On the dynamics of a spherical scaffold in rotating bioreactors

We analyze the dynamics of a spherical scaffold in rotating bioreactors (or clinostats). The idealized clinostat environment consists of a purely rotational flow that is perpendicular to a gravitational field. We confirm through a detailed analytical study that lift effects considerably alter the position of the equilibrium point reached by the scaffolds in the (vertical) direction collinear to the gravitational field. This result holds for small particle and shear Reynolds numbers. Our analysis shows that the inertial lift effect is negligible in the horizontal direction. We show that for all rotations of practical interest, and for the range of particle Reynolds number smaller than unity, the vertical coordinate of the equilibrium point is strongly affected by consideration of lift effects. For light (heavy) particles, inclusion of lift in the formation forces the equilibrium position to be below (above) the horizontal plane that contains the axis of rotation. The equilibrium point for light particles is stable and therefore is observable experimentally. The equilibrium point for heavy particles is unstable. We also estimate the stress level applied to the scaffold and derive an algebraic expression that indicates that the stress level acting on the scaffold decreases with increasing shear Reynolds number.