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Rectilinear flow of non-Bingham plastic solids and non-Newtonian viscous liquids. II

Published online by Cambridge University Press:  24 October 2008

J. G. Oldroyd
J. G. Oldroyd
Affiliation:
Courtaulds Ltd.Research LaboratoryMaidenhead, Berks.
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Abstract

The equation of steady rectilinear motion of a material of variable viscosity is transformed, when the pressure gradient vanishes, into a second-order differential equation which is linear in the dependent variable. A general solution of the linearized equation can be obtained in the case of a wide class of plastic solids and viscous liquids. By making use of the idealized materials which lend themselves to this method of solution, a theoretical comparison can be made of the behaviour of plastic solids of different types under the same conditions. As an illustration, a plastic solid which yields very sharply when the yield point is first exceeded is compared with one which yields only gradually at the same yield value; the flow caused by the longitudinal motion of an (approximately) elliptic cylinder in an infinite mass of material is investigated in each case.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 2 , April 1951 , pp. 410 - 418
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

REFERENCES

(1)Oldroyd, J. G.Proc. Cambridge Phil. Soc. 45 (1949), 595.CrossRefGoogle Scholar
(2)Darboux, G.Théorie générale des surfaces, 2 (2nd ed., Paris, 1915), §§390–1.Google Scholar
(3)Oldroyd, J. G.Proc. Cambridge Phil. Soc. 44 (1948), 200.CrossRefGoogle Scholar