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Title: Dynamics Of A Spherical Particle In A Model Clinostat Or Bioreactor 
Author: Ramirez, Lynnette E.S.
Date: 2004-12
Abstract: The dynamics of a spherical particle in a fast clinostat or rotating bioreactor is analyzed. The model clinostat environment consists of purely rotational flow that is perpendicular to a gravitational field. The Lagrangian equation of motion is written in terms of dimensionless parameters and solved exactly for small particle and shear Reynolds numbers. The solution shows that lift effects considerably alter the position of the equilibrium point reached by the particles in the (vertical) direction collinear to the gravitational field, and that the inertial lift effect is negligible in the (horizontal) direction perpendicular to the gravitational field. These results are applicable for all practical rotation rates and small shear and particle Reynolds numbers that are characteristic of realistic experimental conditions. For light (heavy) particles, inclusion of lift in the formulation 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, however, the equilibrium point for heavy particles is unstable. The stress level applied to the particle is estimated and an algebraic expression is derived that indicates that the stress level acting on the particle decreases with increasing shear Reynolds number. Finally, the practicality of using the solution to design an experiment to show the vertical displacement of a particle in its equilibrium position is demonstrated.
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