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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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| 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 |
| id | doaj-art-2b2c43f444bc4d1b82a071294448adb6 |
| institution | OA Journals |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| 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 |