Bioreactors are used in tissue engineering applications to grow functional tissue in vitro. A set-up of particular interest
is the rotating bioreactor, which is essentially a cylinder filled with a nutrient solution into which tissue cells, often first "seeded"
onto an appropriate scaffold, are placed. The tissue cells proliferate in response to the supplied nutrient, and the whole assembly is
rotated about the cylinder's axis.
We consider an idealised mathematical model of the rotating bioreactor,in which its aspect ratio is asymptotically small, an assumption that
leads to novel "Hele-Shaw" problems.Two problems of interest are studied: (i) a shape stability problem (irregularly-shaped tissue constructs are observed by our experimental collaborators); and (ii) the motion of a tissue construct within the nutrient solution under fluid-dynamical forces. In the latter case the fluid flow and construct trajectory may be determined analytically, and hence the convection-diffusion
problem governing nutrient transport throughout the bioreactor may be solved, and the subsequent tissue growth-rate determined.
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