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The viscosity of a suspension of spheres

Published online by Cambridge University Press:  28 March 2006

A. D. Maude
A. D. Maude
Affiliation:
City of Liverpool College of Technology
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Abstract

It is shown that in Stokes's flow the perturbation field, due to the addition of one more sphere to a shear flow of a fluid containing a number of non-interacting spheres, has the property that the total additional shearing force, acting on any plane normal to the direction of velocity change, is zero. However, the perturbation velocity, integrated over such a plane, takes a constant value, positive if the plane lies on one side of the sphere and negative if it lies on the other side. It follows that the effect of all the spheres is not to alter the shearing stress at all, but to reduce the mean shear by a factor 1 – 2·5c, where c is the concentration. This suggests that Einstein's viscosity law should be altered to η = η0/(1 – 2·5c) when c is not small.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 7 , Issue 2 , February 1960 , pp. 230 - 236
Copyright
© 1960 Cambridge University Press

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References

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