplified in the weakly advective regime in which the advective Deborah number is comparable to the aspect ratio of the flow, and present illustrative analytical and semi-analytical solutions for particular choices of the constitutive and kinetic laws, including a purely viscous Moore-Mewis-Wagner model and a regularised viscoplastic Houska model. The lubrication results also allow the calibration and validation of cross-sectionally averaged, or otherwise reduced, descriptions of thixotropic channel flow which provide a first step towards models of thixotropic flow in porous media, and we employ them to explain why such descriptions may be inadequate.",
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author = "David Pritchard and Stephen Wilson and Catriona McArdle",
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AU - Pritchard, David

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N2 - A general formulation of the governing equations for the slow, steady, two-dimensional flow of a thixotropic or antithixotropic fluid in a channel of slowly varying width is described. These equations are equivalent to the equations of classical lubrication theory for a Newtonian fluid, but incorporate the evolving microstructure of the fluid, described in terms of a scalar structure parameter. We demonstrate how the lubrication equations can be further simplified in the weakly advective regime in which the advective Deborah number is comparable to the aspect ratio of the flow, and present illustrative analytical and semi-analytical solutions for particular choices of the constitutive and kinetic laws, including a purely viscous Moore-Mewis-Wagner model and a regularised viscoplastic Houska model. The lubrication results also allow the calibration and validation of cross-sectionally averaged, or otherwise reduced, descriptions of thixotropic channel flow which provide a first step towards models of thixotropic flow in porous media, and we employ them to explain why such descriptions may be inadequate.

AB - A general formulation of the governing equations for the slow, steady, two-dimensional flow of a thixotropic or antithixotropic fluid in a channel of slowly varying width is described. These equations are equivalent to the equations of classical lubrication theory for a Newtonian fluid, but incorporate the evolving microstructure of the fluid, described in terms of a scalar structure parameter. We demonstrate how the lubrication equations can be further simplified in the weakly advective regime in which the advective Deborah number is comparable to the aspect ratio of the flow, and present illustrative analytical and semi-analytical solutions for particular choices of the constitutive and kinetic laws, including a purely viscous Moore-Mewis-Wagner model and a regularised viscoplastic Houska model. The lubrication results also allow the calibration and validation of cross-sectionally averaged, or otherwise reduced, descriptions of thixotropic channel flow which provide a first step towards models of thixotropic flow in porous media, and we employ them to explain why such descriptions may be inadequate.

KW - thixotropic fluid

KW - antithixotropic fluid

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