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On the sedimentation of a sphere in a centrifuge

Published online by Cambridge University Press:  29 March 2006

Isom H. Herron ,
Stephen H. Davis  and
Francis P. Bretherton
Isom H. Herron
Affiliation:
Department of Mechanics and Materials Science, The Johns Hopkins University, Baltimore, Maryland 21218 Present address: Department of Mathematics, Howard University, Washington, D.C. 20059.
Stephen H. Davis
Affiliation:
Department of Mechanics and Materials Science, The Johns Hopkins University, Baltimore, Maryland 21218
Francis P. Bretherton
Affiliation:
Department of Mechanics and Materials Science, The Johns Hopkins University, Baltimore, Maryland 21218 Present address: National Center for Atmospheric Research, Boulder, Colorado 80302.
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Abstract

The flow field about a small, slowly sedimenting particle in a centrifuge is examined using matched asymptotic expansions. The near field is dominated by Stokes flow while in the far field a non-axisymmetric cubical conical structure (a viscously modified Taylor column) is found. This far field induces a Coriolis modification in the near field leading to Coriolis corrections to the Stokes drag law. The Coriolis modification of the predicted molecular weight (if the particle were a molecule) of a small particle is calculated. The analysis is applied to an unbounded fluid as well as to a fluid bounded between parallel plates oriented normal to the rotation vector. In the latter case the governing equations for the rotating fluid are posed as a self-adjoint system of partial differential equations and solved using (symmetric) Green's matrices.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 2 , 25 March 1975 , pp. 209 - 234
Copyright
© 1975 Cambridge University Press

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