Oscillatory counter-centrifugation

Abstract

In ordinary centrifugation, a suspended particle that is heavier than the displaced fluid migrates away from the rotation axis when the fluid-filled container rotates steadily about that axis. In contrast a particle that is lighter than the displaced fluid (e.g., a bubble) migrates toward the rotation axis in a centrifuge. In this paper, we show theoretically that if a fluid-filled container rotates in an oscillatory manner as a rigid body about an axis, at high enough oscillation frequencies, the sense of migration of suspended particles is reversed. That is, in that case particles denser than the fluid migrate inward, while those that are lighter than the fluid move outward. We term this unusual phenomenon “Oscillatory Counter-Centrifugation” or OCC, for short. Through application of the method of averaging to the equations of motion, we derive a simple criterion to predict the occurrence of OCC. The analysis also reveals that the time-average of the Coriolis force in the radial direction is the term that is responsible for this effect. In addition, we analyze the effects of the Basset history force and the Rubinow–Keller lift force on particle trajectories and find that OCC persists even when these forces are active. The phenomenon awaits experimental verification.