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Variational inequalities for a body in a viscous shearing flow

Published online by Cambridge University Press:  29 March 2006

A. Nir ,
H. F. Weinberger  and
A. Acrivos
A. Nir
Affiliation:
Department of Chemical Engineering, Israel Institute of Technology Haifa
H. F. Weinberger
Affiliation:
Department of Mathematics, University of Minnesota, Mineapolis
A. Acrivos
Affiliation:
Department of Chemical Engineeing, Stanford University, Stanford, California 94305
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Abstract

The slow motion of a body in a viscous shearing field is examined. Variational principles are used to derive inequalities which approximate the elements of the shearing matrix M of a body of arbitrary shape, where M is the matrix relating the force, torque and stresslet exerted by the body on the fluid to the relative translational and rotational velocities of the body and the rate of deformation of the undisturbed linear field. An upper bound for the elements of M is obtained by showing that the quadratic form of M increases monotonically with B, the region occupied by the body, while a lower bound for this form is given in terms of the electrostatic properties of a conductor and a dielectric of the same shape as B. Particular attention is paid to bodies of revolution, for which certain more definitive results are obtained: for example, their resistance to a rotation with axial symmetry is always less than twice their resistance to a rotation perpendicular to their axis.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 4 , 29 April 1975 , pp. 739 - 755
Copyright
© 1975 Cambridge University Press

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