Journal article

Homogenised models of nutrient transport in a fibrous bioreactor scaffold

Abstract:: 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.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Kent, A., Waters, S. L., Oliver, J. M., & Chapman, S. J. (2025). Homogenised models of nutrient transport in a fibrous bioreactor scaffold. European Journal of Applied Mathematics, 37(2), 339–366.

MLA Style

Kent, A, et al. “Homogenised Models of Nutrient Transport in a Fibrous Bioreactor Scaffold.” European Journal of Applied Mathematics, vol. 37, no. 2, 2025, pp. 339–66.

Chicago Style

Kent, A, SL Waters, JM Oliver, and SJ Chapman. 2025. “Homogenised Models of Nutrient Transport in a Fibrous Bioreactor Scaffold.” European Journal of Applied Mathematics 37 (2): 339–66.
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Files:: Kent_et_al_2025_Homogenised_models_of.pdf

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Publisher copy:: 10.1017/S0956792525000129

Authors

+ Kent, A More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Waters, SL More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Oliver, JM More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Chapman, SJ More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Oxford college:: Mansfield College
Role:: Author
ORCID:: 0000-0003-3347-6024

Publisher:: Cambridge University Press
Journal:: European Journal of Applied Mathematics More from this journal
Volume:: 37
Issue:: 2
Pages:: 339-366
Publication date:: 2025-04-21
Acceptance date:: 2025-03-11
DOI:: 10.1017/S0956792525000129
EISSN:: 1469-4425
ISSN:: 0956-7925

Language:: English
Keywords:: homogenisation

diffusion

advection
Pubs id:: 2093656
Local pid:: pubs:2093656
Deposit date:: 2025-03-11
ARK identifier:: ark:/29072/ora_d8934f921748435b821501097c169915

Terms of use

Copyright holder:: Kent et al.
Copyright date:: 2025
Rights statement:: © The Author(s), 2025. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.

Licence:: CC Attribution (CC BY)

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