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Particle orbits in a rotating liquid

  • Glyn O. Roberts (a1), Dale M. Kornfeld (a2) and William W. Fowlis (a2)

Abstract

Monodisperse latex microspheres ranging in size from submicrometer to several micrometers in diameter can be prepared in the laboratory. The uniformity of diameter is important for instrument calibration and other applications. However it has proved very difficult to manufacture commercial quantities of mondisperse latex microspheres with diameters larger than about 3 micrometers owing to buoyancy and sedimentation effects. In an attempt to eliminate these effects NASA sponsored a Space Shuttle experiment called the Monodisperse Latex Reactor (MLR) to produce these monodisperse microspheres in larger sizes in microgravity. Results have been highly successful.

Using technology gained from this space experiment, a ground-based rotating latex reactor has been fabricated in an attempt to minimize sedimentation without using microgravity. The entire reactor cylinder is rotated about a horizontal axis to keep the particles in suspension.

In this paper we determine the motion of small spherical particles under gravity, in a viscous fluid rotating uniformly about a horizontal axis. The particle orbits are approximately circles, with centres displaced horizontally from the axis of rotation. Owing to net centrifugal buoyancy, the radius of the circles increases (for heavy particles) or decreases (for light particles) with time, so that the particles gradually spiral inward or outward.

For a large rotation rate, the particles spiral outwards or inwards too fast, while for a small rotation rate, the displacement of the orbit centre from the rotation axis is excessive in relation to the reactor radius. We determine the rotation rate that maximizes the fraction of the reactor cross-section area that contains particles that will not spiral out to the wall in the experimental time (for heavy particles), or that have spiralled in without hitting the wall (for light particles). Typically, the rate is close to 1 r.p.m., and design rotation rate ranges should span this value.

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