Homogenised models of nutrient transport in a fibrous bioreactor scaffold
Bioreactor scaffolds must be designed to facilitate adequate nutrient delivery to the growing tissue they support. For perfusion bioreactors, the dominant transport process is determined by the scale of fluid velocity relative to diffusion and the geometry of the scaffold. In this paper, models of n...
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Cambridge University Press
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| Series: | European Journal of Applied Mathematics |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S0956792525000129/type/journal_article |
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| author | Amy Kent Sarah L. Waters James M. Oliver Stephen J. Chapman |
| author_facet | Amy Kent Sarah L. Waters James M. Oliver Stephen J. Chapman |
| author_sort | Amy Kent |
| collection | DOAJ |
| description | Bioreactor scaffolds must be designed to facilitate adequate nutrient delivery to the growing tissue they support. For perfusion bioreactors, the dominant transport process is determined by the scale of fluid velocity relative to diffusion and the geometry of the scaffold. In this paper, models of nutrient transport in a fibrous bioreactor scaffold are developed using homogenisation via multiscale asymptotics. The scaffold is modelled as an ensemble of aligned strings surrounded by viscous, slowly flowing fluid. Multiple scales analysis is carried out for various parameter regimes which give rise to macroscale transport models that incorporate the effects of advection, reaction and diffusion. Multiple scales in both space and time are employed when macroscale advection balances macroscale diffusion. The microscale model is solved to obtain the effective diffusion coefficient and simple solutions to the macroscale problem are presented for each regime. |
| format | Article |
| id | doaj-art-e7b5029ca39a410099997e7bab2357cc |
| institution | DOAJ |
| issn | 0956-7925 1469-4425 |
| language | English |
| publisher | Cambridge University Press |
| record_format | Article |
| series | European Journal of Applied Mathematics |
| spelling | doaj-art-e7b5029ca39a410099997e7bab2357cc2025-08-20T03:18:37ZengCambridge University PressEuropean Journal of Applied Mathematics0956-79251469-442512810.1017/S0956792525000129Homogenised models of nutrient transport in a fibrous bioreactor scaffoldAmy Kent0https://orcid.org/0000-0001-5905-962XSarah L. Waters1James M. Oliver2Stephen J. Chapman3https://orcid.org/0000-0003-3347-6024Mathematical Institute, University of Oxford, Oxford, UKMathematical Institute, University of Oxford, Oxford, UKMathematical Institute, University of Oxford, Oxford, UKMathematical Institute, University of Oxford, Oxford, UKBioreactor scaffolds must be designed to facilitate adequate nutrient delivery to the growing tissue they support. For perfusion bioreactors, the dominant transport process is determined by the scale of fluid velocity relative to diffusion and the geometry of the scaffold. In this paper, models of nutrient transport in a fibrous bioreactor scaffold are developed using homogenisation via multiscale asymptotics. The scaffold is modelled as an ensemble of aligned strings surrounded by viscous, slowly flowing fluid. Multiple scales analysis is carried out for various parameter regimes which give rise to macroscale transport models that incorporate the effects of advection, reaction and diffusion. Multiple scales in both space and time are employed when macroscale advection balances macroscale diffusion. The microscale model is solved to obtain the effective diffusion coefficient and simple solutions to the macroscale problem are presented for each regime.https://www.cambridge.org/core/product/identifier/S0956792525000129/type/journal_articleHomogenisationdiffusionadvection35B2776S0535Q49 |
| spellingShingle | Amy Kent Sarah L. Waters James M. Oliver Stephen J. Chapman Homogenised models of nutrient transport in a fibrous bioreactor scaffold European Journal of Applied Mathematics Homogenisation diffusion advection 35B27 76S05 35Q49 |
| title | Homogenised models of nutrient transport in a fibrous bioreactor scaffold |
| title_full | Homogenised models of nutrient transport in a fibrous bioreactor scaffold |
| title_fullStr | Homogenised models of nutrient transport in a fibrous bioreactor scaffold |
| title_full_unstemmed | Homogenised models of nutrient transport in a fibrous bioreactor scaffold |
| title_short | Homogenised models of nutrient transport in a fibrous bioreactor scaffold |
| title_sort | homogenised models of nutrient transport in a fibrous bioreactor scaffold |
| topic | Homogenisation diffusion advection 35B27 76S05 35Q49 |
| url | https://www.cambridge.org/core/product/identifier/S0956792525000129/type/journal_article |
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