Dalwadi, Mohit P. and Chapman, S. Jonathan and Oliver, James M. and Waters, Sarah L.
(2017)
The effect of weak inertia in rotating highaspectratio vessel bioreactors.
Journal of Fluid Mechanics
.
ISSN 14697645
(In Press)
Abstract
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 nutrientrich 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 highaspect 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 inertiafree problem analytically, calculating the periodic orbits in terms of the system parameters. Using a multiplescale analysis, we then systematically derive a simpler system of nonlinear ordinary differential equations that describe the longtime 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
Item Type: 
Article

Keywords: 
biological fluid dynamics, lubrication theory, bifurcation 
Schools/Departments: 
University of Nottingham, UK > Faculty of Medicine and Health Sciences > School of Life Sciences 
Depositing User: 
Dalwadi, Dr Mohit

Date Deposited: 
09 Oct 2017 10:05 
Last Modified: 
18 Oct 2017 10:34 
URI: 
http://eprints.nottingham.ac.uk/id/eprint/47054 
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