Non-newtonian Effects in Viscous Flows

Revision of the mathematical formalism of fluid dynamics suggests that some physical inconsistencies (infinite time of approaching equilibrium and fully deterministic solutions to the Navier-Stokes equations) can be removed by relaxing the Lipschitz conditions, i.e., the boundedness of the derivativ...

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Bibliographic Details
Published in:International journal of theoretical physics 1996-07, Vol.35 (7), p.1423-1460
Main Authors: Zak, Michail, Meyers, Ronald E.
Format: Article
Language:English
Subjects:
Fluid Mechanics And Heat Transfer
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Summary:Revision of the mathematical formalism of fluid dynamics suggests that some physical inconsistencies (infinite time of approaching equilibrium and fully deterministic solutions to the Navier-Stokes equations) can be removed by relaxing the Lipschitz conditions, i.e., the boundedness of the derivatives, in the constitutive equations. Physically such a modification can be interpreted as an incorporation of an infinitesimal static friction in the constitutive law. A modified version of the Navier-Stokes equations is introduced, discussed, and illustrated by examples. It is demonstrated that all the new effects in the modified model emerge within vanishingly small neighborhoods of equilibrium states which are the only domains where the governing equations are different from classical.
ISSN:0020-7748
1572-9575
DOI:10.1007/BF02084951