A variational principle is given which describes the steady laminar motion of simple non‐Newtonian fluids, for which the viscosity is a function of the second invariant of the rate of deformation tensor. This principle simplifies to von Helmholtz's principle for the Newtonian fluid, and to Tomita's principle for the Ostwald‐de Waele fluid. For the latter two types of fluids, the equations of continuity and motion are equivalent to the statement that the rate of entropy production in the system is a minimum; for more general fluids, the variational principle does not admit this simple interpretation.
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J. G. Oldroyd, Rheology edited by F. Eirich (Academic Press, Inc., New York, 1956), Chap. 16, p. 653ff.
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M. Reiner, Deformation, Strain and Flow (Interscience Publishers, Inc., New York, 1960), Chap. 17.
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A. G. Fredrickson, Ph.D. thesis, University of Wisconsin, 1959.
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J. C. Slattery, Ph.D. thesis, University of Wisconsin, 1959.
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H. Lamb, Hydrodynamics (Dover Publications, New York, 1945), pp. 617–619.
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H. Villat, Leçons sur les Fluides Visqueux (Gauthier‐Villars, Paris, France, 1943), pp. 84–112.
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E. Madelung, Die Mathematischen Hilfsmittel des Physikers (Dover Publications, New York, 1943), pp. 214–216.
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© 1960 The American Institute of Physics.
1960
The American Institute of Physics
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