The effect of weak inertia in rotating high-aspect-ratio vessel bioreactors
One method to grow artificial body tissue is to place a porous scaffold seeded with cells, known as a tissue construct, into a rotating bioreactor filled with a nutrient-rich fluid. The flow within the bioreactor is affected by the movement of the construct relative to the bioreactor which, in turn,...
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Cambridge University Press
2018
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| Online Access: | https://eprints.nottingham.ac.uk/47054/ |
| _version_ | 1848797457315528704 |
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| author | Dalwadi, Mohit P. Chapman, S. Jonathan Oliver, James M. Waters, Sarah L. |
| author_facet | Dalwadi, Mohit P. Chapman, S. Jonathan Oliver, James M. Waters, Sarah L. |
| author_sort | Dalwadi, Mohit P. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | One method to grow artificial body tissue is to place a porous scaffold seeded with cells, known as a tissue construct, into a rotating bioreactor filled with a nutrient-rich fluid. The flow within the bioreactor is affected by the movement of the construct relative to the bioreactor which, in turn, is affected by the hydrodynamical and gravitational forces the construct experiences. The construct motion is thus coupled to the flow within the bioreactor. Over the timescale of a few hours, the construct appears to move in a periodic orbit but, over tens of hours, the construct drifts from periodicity. In the biological literature, this effect is often attributed to the change in density of the construct that occurs via tissue growth. In this paper, we show that weak inertia can cause the construct to drift from its periodic orbit over the same timescale as tissue growth.
We consider the coupled flow and construct motion problem within a rotating high-aspect- ratio vessel bioreactor. Using an asymptotic analysis, we investigate the case where the Reynolds number is large but the geometry of the bioreactor yields a small reduced Reynolds number, resulting in a weak inertial effect. In particular, to accurately couple the bioreactor and porous flow regions, we extend the nested boundary layer analysis of Dalwadi et al. (J. Fluid Mech. vol. 798, pp. 88–139, 2016) to include moving walls and the thin region between the porous construct and the bioreactor wall. This allows us to derive a closed system of nonlinear ordinary differential equations for the construct trajectory, from which we show that neglecting inertia results in periodic orbits; we solve the inertia-free problem analytically, calculating the periodic orbits in terms of the system parameters. Using a multiple-scale analysis, we then systematically derive a simpler system of nonlinear ordinary differential equations that describe the long-time drift of the construct due to the effect of weak inertia. We investigate the bifurcations of the construct trajectory behaviour, and the limit cycles that appear when the construct is less dense than the surrounding fluid and the rotation rate is large enough. Thus, we are able to predict when the tissue construct will drift towards a stable limit cycle within the bioreactor and when it will drift out until it hits the bioreactor edge |
| first_indexed | 2025-11-14T20:04:11Z |
| format | Article |
| id | nottingham-47054 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:04:11Z |
| publishDate | 2018 |
| publisher | Cambridge University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-470542020-05-04T19:27:57Z https://eprints.nottingham.ac.uk/47054/ The effect of weak inertia in rotating high-aspect-ratio vessel bioreactors Dalwadi, Mohit P. Chapman, S. Jonathan Oliver, James M. Waters, Sarah L. One method to grow artificial body tissue is to place a porous scaffold seeded with cells, known as a tissue construct, into a rotating bioreactor filled with a nutrient-rich fluid. The flow within the bioreactor is affected by the movement of the construct relative to the bioreactor which, in turn, is affected by the hydrodynamical and gravitational forces the construct experiences. The construct motion is thus coupled to the flow within the bioreactor. Over the timescale of a few hours, the construct appears to move in a periodic orbit but, over tens of hours, the construct drifts from periodicity. In the biological literature, this effect is often attributed to the change in density of the construct that occurs via tissue growth. In this paper, we show that weak inertia can cause the construct to drift from its periodic orbit over the same timescale as tissue growth. We consider the coupled flow and construct motion problem within a rotating high-aspect- ratio vessel bioreactor. Using an asymptotic analysis, we investigate the case where the Reynolds number is large but the geometry of the bioreactor yields a small reduced Reynolds number, resulting in a weak inertial effect. In particular, to accurately couple the bioreactor and porous flow regions, we extend the nested boundary layer analysis of Dalwadi et al. (J. Fluid Mech. vol. 798, pp. 88–139, 2016) to include moving walls and the thin region between the porous construct and the bioreactor wall. This allows us to derive a closed system of nonlinear ordinary differential equations for the construct trajectory, from which we show that neglecting inertia results in periodic orbits; we solve the inertia-free problem analytically, calculating the periodic orbits in terms of the system parameters. Using a multiple-scale analysis, we then systematically derive a simpler system of nonlinear ordinary differential equations that describe the long-time drift of the construct due to the effect of weak inertia. We investigate the bifurcations of the construct trajectory behaviour, and the limit cycles that appear when the construct is less dense than the surrounding fluid and the rotation rate is large enough. Thus, we are able to predict when the tissue construct will drift towards a stable limit cycle within the bioreactor and when it will drift out until it hits the bioreactor edge Cambridge University Press 2018-01-25 Article PeerReviewed Dalwadi, Mohit P., Chapman, S. Jonathan, Oliver, James M. and Waters, Sarah L. (2018) The effect of weak inertia in rotating high-aspect-ratio vessel bioreactors. Journal of Fluid Mechanics, 835 . pp. 674-720. ISSN 1469-7645 biological fluid dynamics lubrication theory bifurcation https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/effect-of-weak-inertia-in-rotating-highaspectratio-vessel-bioreactors/D6F9688DE995AB5CB086E70DF7120D65 https://doi.org/10.1017/jfm.2017.760 https://doi.org/10.1017/jfm.2017.760 |
| spellingShingle | biological fluid dynamics lubrication theory bifurcation Dalwadi, Mohit P. Chapman, S. Jonathan Oliver, James M. Waters, Sarah L. The effect of weak inertia in rotating high-aspect-ratio vessel bioreactors |
| title | The effect of weak inertia in rotating high-aspect-ratio vessel bioreactors |
| title_full | The effect of weak inertia in rotating high-aspect-ratio vessel bioreactors |
| title_fullStr | The effect of weak inertia in rotating high-aspect-ratio vessel bioreactors |
| title_full_unstemmed | The effect of weak inertia in rotating high-aspect-ratio vessel bioreactors |
| title_short | The effect of weak inertia in rotating high-aspect-ratio vessel bioreactors |
| title_sort | effect of weak inertia in rotating high-aspect-ratio vessel bioreactors |
| topic | biological fluid dynamics lubrication theory bifurcation |
| url | https://eprints.nottingham.ac.uk/47054/ https://eprints.nottingham.ac.uk/47054/ https://eprints.nottingham.ac.uk/47054/ |