Combing carbon fibre arrays

Before they can be reused, recycled carbon fibres are combed using a carding machine which is a technology widely used in the textile industry. We revisit the carding model of Lee and Ockendon (2005) to develop a continuum model for the alignment of an initially random ‘web’ of carbon fibres passing...

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Main Authors: P.D. Howell, H. Ockendon, J.R. Ockendon, J. Roberts
Format: Article
Language:English
Published: Elsevier 2025-03-01
Series:Partial Differential Equations in Applied Mathematics
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S2666818124004078
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author P.D. Howell
H. Ockendon
J.R. Ockendon
J. Roberts
author_facet P.D. Howell
H. Ockendon
J.R. Ockendon
J. Roberts
author_sort P.D. Howell
collection DOAJ
description Before they can be reused, recycled carbon fibres are combed using a carding machine which is a technology widely used in the textile industry. We revisit the carding model of Lee and Ockendon (2005) to develop a continuum model for the alignment of an initially random ‘web’ of carbon fibres passing between two toothed cylinders in a carding machine. The web is modelled as a compressible viscous fluid with density-dependent viscosity coefficients. The model reveals how the ultimate alignment of the fibres depends on key control parameters, including the gap between the cylinders and their relative velocities. We also find a small region of parameter space where solutions may exhibit singularities.
format Article
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issn 2666-8181
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publishDate 2025-03-01
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series Partial Differential Equations in Applied Mathematics
spelling doaj-art-2b2c43f444bc4d1b82a071294448adb62025-08-20T02:39:07ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-011310102110.1016/j.padiff.2024.101021Combing carbon fibre arraysP.D. Howell0H. Ockendon1J.R. Ockendon2J. Roberts3Mathematical Institute, University of Oxford, OX2 6GG, UKCorresponding author.; Mathematical Institute, University of Oxford, OX2 6GG, UKMathematical Institute, University of Oxford, OX2 6GG, UKMathematical Institute, University of Oxford, OX2 6GG, UKBefore they can be reused, recycled carbon fibres are combed using a carding machine which is a technology widely used in the textile industry. We revisit the carding model of Lee and Ockendon (2005) to develop a continuum model for the alignment of an initially random ‘web’ of carbon fibres passing between two toothed cylinders in a carding machine. The web is modelled as a compressible viscous fluid with density-dependent viscosity coefficients. The model reveals how the ultimate alignment of the fibres depends on key control parameters, including the gap between the cylinders and their relative velocities. We also find a small region of parameter space where solutions may exhibit singularities.http://www.sciencedirect.com/science/article/pii/S2666818124004078Carbon fibresTextilesContinuum model
spellingShingle P.D. Howell
H. Ockendon
J.R. Ockendon
J. Roberts
Combing carbon fibre arrays
Partial Differential Equations in Applied Mathematics
Carbon fibres
Textiles
Continuum model
title Combing carbon fibre arrays
title_full Combing carbon fibre arrays
title_fullStr Combing carbon fibre arrays
title_full_unstemmed Combing carbon fibre arrays
title_short Combing carbon fibre arrays
title_sort combing carbon fibre arrays
topic Carbon fibres
Textiles
Continuum model
url http://www.sciencedirect.com/science/article/pii/S2666818124004078
work_keys_str_mv AT pdhowell combingcarbonfibrearrays
AT hockendon combingcarbonfibrearrays
AT jrockendon combingcarbonfibrearrays
AT jroberts combingcarbonfibrearrays