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The stress system in a suspension of heavy particles: antisymmetric contribution

Published online by Cambridge University Press:  24 April 2006

A. PROSPERETTI ,
Q. ZHANG  and
K. ICHIKI
A. PROSPERETTI
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA Faculty of Applied Physics, Twente Institute of Mechanics, and Burgerscentrum, University of Twente, AE 7500 Enschede, The Netherlands
Q. ZHANG
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
K. ICHIKI
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA Current address: Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada.
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Abstract

The nature of the stress in a suspension of equal homogeneous spheres all subject to the same force, such as weight, is considered; inertial effects are neglected. This study builds upon some of the well-known work devoted to this problem by the founder of the Journal of Fluid Mechanics, Professor George K. Batchelor. After developing a general theory, the antisymmetric part of the stress tensor is considered in detail. It is shown that, in addition to a term already found by Batchelor and characterized by an axial vector, the antisymmetric stress contains another term characterized by the curl of a polar vector. As a consequence, a suspension will possess, in addition to an axial vortex viscosity, a polar vortex viscosity. Appendix C presents a calculation of the hindrance function for rotation correct to the first order in the particle volume fraction.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 554 , 10 May 2006 , pp. 125 - 146
Copyright
© 2006 Cambridge University Press

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